Metrics for ln(1 + x)

analyze3.0ms (0.1%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
33.3%	25%	50%	0%	0%	25%	0%	3
66.7%	50%	25%	0%	0%	25%	0%	4
83.3%	62.5%	12.5%	0%	0%	25%	0%	5
91.7%	68.7%	6.2%	0%	0%	25%	0%	6
95.8%	71.8%	3.1%	0%	0%	25%	0%	7
97.9%	73.4%	1.6%	0%	0%	25%	0%	8
99%	74.2%	0.8%	0%	0%	25%	0%	9
99.5%	74.6%	0.4%	0%	0%	25%	0%	10
99.7%	74.8%	0.2%	0%	0%	25%	0%	11
99.9%	74.9%	0.1%	0%	0%	25%	0%	12

Compiler

Compiled 6 to 5 computations (16.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

ival-log: 1.0ms (107.2% of total)

ival-add: 0.0ms (0% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

sample1.8s (49.1%)

Results

876.0ms	4092×	1	valid
505.0ms	1291×	2	valid
154.0ms	2873×	0	valid
0.0ms	3×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 1.1s

ival-log: 859.0ms (79.3% of total)

ival-add: 114.0ms (10.5% of total)

backward-pass: 92.0ms (8.5% of total)

const: 19.0ms (1.8% of total)

Bogosity

preprocess18.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

52×	`sum3-define`
20×	`sub-neg`
16×	`fma-define`
16×	`fmsub-define`
14×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	9
1	20	9
2	28	9
3	38	9
4	57	9
5	77	9
6	98	9
7	118	9
8	120	9
0	4	2
1	8	2
0	8	2

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(log (+ 1 x))

Outputs
(log (+ 1 x))
(log1p.f64 x)

Call 2

Inputs
(log (+ 1 x))
(log (+ 1 (neg x)))
(neg (log (+ 1 (neg x))))

Outputs
(log (+ 1 x))
(log1p x)
(log (+ 1 (neg x)))
(log1p (neg x))
(neg (log (+ 1 (neg x))))
(neg (log1p (neg x)))

explain242.0ms (6.7%)

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
167	-	-	`(log.f64 (+.f64 #s(literal 1 binary64) x))`
0	-	-	`x`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(+.f64 #s(literal 1 binary64) x)`

Results

61.0ms	254×	1	valid
30.0ms	78×	2	valid
11.0ms	180×	0	valid

Compiler

Compiled 27 to 14 computations (48.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 62.0ms

ival-log: 47.0ms (75.9% of total)

backward-pass: 7.0ms (11.3% of total)

ival-add: 6.0ms (9.7% of total)

const: 1.0ms (1.6% of total)

eval0.0ms (0%)

Compiler: Compiled 3 to 2 computations (33.3% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(log1p.f64 x)

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(log1p.f64 x)

Rules

4×	`+-lowering-+.f64`
4×	`+-lowering-+.f32`
2×	`log1p-lowering-log1p.f32`
2×	`log-lowering-log.f64`
2×	`log1p-lowering-log1p.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	3
1	8	3
0	8	3

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(log (+ 1 x))
x

Outputs
(log (+ 1 x))
(log1p.f64 x)
x

localize52.0ms (1.4%)

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(log1p.f64 x)

Results

40.0ms	166×	5	exit
5.0ms	90×	0	valid

Compiler

Compiled 5 to 3 computations (40% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

compiled-spec: 8.0ms (43.2% of total)

ival-log: 5.0ms (27% of total)

backward-pass: 4.0ms (21.6% of total)

ival-add: 2.0ms (10.8% of total)

const: 0.0ms (0% of total)

series1.0ms (0%)

Counts

1 → 12

Calls

Call 1

Inputs
#<alt (log (+ 1 x))>

Outputs
#<alt x>
#<alt (* x (+ 1 (* -1/2 x)))>
#<alt (* x (+ 1 (* x (- (* 1/3 x) 1/2))))>
#<alt (* x (+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2))))>
#<alt (* -1 (log (/ 1 x)))>
#<alt (+ (* -1 (log (/ 1 x))) (/ 1 x))>
#<alt (- (+ (* -1 (log (/ 1 x))) (/ 1 x)) (/ 1/2 (pow x 2)))>
#<alt (- (+ (* -1 (log (/ 1 x))) (+ (/ 1 x) (* 1/3 (/ 1 (pow x 3))))) (/ 1/2 (pow x 2)))>
#<alt (+ (log -1) (* -1 (log (/ -1 x))))>
#<alt (+ (log -1) (+ (* -1 (log (/ -1 x))) (/ 1 x)))>
#<alt (+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* 1/2 (/ 1 x)) 1) x))))>
#<alt (+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* -1 (/ (- (* 1/3 (/ 1 x)) 1/2) x)) 1) x))))>

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(log (+ 1 x))
0.0ms	x	@	0	(log (+ 1 x))
0.0ms	x	@	-inf	(log (+ 1 x))

rewrite29.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

4×	`+-lowering-+.f64`
4×	`+-lowering-+.f32`
2×	`log1p-lowering-log1p.f32`
2×	`log1p-lowering-log1p.f64`
2×	`log1p-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	2
1	8	2
0	8	2

Stop Event

1×	iter limit
1×	saturated

Counts

1 → 2

Calls

Call 1

Inputs
(log (+ 1 x))

Outputs
(log.f64 (+.f64 #s(literal 1 binary64) x))
(log1p.f64 x)

simplify214.0ms (6%)

Algorithm

1×	egg-herbie

Rules

1970×	`fmsub-define`
1904×	`sum3-define`
1846×	`fma-lowering-fma.f32`
1846×	`fma-lowering-fma.f64`
1776×	`fmm-def`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	59	133
1	178	111
2	443	105
3	1212	103
4	3930	96
0	8245	96

Stop Event

1×	iter limit
1×	node limit

Counts

12 → 12

Calls

Call 1

Inputs
x
(* x (+ 1 (* -1/2 x)))
(* x (+ 1 (* x (- (* 1/3 x) 1/2))))
(* x (+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2))))
(* -1 (log (/ 1 x)))
(+ (* -1 (log (/ 1 x))) (/ 1 x))
(- (+ (* -1 (log (/ 1 x))) (/ 1 x)) (/ 1/2 (pow x 2)))
(- (+ (* -1 (log (/ 1 x))) (+ (/ 1 x) (* 1/3 (/ 1 (pow x 3))))) (/ 1/2 (pow x 2)))
(+ (log -1) (* -1 (log (/ -1 x))))
(+ (log -1) (+ (* -1 (log (/ -1 x))) (/ 1 x)))
(+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* 1/2 (/ 1 x)) 1) x))))
(+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* -1 (/ (- (* 1/3 (/ 1 x)) 1/2) x)) 1) x))))

Outputs
x
(* x (+ 1 (* -1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(* x (+ 1 (* x (- (* 1/3 x) 1/2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))))
(* x (+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))))
(* -1 (log (/ 1 x)))
(log.f64 x)
(+ (* -1 (log (/ 1 x))) (/ 1 x))
(+.f64 (/.f64 #s(literal 1 binary64) x) (log.f64 x))
(- (+ (* -1 (log (/ 1 x))) (/ 1 x)) (/ 1/2 (pow x 2)))
(+.f64 (log.f64 x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) x)) x))
(- (+ (* -1 (log (/ 1 x))) (+ (/ 1 x) (* 1/3 (/ 1 (pow x 3))))) (/ 1/2 (pow x 2)))
(+.f64 (log.f64 x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/3 binary64) x)) x)) x))
(+ (log -1) (* -1 (log (/ -1 x))))
(+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (-.f64 #s(literal 0 binary64) x)))
(+ (log -1) (+ (* -1 (log (/ -1 x))) (/ 1 x)))
(+.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (-.f64 #s(literal 0 binary64) x))))
(+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* 1/2 (/ 1 x)) 1) x))))
(-.f64 (log.f64 #s(literal -1 binary64)) (-.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) x)) x)))
(+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* -1 (/ (- (* 1/3 (/ 1 x)) 1/2) x)) 1) x))))
(+.f64 (log.f64 #s(literal -1 binary64)) (+.f64 (log.f64 (-.f64 #s(literal 0 binary64) x)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/3 binary64) x)) x)) x)))

eval1.0ms (0%)

Compiler: Compiled 125 to 49 computations (60.8% saved)

prune3.0ms (0.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	10	4	14
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	10	5	15

Accuracy

100.0%

Counts

15 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	65.7%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))))
▶	66.7%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))))
▶	65.6%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
✓	100.0%	(log1p.f64 x)
▶	66.5%	x

Compiler

Compiled 41 to 30 computations (26.8% saved)

simplify48.0ms (1.3%)

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

New	Metric	Program
✓	cost-diff	(+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))
✓	cost-diff	(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64))))))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64)))))))
✓	cost-diff	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))))
✓	cost-diff	(+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))
✓	cost-diff	(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))))
✓	cost-diff	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))))
✓	cost-diff	(*.f64 x #s(literal -1/2 binary64))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))
✓	cost-diff	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))

Rules

1430×	`fma-define`
1068×	`fma-lowering-fma.f32`
1068×	`fma-lowering-fma.f64`
336×	`-lowering-.f32`
336×	`-lowering-.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	126
1	66	106
2	184	103
3	457	103
4	969	103
5	1396	103
6	1552	103
7	1554	103
0	1554	103

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
x
(* x (+ 1 (* x -1/2)))
x
(+ 1 (* x -1/2))
1
(* x -1/2)
-1/2
(* x (+ 1 (* x (+ -1/2 (* x 1/3)))))
x
(+ 1 (* x (+ -1/2 (* x 1/3))))
1
(* x (+ -1/2 (* x 1/3)))
(+ -1/2 (* x 1/3))
-1/2
(* x 1/3)
1/3
(* x (+ 1 (* x (+ -1/2 (* x (+ 1/3 (* x -1/4)))))))
x
(+ 1 (* x (+ -1/2 (* x (+ 1/3 (* x -1/4))))))
1
(* x (+ -1/2 (* x (+ 1/3 (* x -1/4)))))
(+ -1/2 (* x (+ 1/3 (* x -1/4))))
-1/2
(* x (+ 1/3 (* x -1/4)))
(+ 1/3 (* x -1/4))
1/3
(* x -1/4)
-1/4

Outputs
x
(* x (+ 1 (* x -1/2)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
x
(+ 1 (* x -1/2))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))
1
#s(literal 1 binary64)
(* x -1/2)
(*.f64 x #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
(* x (+ 1 (* x (+ -1/2 (* x 1/3)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))))
x
(+ 1 (* x (+ -1/2 (* x 1/3))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))))
1
#s(literal 1 binary64)
(* x (+ -1/2 (* x 1/3)))
(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))
(+ -1/2 (* x 1/3))
(+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))
-1/2
#s(literal -1/2 binary64)
(* x 1/3)
(*.f64 x #s(literal 1/3 binary64))
1/3
#s(literal 1/3 binary64)
(* x (+ 1 (* x (+ -1/2 (* x (+ 1/3 (* x -1/4)))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))))
x
(+ 1 (* x (+ -1/2 (* x (+ 1/3 (* x -1/4))))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64)))))))
1
#s(literal 1 binary64)
(* x (+ -1/2 (* x (+ 1/3 (* x -1/4)))))
(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64))))))
(+ -1/2 (* x (+ 1/3 (* x -1/4))))
(+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))
-1/2
#s(literal -1/2 binary64)
(* x (+ 1/3 (* x -1/4)))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))
(+ 1/3 (* x -1/4))
(+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64)))
1/3
#s(literal 1/3 binary64)
(* x -1/4)
(*.f64 x #s(literal -1/4 binary64))
-1/4
#s(literal -1/4 binary64)

localize114.0ms (3.2%)

Localize:

Found 11 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64)))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64))))))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))))
✓	accuracy	99.7%	(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))
✓	accuracy	100.0%	(+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))))
✓	accuracy	99.9%	(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))
✓	accuracy	99.5%	(*.f64 x #s(literal 1/3 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))
✓	accuracy	100.0%	(*.f64 x #s(literal -1/2 binary64))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))

Results

81.0ms

256×

valid

Compiler

Compiled 128 to 21 computations (83.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 30.0ms

ival-mult: 16.0ms (53.7% of total)

ival-add: 8.0ms (26.9% of total)

...c/correct-round.rkt:119:19: 4.0ms (13.4% of total)

const: 1.0ms (3.4% of total)

backward-pass: 0.0ms (0% of total)

series14.0ms (0.4%)

Counts

14 → 168

Calls

Call 1

Inputs
#<alt (* x (+ 1 (* x -1/2)))>
#<alt (+ 1 (* x -1/2))>
#<alt (* x -1/2)>
#<alt (* x (+ 1 (* x (+ -1/2 (* x 1/3)))))>
#<alt (+ 1 (* x (+ -1/2 (* x 1/3))))>
#<alt (* x (+ -1/2 (* x 1/3)))>
#<alt (+ -1/2 (* x 1/3))>
#<alt (* x (+ 1 (* x (+ -1/2 (* x (+ 1/3 (* x -1/4)))))))>
#<alt (+ 1 (* x (+ -1/2 (* x (+ 1/3 (* x -1/4))))))>
#<alt (* x (+ -1/2 (* x (+ 1/3 (* x -1/4)))))>
#<alt (+ -1/2 (* x (+ 1/3 (* x -1/4))))>
#<alt (* x 1/3)>
#<alt (* x (+ 1/3 (* x -1/4)))>
#<alt (+ 1/3 (* x -1/4))>

Outputs
#<alt x>
#<alt (* x (+ 1 (* -1/2 x)))>
#<alt (* x (+ 1 (* -1/2 x)))>
#<alt (* x (+ 1 (* -1/2 x)))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 x) 1/2))>
#<alt (* (pow x 2) (- (/ 1 x) 1/2))>
#<alt (* (pow x 2) (- (/ 1 x) 1/2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 x) 1/2))>
#<alt (* (pow x 2) (- (/ 1 x) 1/2))>
#<alt (* (pow x 2) (- (/ 1 x) 1/2))>
#<alt 1>
#<alt (+ 1 (* -1/2 x))>
#<alt (+ 1 (* -1/2 x))>
#<alt (+ 1 (* -1/2 x))>
#<alt (* -1/2 x)>
#<alt (* x (- (/ 1 x) 1/2))>
#<alt (* x (- (/ 1 x) 1/2))>
#<alt (* x (- (/ 1 x) 1/2))>
#<alt (* -1/2 x)>
#<alt (* -1 (* x (- 1/2 (/ 1 x))))>
#<alt (* -1 (* x (- 1/2 (/ 1 x))))>
#<alt (* -1 (* x (- 1/2 (/ 1 x))))>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt x>
#<alt (* x (+ 1 (* -1/2 x)))>
#<alt (* x (+ 1 (* x (- (* 1/3 x) 1/2))))>
#<alt (* x (+ 1 (* x (- (* 1/3 x) 1/2))))>
#<alt (* 1/3 (pow x 3))>
#<alt (* (pow x 3) (- 1/3 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ 1/3 (/ 1 (pow x 2))) (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ 1/3 (/ 1 (pow x 2))) (* 1/2 (/ 1 x))))>
#<alt (* 1/3 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (* 1/2 (/ 1 x)) 1/3)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/3)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/3)))>
#<alt 1>
#<alt (+ 1 (* -1/2 x))>
#<alt (+ 1 (* x (- (* 1/3 x) 1/2)))>
#<alt (+ 1 (* x (- (* 1/3 x) 1/2)))>
#<alt (* 1/3 (pow x 2))>
#<alt (* (pow x 2) (- 1/3 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (- (+ 1/3 (/ 1 (pow x 2))) (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (- (+ 1/3 (/ 1 (pow x 2))) (* 1/2 (/ 1 x))))>
#<alt (* 1/3 (pow x 2))>
#<alt (* (pow x 2) (- 1/3 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/3 (* -1 (/ (- 1/2 (/ 1 x)) x))))>
#<alt (* (pow x 2) (+ 1/3 (* -1 (/ (- 1/2 (/ 1 x)) x))))>
#<alt (* -1/2 x)>
#<alt (* x (- (* 1/3 x) 1/2))>
#<alt (* x (- (* 1/3 x) 1/2))>
#<alt (* x (- (* 1/3 x) 1/2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* (pow x 2) (- 1/3 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (- 1/3 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (- 1/3 (* 1/2 (/ 1 x))))>
#<alt (* 1/3 (pow x 2))>
#<alt (* (pow x 2) (- 1/3 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (- 1/3 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (- 1/3 (* 1/2 (/ 1 x))))>
#<alt -1/2>
#<alt (- (* 1/3 x) 1/2)>
#<alt (- (* 1/3 x) 1/2)>
#<alt (- (* 1/3 x) 1/2)>
#<alt (* 1/3 x)>
#<alt (* x (- 1/3 (* 1/2 (/ 1 x))))>
#<alt (* x (- 1/3 (* 1/2 (/ 1 x))))>
#<alt (* x (- 1/3 (* 1/2 (/ 1 x))))>
#<alt (* 1/3 x)>
#<alt (* -1 (* x (- (* 1/2 (/ 1 x)) 1/3)))>
#<alt (* -1 (* x (- (* 1/2 (/ 1 x)) 1/3)))>
#<alt (* -1 (* x (- (* 1/2 (/ 1 x)) 1/3)))>
#<alt x>
#<alt (* x (+ 1 (* -1/2 x)))>
#<alt (* x (+ 1 (* x (- (* 1/3 x) 1/2))))>
#<alt (* x (+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2))))>
#<alt (* -1/4 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/3 (/ 1 x)) 1/4))>
#<alt (* (pow x 4) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ (* 1/3 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/4 (/ 1/2 (pow x 2)))))>
#<alt (* -1/4 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/3 (/ 1 x)) 1/4))>
#<alt (* (pow x 4) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/3) x)) 1/4))>
#<alt (* (pow x 4) (- (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/3) x)) 1/4))>
#<alt 1>
#<alt (+ 1 (* -1/2 x))>
#<alt (+ 1 (* x (- (* 1/3 x) 1/2)))>
#<alt (+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2)))>
#<alt (* -1/4 (pow x 3))>
#<alt (* (pow x 3) (- (* 1/3 (/ 1 x)) 1/4))>
#<alt (* (pow x 3) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))>
#<alt (* (pow x 3) (- (+ (* 1/3 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/4 (/ 1/2 (pow x 2)))))>
#<alt (* -1/4 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/4 (* 1/3 (/ 1 x)))))>
#<alt (* -1 (* (pow x 3) (+ 1/4 (* -1 (/ (- 1/3 (* 1/2 (/ 1 x))) x)))))>
#<alt (* -1 (* (pow x 3) (+ 1/4 (* -1 (/ (+ 1/3 (* -1 (/ (- 1/2 (/ 1 x)) x))) x)))))>
#<alt (* -1/2 x)>
#<alt (* x (- (* 1/3 x) 1/2))>
#<alt (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2))>
#<alt (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2))>
#<alt (* -1/4 (pow x 3))>
#<alt (* (pow x 3) (- (* 1/3 (/ 1 x)) 1/4))>
#<alt (* (pow x 3) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))>
#<alt (* (pow x 3) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))>
#<alt (* -1/4 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/4 (* 1/3 (/ 1 x)))))>
#<alt (* -1 (* (pow x 3) (+ 1/4 (* -1 (/ (- 1/3 (* 1/2 (/ 1 x))) x)))))>
#<alt (* -1 (* (pow x 3) (+ 1/4 (* -1 (/ (- 1/3 (* 1/2 (/ 1 x))) x)))))>
#<alt -1/2>
#<alt (- (* 1/3 x) 1/2)>
#<alt (- (* x (+ 1/3 (* -1/4 x))) 1/2)>
#<alt (- (* x (+ 1/3 (* -1/4 x))) 1/2)>
#<alt (* -1/4 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))>
#<alt (* (pow x 2) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))>
#<alt (* (pow x 2) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))>
#<alt (* -1/4 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))>
#<alt (* (pow x 2) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/3) x)) 1/4))>
#<alt (* (pow x 2) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/3) x)) 1/4))>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* x (+ 1/3 (* -1/4 x)))>
#<alt (* x (+ 1/3 (* -1/4 x)))>
#<alt (* x (+ 1/3 (* -1/4 x)))>
#<alt (* -1/4 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))>
#<alt (* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))>
#<alt (* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))>
#<alt (* -1/4 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))>
#<alt (* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))>
#<alt (* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))>
#<alt 1/3>
#<alt (+ 1/3 (* -1/4 x))>
#<alt (+ 1/3 (* -1/4 x))>
#<alt (+ 1/3 (* -1/4 x))>
#<alt (* -1/4 x)>
#<alt (* x (- (* 1/3 (/ 1 x)) 1/4))>
#<alt (* x (- (* 1/3 (/ 1 x)) 1/4))>
#<alt (* x (- (* 1/3 (/ 1 x)) 1/4))>
#<alt (* -1/4 x)>
#<alt (* -1 (* x (- 1/4 (* 1/3 (/ 1 x)))))>
#<alt (* -1 (* x (- 1/4 (* 1/3 (/ 1 x)))))>
#<alt (* -1 (* x (- 1/4 (* 1/3 (/ 1 x)))))>

Calls

42 calls:

Time	Variable		Point	Expression
4.0ms	x	@	inf	(* x (+ -1/2 (* x 1/3)))
1.0ms	x	@	inf	(* x 1/3)
1.0ms	x	@	0	(* x (+ 1 (* x (+ -1/2 (* x 1/3)))))
0.0ms	x	@	inf	(* x (+ 1 (* x -1/2)))
0.0ms	x	@	0	(* x (+ 1 (* x -1/2)))

rewrite97.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1464×	`fma-define`
1096×	`fma-lowering-fma.f32`
1096×	`fma-lowering-fma.f64`
354×	`-lowering-.f32`
354×	`-lowering-.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	110
1	66	90
2	184	87
3	459	87
4	973	87
5	1409	87
6	1607	87
7	1654	87
8	1767	87
9	1828	87
0	1828	87

Stop Event

1×	iter limit
1×	saturated

Counts

14 → 370

Calls

Call 1

Inputs
(* x (+ 1 (* x -1/2)))
(+ 1 (* x -1/2))
(* x -1/2)
(* x (+ 1 (* x (+ -1/2 (* x 1/3)))))
(+ 1 (* x (+ -1/2 (* x 1/3))))
(* x (+ -1/2 (* x 1/3)))
(+ -1/2 (* x 1/3))
(* x (+ 1 (* x (+ -1/2 (* x (+ 1/3 (* x -1/4)))))))
(+ 1 (* x (+ -1/2 (* x (+ 1/3 (* x -1/4))))))
(* x (+ -1/2 (* x (+ 1/3 (* x -1/4)))))
(+ -1/2 (* x (+ 1/3 (* x -1/4))))
(* x 1/3)
(* x (+ 1/3 (* x -1/4)))
(+ 1/3 (* x -1/4))

Outputs
(+.f64 x (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) x)
(fma.f64 x #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) x)
(fma.f64 #s(literal 1 binary64) x (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(fma.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)) x)
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) x)
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) x x)
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64) x)
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) x)
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))) x)
(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))
(+.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64))
(*.f64 x #s(literal -1/2 binary64))
(.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64)))
(*.f64 #s(literal -1/2 binary64) x)
(.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+.f64 x (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) (*.f64 x x)))
(+.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64)))) (.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x x))))
(+.f64 (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) (*.f64 x x)) x)
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/3 binary64))))))
(+.f64 (.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x x))) (.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/3 binary64))))) (.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(fma.f64 x #s(literal 1 binary64) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) (*.f64 x x)))
(fma.f64 x (.f64 x #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/3 binary64))))))
(fma.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))) (.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x x))))
(fma.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))) x)
(fma.f64 x (.f64 x (.f64 x #s(literal 1/3 binary64))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64)))))
(fma.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/3 binary64)))) (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(fma.f64 #s(literal 1 binary64) x (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) (*.f64 x x)))
(fma.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64)))) (.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x x))))
(fma.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) (*.f64 x x)) x)
(fma.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/3 binary64))))))
(fma.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x x))) (.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))))
(fma.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/3 binary64))))) (.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(fma.f64 #s(literal -1/2 binary64) (.f64 x x) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/3 binary64))))))
(fma.f64 (.f64 x #s(literal -1/2 binary64)) x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/3 binary64))))))
(fma.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))) x (.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x x))))
(fma.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64)))) #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x x))))
(fma.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64)))))
(fma.f64 (.f64 x #s(literal 1/3 binary64)) (.f64 x x) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64)))))
(fma.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) (.f64 x x) x)
(fma.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))) x x)
(fma.f64 (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) (*.f64 x x)) #s(literal 1 binary64) x)
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/3 binary64))))))
(fma.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64)))))
(fma.f64 (.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x x))) #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))))
(fma.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/3 binary64)))) x (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(fma.f64 (.f64 x x) #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/3 binary64))))))
(fma.f64 (.f64 x x) (.f64 x #s(literal 1/3 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64)))))
(fma.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) x)
(fma.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/3 binary64))))) #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/3 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))))
(.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))) x)
(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))))) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))))
(+.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/3 binary64)))))
(+.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))) (.f64 x (*.f64 x #s(literal 1/3 binary64))))
(+.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))) #s(literal 1 binary64))
(+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64))))
(+.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/3 binary64)))) (*.f64 x #s(literal -1/2 binary64)))
(fma.f64 x #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/3 binary64)))))
(fma.f64 x (.f64 x #s(literal 1/3 binary64)) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64)) (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/3 binary64)))))
(fma.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))) (.f64 x (*.f64 x #s(literal 1/3 binary64))))
(fma.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/3 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64))))
(fma.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/3 binary64)))) (*.f64 x #s(literal -1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/3 binary64)))))
(fma.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/3 binary64)))))
(fma.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/3 binary64))))
(fma.f64 #s(literal 1/3 binary64) (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(fma.f64 (.f64 x #s(literal 1/3 binary64)) x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(fma.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))) x #s(literal 1 binary64))
(fma.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64))))
(fma.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/3 binary64)))) #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))
(fma.f64 (.f64 x x) #s(literal 1/3 binary64) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))) #s(literal 1 binary64))
(+.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 x (*.f64 x #s(literal 1/3 binary64))))
(+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) (*.f64 x #s(literal -1/2 binary64)))
(fma.f64 x #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/3 binary64))))
(fma.f64 x (.f64 x #s(literal 1/3 binary64)) (.f64 x #s(literal -1/2 binary64)))
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(fma.f64 #s(literal -1/4 binary64) (.f64 x (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))))
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(fma.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal -1/4 binary64))))) #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/3 binary64))))
(fma.f64 (.f64 x (.f64 x x)) #s(literal -1/4 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))))
(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64))))))
(.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))))
(.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64))))) x)
(.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))) #s(literal 1 binary64))
(+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))
(+.f64 (.f64 x #s(literal 1/3 binary64)) (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal -1/4 binary64)))))
(+.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) (.f64 x (*.f64 x #s(literal -1/4 binary64))))
(+.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))) #s(literal -1/2 binary64))
(+.f64 (.f64 x (.f64 x #s(literal -1/4 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))
(+.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal -1/4 binary64)))) (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 x #s(literal 1/3 binary64) (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal -1/4 binary64)))))
(fma.f64 x (.f64 x #s(literal -1/4 binary64)) (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))
(fma.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64))
(fma.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/3 binary64)) (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal -1/4 binary64)))))
(fma.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) (.f64 x (*.f64 x #s(literal -1/4 binary64))))
(fma.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))) #s(literal -1/2 binary64))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/4 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))
(fma.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal -1/4 binary64)))) (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 #s(literal 1/3 binary64) x (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal -1/4 binary64)))))
(fma.f64 (.f64 x #s(literal 1/3 binary64)) #s(literal 1 binary64) (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal -1/4 binary64)))))
(fma.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/4 binary64))))
(fma.f64 #s(literal -1/4 binary64) (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))
(fma.f64 (.f64 x #s(literal -1/4 binary64)) x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))
(fma.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64))) x #s(literal -1/2 binary64))
(fma.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))) #s(literal 1 binary64) #s(literal -1/2 binary64))
(fma.f64 (.f64 x (.f64 x #s(literal -1/4 binary64))) #s(literal 1 binary64) (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))
(fma.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal -1/4 binary64)))) #s(literal 1 binary64) (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 (.f64 x x) #s(literal -1/4 binary64) (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))
(.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64))))))
(.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64))))) #s(literal 1 binary64))
(*.f64 x #s(literal 1/3 binary64))
(.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/3 binary64)))
(*.f64 #s(literal 1/3 binary64) x)
(.f64 (.f64 x #s(literal 1/3 binary64)) #s(literal 1 binary64))
(+.f64 (.f64 x #s(literal 1/3 binary64)) (.f64 x (*.f64 x #s(literal -1/4 binary64))))
(+.f64 (.f64 x (.f64 x #s(literal -1/4 binary64))) (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 x #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/4 binary64))))
(fma.f64 x (.f64 x #s(literal -1/4 binary64)) (.f64 x #s(literal 1/3 binary64)))
(fma.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/3 binary64)) (.f64 x (*.f64 x #s(literal -1/4 binary64))))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/4 binary64))) (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 #s(literal 1/3 binary64) x (.f64 x (.f64 x #s(literal -1/4 binary64))))
(fma.f64 (.f64 x #s(literal 1/3 binary64)) #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/4 binary64))))
(fma.f64 #s(literal -1/4 binary64) (.f64 x x) (.f64 x #s(literal 1/3 binary64)))
(fma.f64 (.f64 x #s(literal -1/4 binary64)) x (.f64 x #s(literal 1/3 binary64)))
(fma.f64 (.f64 x (.f64 x #s(literal -1/4 binary64))) #s(literal 1 binary64) (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 (.f64 x x) #s(literal -1/4 binary64) (.f64 x #s(literal 1/3 binary64)))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))
(.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64)))))
(.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) x)
(.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64)))) #s(literal 1 binary64))
(+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64)))
(+.f64 (*.f64 x #s(literal -1/4 binary64)) #s(literal 1/3 binary64))
(fma.f64 x #s(literal -1/4 binary64) #s(literal 1/3 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/4 binary64)) #s(literal 1/3 binary64))
(fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64))
(fma.f64 (*.f64 x #s(literal -1/4 binary64)) #s(literal 1 binary64) #s(literal 1/3 binary64))
(.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))
(.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) #s(literal 1 binary64))

simplify175.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

2650×	`-lowering-.f32`
2650×	`-lowering-.f64`
1632×	`+-lowering-+.f64`
1632×	`+-lowering-+.f32`
1110×	`/-lowering-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	107	1108
1	322	992
2	1068	913
3	3973	879
0	8290	879

Stop Event

1×	iter limit
1×	node limit

Counts

168 → 168

Calls

Call 1

Inputs
x
(* x (+ 1 (* -1/2 x)))
(* x (+ 1 (* -1/2 x)))
(* x (+ 1 (* -1/2 x)))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 x) 1/2))
(* (pow x 2) (- (/ 1 x) 1/2))
(* (pow x 2) (- (/ 1 x) 1/2))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 x) 1/2))
(* (pow x 2) (- (/ 1 x) 1/2))
(* (pow x 2) (- (/ 1 x) 1/2))
1
(+ 1 (* -1/2 x))
(+ 1 (* -1/2 x))
(+ 1 (* -1/2 x))
(* -1/2 x)
(* x (- (/ 1 x) 1/2))
(* x (- (/ 1 x) 1/2))
(* x (- (/ 1 x) 1/2))
(* -1/2 x)
(* -1 (* x (- 1/2 (/ 1 x))))
(* -1 (* x (- 1/2 (/ 1 x))))
(* -1 (* x (- 1/2 (/ 1 x))))
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
x
(* x (+ 1 (* -1/2 x)))
(* x (+ 1 (* x (- (* 1/3 x) 1/2))))
(* x (+ 1 (* x (- (* 1/3 x) 1/2))))
(* 1/3 (pow x 3))
(* (pow x 3) (- 1/3 (* 1/2 (/ 1 x))))
(* (pow x 3) (- (+ 1/3 (/ 1 (pow x 2))) (* 1/2 (/ 1 x))))
(* (pow x 3) (- (+ 1/3 (/ 1 (pow x 2))) (* 1/2 (/ 1 x))))
(* 1/3 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 x)) 1/3)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/3)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/3)))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* 1/3 x) 1/2)))
(+ 1 (* x (- (* 1/3 x) 1/2)))
(* 1/3 (pow x 2))
(* (pow x 2) (- 1/3 (* 1/2 (/ 1 x))))
(* (pow x 2) (- (+ 1/3 (/ 1 (pow x 2))) (* 1/2 (/ 1 x))))
(* (pow x 2) (- (+ 1/3 (/ 1 (pow x 2))) (* 1/2 (/ 1 x))))
(* 1/3 (pow x 2))
(* (pow x 2) (- 1/3 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/3 (* -1 (/ (- 1/2 (/ 1 x)) x))))
(* (pow x 2) (+ 1/3 (* -1 (/ (- 1/2 (/ 1 x)) x))))
(* -1/2 x)
(* x (- (* 1/3 x) 1/2))
(* x (- (* 1/3 x) 1/2))
(* x (- (* 1/3 x) 1/2))
(* 1/3 (pow x 2))
(* (pow x 2) (- 1/3 (* 1/2 (/ 1 x))))
(* (pow x 2) (- 1/3 (* 1/2 (/ 1 x))))
(* (pow x 2) (- 1/3 (* 1/2 (/ 1 x))))
(* 1/3 (pow x 2))
(* (pow x 2) (- 1/3 (* 1/2 (/ 1 x))))
(* (pow x 2) (- 1/3 (* 1/2 (/ 1 x))))
(* (pow x 2) (- 1/3 (* 1/2 (/ 1 x))))
-1/2
(- (* 1/3 x) 1/2)
(- (* 1/3 x) 1/2)
(- (* 1/3 x) 1/2)
(* 1/3 x)
(* x (- 1/3 (* 1/2 (/ 1 x))))
(* x (- 1/3 (* 1/2 (/ 1 x))))
(* x (- 1/3 (* 1/2 (/ 1 x))))
(* 1/3 x)
(* -1 (* x (- (* 1/2 (/ 1 x)) 1/3)))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1/3)))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1/3)))
x
(* x (+ 1 (* -1/2 x)))
(* x (+ 1 (* x (- (* 1/3 x) 1/2))))
(* x (+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2))))
(* -1/4 (pow x 4))
(* (pow x 4) (- (* 1/3 (/ 1 x)) 1/4))
(* (pow x 4) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))
(* (pow x 4) (- (+ (* 1/3 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/4 (/ 1/2 (pow x 2)))))
(* -1/4 (pow x 4))
(* (pow x 4) (- (* 1/3 (/ 1 x)) 1/4))
(* (pow x 4) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/3) x)) 1/4))
(* (pow x 4) (- (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/3) x)) 1/4))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* 1/3 x) 1/2)))
(+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2)))
(* -1/4 (pow x 3))
(* (pow x 3) (- (* 1/3 (/ 1 x)) 1/4))
(* (pow x 3) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))
(* (pow x 3) (- (+ (* 1/3 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/4 (/ 1/2 (pow x 2)))))
(* -1/4 (pow x 3))
(* -1 (* (pow x 3) (- 1/4 (* 1/3 (/ 1 x)))))
(* -1 (* (pow x 3) (+ 1/4 (* -1 (/ (- 1/3 (* 1/2 (/ 1 x))) x)))))
(* -1 (* (pow x 3) (+ 1/4 (* -1 (/ (+ 1/3 (* -1 (/ (- 1/2 (/ 1 x)) x))) x)))))
(* -1/2 x)
(* x (- (* 1/3 x) 1/2))
(* x (- (* x (+ 1/3 (* -1/4 x))) 1/2))
(* x (- (* x (+ 1/3 (* -1/4 x))) 1/2))
(* -1/4 (pow x 3))
(* (pow x 3) (- (* 1/3 (/ 1 x)) 1/4))
(* (pow x 3) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))
(* (pow x 3) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))
(* -1/4 (pow x 3))
(* -1 (* (pow x 3) (- 1/4 (* 1/3 (/ 1 x)))))
(* -1 (* (pow x 3) (+ 1/4 (* -1 (/ (- 1/3 (* 1/2 (/ 1 x))) x)))))
(* -1 (* (pow x 3) (+ 1/4 (* -1 (/ (- 1/3 (* 1/2 (/ 1 x))) x)))))
-1/2
(- (* 1/3 x) 1/2)
(- (* x (+ 1/3 (* -1/4 x))) 1/2)
(- (* x (+ 1/3 (* -1/4 x))) 1/2)
(* -1/4 (pow x 2))
(* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))
(* (pow x 2) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))
(* (pow x 2) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))
(* -1/4 (pow x 2))
(* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/3) x)) 1/4))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/3) x)) 1/4))
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* x (+ 1/3 (* -1/4 x)))
(* x (+ 1/3 (* -1/4 x)))
(* x (+ 1/3 (* -1/4 x)))
(* -1/4 (pow x 2))
(* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))
(* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))
(* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))
(* -1/4 (pow x 2))
(* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))
(* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))
(* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))
1/3
(+ 1/3 (* -1/4 x))
(+ 1/3 (* -1/4 x))
(+ 1/3 (* -1/4 x))
(* -1/4 x)
(* x (- (* 1/3 (/ 1 x)) 1/4))
(* x (- (* 1/3 (/ 1 x)) 1/4))
(* x (- (* 1/3 (/ 1 x)) 1/4))
(* -1/4 x)
(* -1 (* x (- 1/4 (* 1/3 (/ 1 x)))))
(* -1 (* x (- 1/4 (* 1/3 (/ 1 x)))))
(* -1 (* x (- 1/4 (* 1/3 (/ 1 x)))))

Outputs
x
(* x (+ 1 (* -1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(* x (+ 1 (* -1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(* x (+ 1 (* -1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* (pow x 2) (- (/ 1 x) 1/2))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(* (pow x 2) (- (/ 1 x) 1/2))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(* (pow x 2) (- (/ 1 x) 1/2))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* (pow x 2) (- (/ 1 x) 1/2))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(* (pow x 2) (- (/ 1 x) 1/2))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(* (pow x 2) (- (/ 1 x) 1/2))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))
(+ 1 (* -1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))
(+ 1 (* -1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* x (- (/ 1 x) 1/2))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))
(* x (- (/ 1 x) 1/2))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))
(* x (- (/ 1 x) 1/2))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1 (* x (- 1/2 (/ 1 x))))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))
(* -1 (* x (- 1/2 (/ 1 x))))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))
(* -1 (* x (- 1/2 (/ 1 x))))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
x
(* x (+ 1 (* -1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(* x (+ 1 (* x (- (* 1/3 x) 1/2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))))
(* x (+ 1 (* x (- (* 1/3 x) 1/2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))))
(* 1/3 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/3 binary64)))
(* (pow x 3) (- 1/3 (* 1/2 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))
(* (pow x 3) (- (+ 1/3 (/ 1 (pow x 2))) (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))))
(* (pow x 3) (- (+ 1/3 (/ 1 (pow x 2))) (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))))
(* 1/3 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/3 binary64)))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 x)) 1/3)))
(.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))
(* -1 (* (pow x 3) (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/3)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))))
(* -1 (* (pow x 3) (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/3)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))
(+ 1 (* x (- (* 1/3 x) 1/2)))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))))
(+ 1 (* x (- (* 1/3 x) 1/2)))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))))
(* 1/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/3 binary64))
(* (pow x 2) (- 1/3 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))
(* (pow x 2) (- (+ 1/3 (/ 1 (pow x 2))) (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))))
(* (pow x 2) (- (+ 1/3 (/ 1 (pow x 2))) (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))))
(* 1/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/3 binary64))
(* (pow x 2) (- 1/3 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))
(* (pow x 2) (+ 1/3 (* -1 (/ (- 1/2 (/ 1 x)) x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))))
(* (pow x 2) (+ 1/3 (* -1 (/ (- 1/2 (/ 1 x)) x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* x (- (* 1/3 x) 1/2))
(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))
(* x (- (* 1/3 x) 1/2))
(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))
(* x (- (* 1/3 x) 1/2))
(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))
(* 1/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/3 binary64))
(* (pow x 2) (- 1/3 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))
(* (pow x 2) (- 1/3 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))
(* (pow x 2) (- 1/3 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))
(* 1/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/3 binary64))
(* (pow x 2) (- 1/3 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))
(* (pow x 2) (- 1/3 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))
(* (pow x 2) (- 1/3 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))
-1/2
#s(literal -1/2 binary64)
(- (* 1/3 x) 1/2)
(+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))
(- (* 1/3 x) 1/2)
(+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))
(- (* 1/3 x) 1/2)
(+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (- 1/3 (* 1/2 (/ 1 x))))
(+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))
(* x (- 1/3 (* 1/2 (/ 1 x))))
(+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))
(* x (- 1/3 (* 1/2 (/ 1 x))))
(+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1/3)))
(+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1/3)))
(+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1/3)))
(+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))
x
(* x (+ 1 (* -1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(* x (+ 1 (* x (- (* 1/3 x) 1/2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))))
(* x (+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 x #s(literal 1/4 binary64))))))))
(* -1/4 (pow x 4))
(*.f64 #s(literal -1/4 binary64) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (- (* 1/3 (/ 1 x)) 1/4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1/3 binary64) x)))
(* (pow x 4) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal -1/4 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/2 binary64) x)) x)))
(* (pow x 4) (- (+ (* 1/3 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/4 (/ 1/2 (pow x 2)))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal -1/4 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x)))
(* -1/4 (pow x 4))
(*.f64 #s(literal -1/4 binary64) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (- (* 1/3 (/ 1 x)) 1/4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1/3 binary64) x)))
(* (pow x 4) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/3) x)) 1/4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal -1/4 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/2 binary64) x)) x)))
(* (pow x 4) (- (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/3) x)) 1/4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal -1/4 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x)))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))
(+ 1 (* x (- (* 1/3 x) 1/2)))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))))
(+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2)))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (-.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal 1/4 binary64)))))))
(* -1/4 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal -1/4 binary64))
(* (pow x 3) (- (* 1/3 (/ 1 x)) 1/4))
(.f64 (.f64 x x) (-.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal 1/4 binary64))))
(* (pow x 3) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))
(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (-.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal 1/4 binary64))))))
(* (pow x 3) (- (+ (* 1/3 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/4 (/ 1/2 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (-.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal 1/4 binary64)))))))
(* -1/4 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal -1/4 binary64))
(* -1 (* (pow x 3) (- 1/4 (* 1/3 (/ 1 x)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal 1/4 binary64))))
(* -1 (* (pow x 3) (+ 1/4 (* -1 (/ (- 1/3 (* 1/2 (/ 1 x))) x)))))
(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (-.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal 1/4 binary64))))))
(* -1 (* (pow x 3) (+ 1/4 (* -1 (/ (+ 1/3 (* -1 (/ (- 1/2 (/ 1 x)) x))) x)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (-.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal 1/4 binary64)))))))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* x (- (* 1/3 x) 1/2))
(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))
(* x (- (* x (+ 1/3 (* -1/4 x))) 1/2))
(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (-.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal 1/4 binary64))))))
(* x (- (* x (+ 1/3 (* -1/4 x))) 1/2))
(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (-.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal 1/4 binary64))))))
(* -1/4 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal -1/4 binary64))
(* (pow x 3) (- (* 1/3 (/ 1 x)) 1/4))
(.f64 (.f64 x x) (-.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal 1/4 binary64))))
(* (pow x 3) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))
(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (-.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal 1/4 binary64))))))
(* (pow x 3) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))
(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (-.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal 1/4 binary64))))))
(* -1/4 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal -1/4 binary64))
(* -1 (* (pow x 3) (- 1/4 (* 1/3 (/ 1 x)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal 1/4 binary64))))
(* -1 (* (pow x 3) (+ 1/4 (* -1 (/ (- 1/3 (* 1/2 (/ 1 x))) x)))))
(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (-.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal 1/4 binary64))))))
(* -1 (* (pow x 3) (+ 1/4 (* -1 (/ (- 1/3 (* 1/2 (/ 1 x))) x)))))
(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (-.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal 1/4 binary64))))))
-1/2
#s(literal -1/2 binary64)
(- (* 1/3 x) 1/2)
(+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))
(- (* x (+ 1/3 (* -1/4 x))) 1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 x #s(literal 1/4 binary64)))))
(- (* x (+ 1/3 (* -1/4 x))) 1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 x #s(literal 1/4 binary64)))))
(* -1/4 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/4 binary64))
(* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 x #s(literal 1/4 binary64))))
(* (pow x 2) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))
(+.f64 #s(literal -1/2 binary64) (.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 x #s(literal 1/4 binary64)))))
(* (pow x 2) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))
(+.f64 #s(literal -1/2 binary64) (.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 x #s(literal 1/4 binary64)))))
(* -1/4 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/4 binary64))
(* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 x #s(literal 1/4 binary64))))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/3) x)) 1/4))
(+.f64 #s(literal -1/2 binary64) (.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 x #s(literal 1/4 binary64)))))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/3) x)) 1/4))
(+.f64 #s(literal -1/2 binary64) (.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 x #s(literal 1/4 binary64)))))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (+ 1/3 (* -1/4 x)))
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 x #s(literal 1/4 binary64))))
(* x (+ 1/3 (* -1/4 x)))
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 x #s(literal 1/4 binary64))))
(* x (+ 1/3 (* -1/4 x)))
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 x #s(literal 1/4 binary64))))
(* -1/4 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/4 binary64))
(* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 x #s(literal 1/4 binary64))))
(* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 x #s(literal 1/4 binary64))))
(* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 x #s(literal 1/4 binary64))))
(* -1/4 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/4 binary64))
(* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 x #s(literal 1/4 binary64))))
(* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 x #s(literal 1/4 binary64))))
(* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 x #s(literal 1/4 binary64))))
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* -1/4 x))
(-.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal 1/4 binary64)))
(+ 1/3 (* -1/4 x))
(-.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal 1/4 binary64)))
(+ 1/3 (* -1/4 x))
(-.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal 1/4 binary64)))
(* -1/4 x)
(*.f64 x #s(literal -1/4 binary64))
(* x (- (* 1/3 (/ 1 x)) 1/4))
(-.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal 1/4 binary64)))
(* x (- (* 1/3 (/ 1 x)) 1/4))
(-.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal 1/4 binary64)))
(* x (- (* 1/3 (/ 1 x)) 1/4))
(-.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal 1/4 binary64)))
(* -1/4 x)
(*.f64 x #s(literal -1/4 binary64))
(* -1 (* x (- 1/4 (* 1/3 (/ 1 x)))))
(-.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal 1/4 binary64)))
(* -1 (* x (- 1/4 (* 1/3 (/ 1 x)))))
(-.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal 1/4 binary64)))
(* -1 (* x (- 1/4 (* 1/3 (/ 1 x)))))
(-.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal 1/4 binary64)))

eval59.0ms (1.6%)

Compiler: Compiled 7699 to 870 computations (88.7% saved)

prune64.0ms (1.8%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	536	2	538
Fresh	0	0	0
Picked	1	3	4
Done	0	1	1
Total	537	6	543

Accuracy

100.0%

Counts

543 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	66.7%	(+.f64 (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) (*.f64 x x)) x)
▶	65.6%	(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) x)
✓	65.7%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))))
✓	65.6%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
✓	100.0%	(log1p.f64 x)
✓	66.5%	x

Compiler

Compiled 49 to 34 computations (30.6% saved)

simplify14.0ms (0.4%)

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 x #s(literal 1/3 binary64))
✓	cost-diff	(+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))
✓	cost-diff	(.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) (*.f64 x x))
✓	cost-diff	(+.f64 (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) (*.f64 x x)) x)
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(.f64 #s(literal -1/2 binary64) (.f64 x x))
✓	cost-diff	(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) x)

Rules

276×	`fma-define`
208×	`fma-lowering-fma.f32`
208×	`fma-lowering-fma.f64`
134×	`-lowering-.f32`
134×	`-lowering-.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	43
1	23	40
2	46	40
3	100	40
4	202	40
5	256	40
6	312	40
7	352	40
8	356	40
0	356	40

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+ (* -1/2 (* x x)) x)
(* -1/2 (* x x))
-1/2
(* x x)
x
(+ (* (+ -1/2 (* x 1/3)) (* x x)) x)
(* (+ -1/2 (* x 1/3)) (* x x))
(+ -1/2 (* x 1/3))
-1/2
(* x 1/3)
x
1/3
(* x x)

Outputs
(+ (* -1/2 (* x x)) x)
(.f64 x (+.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)))
(* -1/2 (* x x))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
-1/2
#s(literal -1/2 binary64)
(* x x)
(*.f64 x x)
x
(+ (* (+ -1/2 (* x 1/3)) (* x x)) x)
(.f64 x (+.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))) #s(literal 1 binary64)))
(* (+ -1/2 (* x 1/3)) (* x x))
(.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))
(+ -1/2 (* x 1/3))
(+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))
-1/2
#s(literal -1/2 binary64)
(* x 1/3)
(*.f64 x #s(literal 1/3 binary64))
x
1/3
#s(literal 1/3 binary64)
(* x x)
(*.f64 x x)

localize58.0ms (1.6%)

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.9%	(.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) (*.f64 x x))
✓	accuracy	99.5%	(*.f64 x #s(literal 1/3 binary64))
✓	accuracy	100.0%	(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) x)
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 #s(literal -1/2 binary64) (.f64 x x))

Results

39.0ms

256×

valid

Compiler

Compiled 53 to 11 computations (79.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-mult: 7.0ms (45.4% of total)

ival-add: 4.0ms (26% of total)

...c/correct-round.rkt:119:19: 4.0ms (26% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series3.0ms (0.1%)

Counts

7 → 84

Calls

Call 1

Inputs
#<alt (+ (* -1/2 (* x x)) x)>
#<alt (* -1/2 (* x x))>
#<alt (* x x)>
#<alt (+ (* (+ -1/2 (* x 1/3)) (* x x)) x)>
#<alt (* (+ -1/2 (* x 1/3)) (* x x))>
#<alt (+ -1/2 (* x 1/3))>
#<alt (* x 1/3)>

Outputs
#<alt x>
#<alt (* x (+ 1 (* -1/2 x)))>
#<alt (* x (+ 1 (* -1/2 x)))>
#<alt (* x (+ 1 (* -1/2 x)))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 x) 1/2))>
#<alt (* (pow x 2) (- (/ 1 x) 1/2))>
#<alt (* (pow x 2) (- (/ 1 x) 1/2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 x) 1/2))>
#<alt (* (pow x 2) (- (/ 1 x) 1/2))>
#<alt (* (pow x 2) (- (/ 1 x) 1/2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt x>
#<alt (* x (+ 1 (* -1/2 x)))>
#<alt (* x (+ 1 (* x (- (* 1/3 x) 1/2))))>
#<alt (* x (+ 1 (* x (- (* 1/3 x) 1/2))))>
#<alt (* 1/3 (pow x 3))>
#<alt (* (pow x 3) (- 1/3 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ 1/3 (/ 1 (pow x 2))) (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ 1/3 (/ 1 (pow x 2))) (* 1/2 (/ 1 x))))>
#<alt (* 1/3 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (* 1/2 (/ 1 x)) 1/3)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/3)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/3)))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/3 x) 1/2))>
#<alt (* (pow x 2) (- (* 1/3 x) 1/2))>
#<alt (* (pow x 2) (- (* 1/3 x) 1/2))>
#<alt (* 1/3 (pow x 3))>
#<alt (* (pow x 3) (- 1/3 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (- 1/3 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (- 1/3 (* 1/2 (/ 1 x))))>
#<alt (* 1/3 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (* 1/2 (/ 1 x)) 1/3)))>
#<alt (* -1 (* (pow x 3) (- (* 1/2 (/ 1 x)) 1/3)))>
#<alt (* -1 (* (pow x 3) (- (* 1/2 (/ 1 x)) 1/3)))>
#<alt -1/2>
#<alt (- (* 1/3 x) 1/2)>
#<alt (- (* 1/3 x) 1/2)>
#<alt (- (* 1/3 x) 1/2)>
#<alt (* 1/3 x)>
#<alt (* x (- 1/3 (* 1/2 (/ 1 x))))>
#<alt (* x (- 1/3 (* 1/2 (/ 1 x))))>
#<alt (* x (- 1/3 (* 1/2 (/ 1 x))))>
#<alt (* 1/3 x)>
#<alt (* -1 (* x (- (* 1/2 (/ 1 x)) 1/3)))>
#<alt (* -1 (* x (- (* 1/2 (/ 1 x)) 1/3)))>
#<alt (* -1 (* x (- (* 1/2 (/ 1 x)) 1/3)))>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>

Calls

21 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(+ (* -1/2 (* x x)) x)
0.0ms	x	@	0	(* -1/2 (* x x))
0.0ms	x	@	0	(+ (* -1/2 (* x x)) x)
0.0ms	x	@	inf	(* -1/2 (* x x))
0.0ms	x	@	inf	(+ (* (+ -1/2 (* x 1/3)) (* x x)) x)

rewrite35.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

290×	`fma-define`
220×	`fma-lowering-fma.f32`
220×	`fma-lowering-fma.f64`
142×	`-lowering-.f32`
142×	`-lowering-.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	36
1	25	33
2	51	33
3	109	33
4	220	33
5	288	33
6	360	33
7	430	33
8	476	33
9	480	33
0	480	33

Stop Event

1×	iter limit
1×	saturated

Counts

7 → 100

Calls

Call 1

Inputs
(+ (* -1/2 (* x x)) x)
(* -1/2 (* x x))
(* x x)
(+ (* (+ -1/2 (* x 1/3)) (* x x)) x)
(* (+ -1/2 (* x 1/3)) (* x x))
(+ -1/2 (* x 1/3))
(* x 1/3)

Outputs
(+.f64 x (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) x)
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) x)
(fma.f64 x (*.f64 #s(literal -1/2 binary64) x) x)
(fma.f64 x #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) x)
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64) x)
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) x x)
(fma.f64 #s(literal 1 binary64) x (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(fma.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)) x)
(.f64 x (+.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)))
(.f64 (.f64 x (+.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x (+.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))))
(.f64 (+.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) x)
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(.f64 x (.f64 #s(literal -1/2 binary64) x))
(.f64 (.f64 x x) #s(literal -1/2 binary64))
(.f64 (.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64))
(.f64 (.f64 #s(literal -1/2 binary64) x) x)
(.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(*.f64 x x)
(.f64 (.f64 x x) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x x))
(+.f64 x (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/3 binary64))))))
(+.f64 (.f64 x (+.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))) (.f64 (.f64 x x) (*.f64 x #s(literal 1/3 binary64))))
(+.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))) x)
(+.f64 (.f64 (.f64 x x) (.f64 x #s(literal 1/3 binary64))) (.f64 x (+.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))))
(+.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/3 binary64))))) (.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(fma.f64 #s(literal -1/2 binary64) (.f64 x x) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/3 binary64))))))
(fma.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))) x)
(fma.f64 x (.f64 #s(literal -1/2 binary64) x) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/3 binary64))))))
(fma.f64 x #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))))
(fma.f64 x (+.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (.f64 (.f64 x x) (.f64 x #s(literal 1/3 binary64))))
(fma.f64 x (.f64 x (.f64 x #s(literal 1/3 binary64))) (.f64 x (+.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))))
(fma.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/3 binary64)))) (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(fma.f64 (.f64 x x) #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/3 binary64))))))
(fma.f64 (.f64 x x) (.f64 x #s(literal 1/3 binary64)) (.f64 x (+.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))))
(fma.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) x)
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/3 binary64))))))
(fma.f64 (.f64 x (+.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))) #s(literal 1 binary64) (.f64 (.f64 x x) (*.f64 x #s(literal 1/3 binary64))))
(fma.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x x)) (.f64 x (+.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))))
(fma.f64 (.f64 x #s(literal 1/3 binary64)) (.f64 x x) (.f64 x (+.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))))
(fma.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) (.f64 x x) x)
(fma.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))) #s(literal 1 binary64) x)
(fma.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))) x x)
(fma.f64 (.f64 #s(literal -1/2 binary64) x) x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/3 binary64))))))
(fma.f64 (.f64 (.f64 x x) (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64) (.f64 x (+.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))))
(fma.f64 #s(literal 1 binary64) x (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))))
(fma.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/3 binary64))))))
(fma.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))) (.f64 (.f64 x x) (*.f64 x #s(literal 1/3 binary64))))
(fma.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))) x)
(fma.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x #s(literal 1/3 binary64))) (.f64 x (+.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))))
(fma.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/3 binary64))))) (.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(fma.f64 (+.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) x (.f64 (.f64 x x) (.f64 x #s(literal 1/3 binary64))))
(fma.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) x (.f64 x (+.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))))
(fma.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/3 binary64))))) #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/3 binary64) (.f64 x (+.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))))
(fma.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/3 binary64)))) x (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(.f64 x (+.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))) #s(literal 1 binary64)))
(.f64 (.f64 x (+.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))) #s(literal 1 binary64))) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))) #s(literal 1 binary64))))
(.f64 (+.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))) #s(literal 1 binary64)) x)
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) (.f64 (.f64 x x) (*.f64 x #s(literal 1/3 binary64))))
(+.f64 (.f64 (.f64 x x) (.f64 x #s(literal 1/3 binary64))) (.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(fma.f64 #s(literal -1/2 binary64) (.f64 x x) (.f64 (.f64 x x) (.f64 x #s(literal 1/3 binary64))))
(fma.f64 x (.f64 #s(literal -1/2 binary64) x) (.f64 (.f64 x x) (.f64 x #s(literal 1/3 binary64))))
(fma.f64 x (.f64 x (.f64 x #s(literal 1/3 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(fma.f64 (.f64 x x) #s(literal -1/2 binary64) (.f64 (.f64 x x) (.f64 x #s(literal 1/3 binary64))))
(fma.f64 (.f64 x x) (.f64 x #s(literal 1/3 binary64)) (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64) (.f64 (.f64 x x) (*.f64 x #s(literal 1/3 binary64))))
(fma.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x x)) (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(fma.f64 (.f64 x #s(literal 1/3 binary64)) (.f64 x x) (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) x (.f64 (.f64 x x) (.f64 x #s(literal 1/3 binary64))))
(fma.f64 (.f64 (.f64 x x) (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(fma.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)) (.f64 (.f64 x x) (*.f64 x #s(literal 1/3 binary64))))
(fma.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x #s(literal 1/3 binary64))) (.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(fma.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) x (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/3 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))))
(.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))
(.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) (*.f64 x x))
(.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))) #s(literal 1 binary64))
(.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))) x)
(.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))))
(+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))
(+.f64 (*.f64 x #s(literal 1/3 binary64)) #s(literal -1/2 binary64))
(fma.f64 x #s(literal 1/3 binary64) #s(literal -1/2 binary64))
(fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64))
(fma.f64 (*.f64 x #s(literal 1/3 binary64)) #s(literal 1 binary64) #s(literal -1/2 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/3 binary64)) #s(literal -1/2 binary64))
(.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))
(*.f64 x #s(literal 1/3 binary64))
(*.f64 #s(literal 1/3 binary64) x)
(.f64 (.f64 x #s(literal 1/3 binary64)) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/3 binary64)))

simplify136.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

2078×	`fma-define`
1828×	`sum3-define`
1654×	`sum4-define`
1380×	`-lowering-.f32`
1380×	`-lowering-.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	42	441
1	119	398
2	324	382
3	1113	360
4	3171	360
5	7065	360
0	8488	360

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 84

Calls

Call 1

Inputs
x
(* x (+ 1 (* -1/2 x)))
(* x (+ 1 (* -1/2 x)))
(* x (+ 1 (* -1/2 x)))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 x) 1/2))
(* (pow x 2) (- (/ 1 x) 1/2))
(* (pow x 2) (- (/ 1 x) 1/2))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 x) 1/2))
(* (pow x 2) (- (/ 1 x) 1/2))
(* (pow x 2) (- (/ 1 x) 1/2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
x
(* x (+ 1 (* -1/2 x)))
(* x (+ 1 (* x (- (* 1/3 x) 1/2))))
(* x (+ 1 (* x (- (* 1/3 x) 1/2))))
(* 1/3 (pow x 3))
(* (pow x 3) (- 1/3 (* 1/2 (/ 1 x))))
(* (pow x 3) (- (+ 1/3 (/ 1 (pow x 2))) (* 1/2 (/ 1 x))))
(* (pow x 3) (- (+ 1/3 (/ 1 (pow x 2))) (* 1/2 (/ 1 x))))
(* 1/3 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 x)) 1/3)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/3)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/3)))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 1/3 x) 1/2))
(* (pow x 2) (- (* 1/3 x) 1/2))
(* (pow x 2) (- (* 1/3 x) 1/2))
(* 1/3 (pow x 3))
(* (pow x 3) (- 1/3 (* 1/2 (/ 1 x))))
(* (pow x 3) (- 1/3 (* 1/2 (/ 1 x))))
(* (pow x 3) (- 1/3 (* 1/2 (/ 1 x))))
(* 1/3 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 x)) 1/3)))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 x)) 1/3)))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 x)) 1/3)))
-1/2
(- (* 1/3 x) 1/2)
(- (* 1/3 x) 1/2)
(- (* 1/3 x) 1/2)
(* 1/3 x)
(* x (- 1/3 (* 1/2 (/ 1 x))))
(* x (- 1/3 (* 1/2 (/ 1 x))))
(* x (- 1/3 (* 1/2 (/ 1 x))))
(* 1/3 x)
(* -1 (* x (- (* 1/2 (/ 1 x)) 1/3)))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1/3)))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1/3)))
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)

Outputs
x
(* x (+ 1 (* -1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(* x (+ 1 (* -1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(* x (+ 1 (* -1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* (pow x 2) (- (/ 1 x) 1/2))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(* (pow x 2) (- (/ 1 x) 1/2))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(* (pow x 2) (- (/ 1 x) 1/2))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* (pow x 2) (- (/ 1 x) 1/2))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(* (pow x 2) (- (/ 1 x) 1/2))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(* (pow x 2) (- (/ 1 x) 1/2))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
x
(* x (+ 1 (* -1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(* x (+ 1 (* x (- (* 1/3 x) 1/2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))))
(* x (+ 1 (* x (- (* 1/3 x) 1/2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))))
(* 1/3 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/3 binary64))))
(* (pow x 3) (- 1/3 (* 1/2 (/ 1 x))))
(.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))))
(* (pow x 3) (- (+ 1/3 (/ 1 (pow x 2))) (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))))
(* (pow x 3) (- (+ 1/3 (/ 1 (pow x 2))) (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))))
(* 1/3 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/3 binary64))))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 x)) 1/3)))
(.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))))
(* -1 (* (pow x 3) (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/3)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))))
(* -1 (* (pow x 3) (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/3)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* (pow x 2) (- (* 1/3 x) 1/2))
(.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))))
(* (pow x 2) (- (* 1/3 x) 1/2))
(.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))))
(* (pow x 2) (- (* 1/3 x) 1/2))
(.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))))
(* 1/3 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/3 binary64))))
(* (pow x 3) (- 1/3 (* 1/2 (/ 1 x))))
(.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))))
(* (pow x 3) (- 1/3 (* 1/2 (/ 1 x))))
(.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))))
(* (pow x 3) (- 1/3 (* 1/2 (/ 1 x))))
(.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))))
(* 1/3 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/3 binary64))))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 x)) 1/3)))
(.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 x)) 1/3)))
(.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 x)) 1/3)))
(.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))))
-1/2
#s(literal -1/2 binary64)
(- (* 1/3 x) 1/2)
(+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))
(- (* 1/3 x) 1/2)
(+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))
(- (* 1/3 x) 1/2)
(+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (- 1/3 (* 1/2 (/ 1 x))))
(+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))
(* x (- 1/3 (* 1/2 (/ 1 x))))
(+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))
(* x (- 1/3 (* 1/2 (/ 1 x))))
(+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1/3)))
(+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1/3)))
(+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1/3)))
(+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))

eval26.0ms (0.7%)

Compiler: Compiled 2119 to 197 computations (90.7% saved)

prune16.0ms (0.4%)

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	202	0	202
Fresh	0	0	0
Picked	0	2	2
Done	0	4	4
Total	202	6	208

Accuracy

100.0%

Counts

208 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	66.7%	(+.f64 (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) (*.f64 x x)) x)
✓	65.6%	(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) x)
✓	65.7%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))))
✓	65.6%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
✓	100.0%	(log1p.f64 x)
✓	66.5%	x

Compiler

Compiled 108 to 62 computations (42.6% saved)

regimes9.0ms (0.2%)

Counts

8 → 1

Calls

Call 1

Inputs
x
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) x)
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))))
(+.f64 (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) (*.f64 x x)) x)
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))))
(log1p.f64 x)
(log.f64 (+.f64 #s(literal 1 binary64) x))

Outputs
(log1p.f64 x)

Calls

3 calls:

3.0ms	x
2.0ms	(log.f64 (+.f64 #s(literal 1 binary64) x))
2.0ms	(+.f64 #s(literal 1 binary64) x)

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(log.f64 (+.f64 #s(literal 1 binary64) x))`
100.0%	1	`(+.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes3.0ms (0.1%)

Counts

6 → 1

Calls

Call 1

Inputs
x
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) x)
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))))
(+.f64 (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) (*.f64 x x)) x)
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))))

Outputs
(+.f64 (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) (*.f64 x x)) x)

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
66.7%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0.1%)

Counts

4 → 1

Calls

Call 1

Inputs
x
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) x)
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))))

Outputs
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))))

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
66.7%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0.1%)

Accuracy

Total -0.9b remaining (-4.4%)

Threshold costs -0.9b (-4.4%)

Counts

3 → 1

Calls

Call 1

Inputs
x
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) x)

Outputs
x

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
66.5%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
6×	`+-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	25
1	23	25

Stop Event

1×

saturated

Calls

Call 1

Inputs
(log1p.f64 x)
(+.f64 (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) (*.f64 x x)) x)
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))))
x

Outputs
(log1p.f64 x)
(+.f64 (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) (*.f64 x x)) x)
(+.f64 x (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) (*.f64 x x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))))
x

soundness327.0ms (9.1%)

Rules

1970×	`fmsub-define`
1904×	`sum3-define`
1846×	`fma-lowering-fma.f32`
1846×	`fma-lowering-fma.f64`
1776×	`fmm-def`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	133
1	178	111
2	443	105
3	1212	103
4	3930	96
0	8245	96
0	4	2
1	8	2
0	8	2
0	20	110
1	66	90
2	184	87
3	459	87
4	973	87
5	1409	87
6	1607	87
7	1654	87
8	1767	87
9	1828	87
0	1828	87

Stop Event

1×	done
1×	iter limit
1×	saturated
1×	iter limit
1×	saturated
1×	iter limit
1×	node limit

Compiler

Compiled 76 to 48 computations (36.8% saved)

preprocess56.0ms (1.6%)

Compiler: Compiled 102 to 52 computations (49% saved)

ln(1 + x)

analyze3.0ms (0.1%)

sample1.8s (49.1%)

preprocess18.0ms (0.5%)

explain242.0ms (6.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize52.0ms (1.4%)

series1.0ms (0%)

rewrite29.0ms (0.8%)

simplify214.0ms (6%)

eval1.0ms (0%)

prune3.0ms (0.1%)

simplify48.0ms (1.3%)

localize114.0ms (3.2%)

series14.0ms (0.4%)

rewrite97.0ms (2.7%)

simplify175.0ms (4.9%)

eval59.0ms (1.6%)

prune64.0ms (1.8%)

simplify14.0ms (0.4%)

localize58.0ms (1.6%)

series3.0ms (0.1%)

rewrite35.0ms (1%)

simplify136.0ms (3.8%)

eval26.0ms (0.7%)

prune16.0ms (0.4%)

regimes9.0ms (0.2%)

regimes3.0ms (0.1%)

regimes2.0ms (0.1%)

regimes2.0ms (0.1%)

simplify8.0ms (0.2%)

soundness327.0ms (9.1%)

preprocess56.0ms (1.6%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	10	36
1	25	33
2	51	33
3	109	33
4	220	33
5	288	33
6	360	33
7	430	33
8	476	33
9	480	33
0	480	33

Iter	Nodes	Cost
0	10	36
1	25	33
2	51	33
3	109	33
4	220	33
5	288	33
6	360	33
7	430	33
8	476	33
9	480	33
0	480	33

Iter	Nodes	Cost
0	10	36
1	25	33
2	51	33
3	109	33
4	220	33
5	288	33
6	360	33
7	430	33
8	476	33
9	480	33
0	480	33