Metrics for Expanding a square

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
100%	100%	0%	0%	0%	0%	0%	1

Compiler

Compiled 11 to 6 computations (45.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

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

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

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

const: 0.0ms (0% of total)

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

sample822.0ms (23.8%)

Results

401.0ms	4018×	1	valid
231.0ms	4238×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 321.0ms

ival-mult: 89.0ms (27.7% of total)

ival-add: 83.0ms (25.8% of total)

ival-sub: 78.0ms (24.3% of total)

backward-pass: 56.0ms (17.4% of total)

const: 15.0ms (4.7% of total)

Bogosity

preprocess285.0ms (8.3%)

Algorithm

2×	egg-herbie

Rules

2954×	`+-lowering-+.f64`
2954×	`+-lowering-+.f32`
2706×	`fma-lowering-fma.f32`
2706×	`fma-lowering-fma.f64`
1988×	`fmsub-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	46	19
2	151	17
3	1114	15
4	4617	15
5	7001	15
0	5	6
1	23	6
2	61	5
3	367	5
4	1235	5
5	2717	5
6	6625	5
0	8378	5

Stop Event

1×	iter limit
1×	node limit
1×	node limit

Calls

Call 1

Inputs
(- (* (+ x 1) (+ x 1)) 1)

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

Call 2

Inputs
(- (* (+ x 1) (+ x 1)) 1)
(- (* (+ (neg x) 1) (+ (neg x) 1)) 1)
(neg (- (* (+ (neg x) 1) (+ (neg x) 1)) 1))

Outputs
(- (* (+ x 1) (+ x 1)) 1)
(* (+ x 2) x)
(- (* (+ (neg x) 1) (+ (neg x) 1)) 1)
(* (+ x -2) x)
(neg (- (* (+ (neg x) 1) (+ (neg x) 1)) 1))
(* (- 2 x) x)

explain83.0ms (2.4%)

FPErrors

Click to see full error table

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

Results

38.0ms	250×	1	valid
20.0ms	262×	0	valid

Compiler

Compiled 56 to 17 computations (69.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-add: 6.0ms (24.1% of total)

ival-sub: 6.0ms (24.1% of total)

backward-pass: 6.0ms (24.1% of total)

ival-mult: 5.0ms (20.1% of total)

const: 1.0ms (4% of total)

eval0.0ms (0%)

Compiler: Compiled 6 to 4 computations (33.3% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.5%	(-.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
▶	100.0%	(*.f64 (+.f64 x #s(literal 2 binary64)) x)

Compiler

Compiled 16 to 9 computations (43.8% saved)

simplify163.0ms (4.7%)

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 x #s(literal 1 binary64))
✓	cost-diff	0	(*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))
✓	cost-diff	256	(-.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
✓	cost-diff	0	(+.f64 x #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 (+.f64 x #s(literal 2 binary64)) x)

Rules

2962×	`+-lowering-+.f64`
2962×	`+-lowering-+.f32`
2718×	`fma-lowering-fma.f32`
2718×	`fma-lowering-fma.f64`
2000×	`fmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	24
1	28	24
2	71	24
3	391	24
4	1266	24
5	2772	24
6	6719	24
0	8479	24

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize56.0ms (1.6%)

Localize:

Found 5 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x #s(literal 1 binary64))
✓	accuracy	100.0%	(*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))
✓	accuracy	53.5%	(-.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
✓	accuracy	100.0%	(+.f64 x #s(literal 2 binary64))
✓	accuracy	100.0%	(*.f64 (+.f64 x #s(literal 2 binary64)) x)

Results

27.0ms	125×	1	valid
17.0ms	131×	0	valid

Compiler

Compiled 33 to 9 computations (72.7% saved)

Precisions

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

ival-mult: 5.0ms (33.2% of total)

ival-add: 4.0ms (26.5% of total)

backward-pass: 3.0ms (19.9% of total)

ival-sub: 2.0ms (13.3% of total)

const: 1.0ms (6.6% of total)

series3.0ms (0.1%)

Counts

5 → 60

Calls

Call 1

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

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

Calls

15 calls:

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

rewrite243.0ms (7.1%)

Algorithm

1×	batch-egg-rewrite

Rules

3690×	`-lowering-.f32`
3690×	`-lowering-.f64`
3314×	`/-lowering-/.f32`
3314×	`/-lowering-/.f64`
1766×	`frac-times`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	64	20
2	516	20
0	8493	20

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 632

Calls

Call 1

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

Outputs
(+.f64 x (*.f64 x (+.f64 x #s(literal 1 binary64))))
(+.f64 (+.f64 x #s(literal 2 binary64)) (*.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 2 binary64))))
(+.f64 (+.f64 x #s(literal 2 binary64)) (*.f64 (+.f64 x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64))))
(+.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (*.f64 x (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)))
(+.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 (*.f64 x (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))
(+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 2 binary64)))) #s(literal -1 binary64))
(+.f64 (*.f64 x (+.f64 x #s(literal 2 binary64))) #s(literal 0 binary64))
(+.f64 (.f64 x (+.f64 x #s(literal 2 binary64))) (.f64 (+.f64 x #s(literal 2 binary64)) #s(literal 0 binary64)))
(+.f64 (.f64 x (+.f64 x #s(literal 2 binary64))) (.f64 #s(literal 0 binary64) (+.f64 x #s(literal 2 binary64))))
(+.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 2 binary64)))))
(+.f64 (.f64 x x) (.f64 x #s(literal 2 binary64)))
(+.f64 (*.f64 x x) (+.f64 x x))
(+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x))
(+.f64 (*.f64 x (+.f64 x #s(literal 1 binary64))) x)
(+.f64 (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 2 binary64)))) (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 2 binary64))))))) (+.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 2 binary64)))))) (+.f64 (.f64 x (+.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 2 binary64)))))) (+.f64 (*.f64 x (+.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))))
(+.f64 (/.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 2 binary64)))))) (+.f64 (.f64 x (+.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x (+.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))))
(+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64)))) (+.f64 x #s(literal -1 binary64)))
(+.f64 (.f64 (+.f64 x #s(literal 2 binary64)) (+.f64 x #s(literal 1 binary64))) (.f64 (+.f64 x #s(literal 2 binary64)) #s(literal -1 binary64)))
(+.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 2 binary64))) (.f64 #s(literal -1 binary64) (+.f64 x #s(literal 2 binary64))))
(+.f64 (+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64)))) (+.f64 x #s(literal 1 binary64)))
(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64))
(-.f64 (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 2 binary64)))) (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 2 binary64))))))) (+.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 2 binary64)))))) (+.f64 (.f64 x (+.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 2 binary64)))))) (+.f64 (*.f64 x (+.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))))
(-.f64 (/.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 2 binary64)))))) (+.f64 (.f64 x (+.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x (+.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
(-.f64 (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 2 binary64)))) (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 2 binary64))))))) (+.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 2 binary64)))))) (-.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 2 binary64)))) #s(literal -1 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 2 binary64)))))) (-.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 2 binary64)))) #s(literal -1 binary64))))))
(fma.f64 x x (*.f64 x #s(literal 2 binary64)))
(fma.f64 x #s(literal 2 binary64) (*.f64 x x))
(fma.f64 x (+.f64 x #s(literal 1 binary64)) x)
(fma.f64 #s(literal 2 binary64) x (*.f64 x x))
(fma.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 2 binary64)))) #s(literal -1 binary64))
(fma.f64 (+.f64 x #s(literal 1 binary64)) x x)
(fma.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64) #s(literal -1 binary64))
(expm1.f64 (*.f64 #s(literal 2 binary64) (log1p.f64 x)))
(neg.f64 (/.f64 (+.f64 #s(literal -1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 2 binary64)))) (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 2 binary64)))))))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 2 binary64)))))) (+.f64 (*.f64 x (+.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))))
(neg.f64 (/.f64 (.f64 (.f64 x (+.f64 x #s(literal 2 binary64))) (+.f64 (.f64 x (+.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x (+.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))))
(neg.f64 (/.f64 (+.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 2 binary64)))) (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 2 binary64)))))))) #s(literal 1 binary64)) (+.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 2 binary64)))))) (+.f64 (*.f64 x (+.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))))
(neg.f64 (/.f64 (.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x (+.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (.f64 x (+.f64 x #s(literal 2 binary64)))) (+.f64 (.f64 x (+.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 2 binary64)))))) (-.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 2 binary64)))) #s(literal -1 binary64)))) (+.f64 #s(literal -1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 2 binary64)))) (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 2 binary64))))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal -2 binary64)) (.f64 x (+.f64 (.f64 x x) #s(literal -4 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 4 binary64) (.f64 x (+.f64 x #s(literal -2 binary64)))) (.f64 x (+.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))))
(/.f64 (*.f64 x (+.f64 x #s(literal 2 binary64))) #s(literal 1 binary64))
(/.f64 (.f64 x (+.f64 x #s(literal 2 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 2 binary64))) (+.f64 x #s(literal 2 binary64))))
(/.f64 (.f64 x (+.f64 x #s(literal 2 binary64))) (.f64 (+.f64 x #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 2 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 2 binary64))))))
(/.f64 (+.f64 #s(literal -1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 2 binary64)))) (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 2 binary64)))))))) (+.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 2 binary64)))))) (+.f64 (*.f64 x (+.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
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(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))
(*.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
(.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))))
(*.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))) #s(literal 1 binary64)))
(.f64 (+.f64 #s(literal -1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(.f64 (+.f64 #s(literal -1 binary64) (.f64 x x)) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64)))
(.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64)))))))
(.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal -1 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (+.f64 #s(literal -1 binary64) (.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))
(.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))) #s(literal 1 binary64)))
(.f64 (pow.f64 (+.f64 #s(literal -1 binary64) (.f64 x x)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)))
(.f64 (/.f64 (+.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 #s(literal -1 binary64) (*.f64 x x))) (+.f64 x #s(literal 1 binary64)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (+.f64 x #s(literal 1 binary64)))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (-.f64 #s(literal 1 binary64) x) (.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 x x)))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64)))) (+.f64 (+.f64 #s(literal -1 binary64) (.f64 x x)) x))) (+.f64 (+.f64 #s(literal -1 binary64) (*.f64 x x)) x))
(.f64 (/.f64 (+.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 (.f64 x (.f64 x x)) #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64)))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64)))))

simplify207.0ms (6%)

Algorithm

1×	egg-herbie

Rules

4948×	`-lowering-.f32`
4948×	`-lowering-.f64`
2248×	`fma-define`
1554×	`fma-lowering-fma.f32`
1554×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	232
1	67	219
2	160	219
3	365	219
4	749	219
5	2686	219
6	4973	219
7	6018	219
8	6716	219
9	7618	219
0	8021	219

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

Calls

Call 1

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

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

eval85.0ms (2.5%)

Compiler: Compiled 22637 to 1665 computations (92.6% saved)

prune77.0ms (2.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	770	3	773
Fresh	0	0	0
Picked	1	1	2
Done	0	0	0
Total	771	4	775

Accuracy

100.0%

Counts

775 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f64 (*.f64 x (+.f64 x #s(literal 1 binary64))) x)
✓	100.0%	(*.f64 (+.f64 x #s(literal 2 binary64)) x)
▶	52.1%	(*.f64 x x)
▶	51.0%	(*.f64 #s(literal 2 binary64) x)

Compiler

Compiled 22 to 14 computations (36.4% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 x #s(literal 1 binary64))
✓	cost-diff	0	(*.f64 x (+.f64 x #s(literal 1 binary64)))
✓	cost-diff	128	(+.f64 (*.f64 x (+.f64 x #s(literal 1 binary64))) x)
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(*.f64 #s(literal 2 binary64) x)

Rules

56×	`fma-define`
52×	`fma-lowering-fma.f32`
52×	`fma-lowering-fma.f64`
42×	`-lowering-.f32`
42×	`-lowering-.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	24
1	20	22
2	33	22
3	66	22
4	86	22
5	87	22
0	87	22

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* 2 x)
2
x
(* x x)
x
(+ (* x (+ x 1)) x)
(* x (+ x 1))
x
(+ x 1)
1

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

localize43.0ms (1.2%)

Localize:

Found 5 expressions of interest:

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

Results

34.0ms

256×

valid

Compiler

Compiled 28 to 9 computations (67.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-mult: 12.0ms (76.4% of total)

ival-add: 3.0ms (19.1% of total)

const: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Counts

5 → 60

Calls

Call 1

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

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

Calls

15 calls:

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

rewrite300.0ms (8.7%)

Algorithm

1×	batch-egg-rewrite

Rules

2148×	`-lowering-.f32`
2148×	`-lowering-.f64`
1990×	`fma-lowering-fma.f32`
1990×	`fma-lowering-fma.f64`
1826×	`fmsub-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	42	17
2	323	17
3	4112	17
0	8005	17

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 202

Calls

Call 1

Inputs
(* 2 x)
(* x x)
(+ (* x (+ x 1)) x)
(* x (+ x 1))
(+ x 1)

Outputs
(+.f64 x x)
(fma.f64 x #s(literal 1 binary64) x)
(fma.f64 #s(literal 1 binary64) x x)
(/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (+.f64 (.f64 x x) (-.f64 (.f64 x x) (*.f64 x x))))
(/.f64 (-.f64 (.f64 x x) (.f64 x x)) #s(literal 0 binary64))
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))
(.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x))
(.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1 binary64))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(*.f64 x x)
(.f64 (.f64 x x) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x x))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(+.f64 x (*.f64 x (+.f64 x #s(literal 1 binary64))))
(+.f64 (.f64 x x) (.f64 #s(literal 2 binary64) x))
(+.f64 (*.f64 x (+.f64 x #s(literal 1 binary64))) x)
(+.f64 (/.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))) (+.f64 (.f64 x x) #s(literal 0 binary64))) (neg.f64 (/.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal 0 binary64)))))
(+.f64 (.f64 #s(literal 2 binary64) x) (.f64 x x))
(-.f64 (/.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))) (+.f64 (.f64 x x) #s(literal 0 binary64))) (/.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal 0 binary64))))
(-.f64 (/.f64 (.f64 x x) (-.f64 #s(literal 0 binary64) (.f64 x x))) (/.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))) (-.f64 #s(literal 0 binary64) (.f64 x x))))
(fma.f64 x x (*.f64 #s(literal 2 binary64) x))
(fma.f64 x #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64))))
(fma.f64 x (+.f64 x #s(literal 1 binary64)) x)
(fma.f64 x (/.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 x (+.f64 x #s(literal 1 binary64)))) (+.f64 (.f64 x x) #s(literal 0 binary64))) (neg.f64 (/.f64 (.f64 x x) (+.f64 (*.f64 x x) #s(literal 0 binary64)))))
(fma.f64 (.f64 x x) (/.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (+.f64 (.f64 x x) #s(literal 0 binary64))) (neg.f64 (/.f64 (.f64 x x) (+.f64 (*.f64 x x) #s(literal 0 binary64)))))
(fma.f64 #s(literal 1 binary64) x (*.f64 x (+.f64 x #s(literal 1 binary64))))
(fma.f64 (+.f64 x #s(literal 1 binary64)) x x)
(fma.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 (.f64 x (.f64 x (+.f64 x #s(literal 1 binary64)))) (+.f64 (.f64 x x) #s(literal 0 binary64))) (neg.f64 (/.f64 (.f64 x x) (+.f64 (*.f64 x x) #s(literal 0 binary64)))))
(fma.f64 (.f64 x (+.f64 x #s(literal 1 binary64))) (/.f64 (.f64 x (+.f64 x #s(literal 1 binary64))) (+.f64 (.f64 x x) #s(literal 0 binary64))) (neg.f64 (/.f64 (.f64 x x) (+.f64 (*.f64 x x) #s(literal 0 binary64)))))
(fma.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal 0 binary64))) (neg.f64 (/.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal 0 binary64)))))
(fma.f64 (.f64 x (.f64 x (+.f64 x #s(literal 1 binary64)))) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (.f64 x x) #s(literal 0 binary64))) (neg.f64 (/.f64 (.f64 x x) (+.f64 (*.f64 x x) #s(literal 0 binary64)))))
(fma.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (/.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal 0 binary64))) (neg.f64 (/.f64 (.f64 x x) (+.f64 (*.f64 x x) #s(literal 0 binary64)))))
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(.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64)))))))
(.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (+.f64 (.f64 x x) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))
(.f64 (/.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) (+.f64 x #s(literal 1 binary64)))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (-.f64 #s(literal 1 binary64) x) (.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))) (+.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 x x)))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64)))) (+.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) x))) (+.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) x))
(.f64 (/.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) (+.f64 (.f64 x (.f64 x x)) #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64)))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64)))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (+.f64 x #s(literal 1 binary64)))

simplify168.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

3912×	`-lowering-.f32`
3912×	`-lowering-.f64`
2344×	`fma-define`
1690×	`cube-prod`
1530×	`times-frac`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	208
1	53	183
2	100	183
3	299	183
4	2659	183
5	3791	183
6	4822	183
7	5660	183
8	6935	183
0	8498	183

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

Calls

Call 1

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

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

eval26.0ms (0.7%)

Compiler: Compiled 5600 to 645 computations (88.5% saved)

prune33.0ms (1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	262	0	262
Fresh	0	0	0
Picked	0	3	3
Done	0	1	1
Total	262	4	266

Accuracy

100.0%

Counts

266 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(+.f64 (*.f64 x (+.f64 x #s(literal 1 binary64))) x)
✓	100.0%	(*.f64 (+.f64 x #s(literal 2 binary64)) x)
✓	52.1%	(*.f64 x x)
✓	51.0%	(*.f64 #s(literal 2 binary64) x)

Compiler

Compiled 50 to 26 computations (48% saved)

regimes10.0ms (0.3%)

Counts

5 → 1

Calls

Call 1

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

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

Calls

4 calls:

4.0ms	(*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))
2.0ms	x
2.0ms	(+.f64 x #s(literal 1 binary64))
2.0ms	(-.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))

Results

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

Compiler

Compiled 24 to 13 computations (45.8% saved)

regimes2.0ms (0.1%)

Counts

3 → 1

Calls

Call 1

Inputs
(*.f64 #s(literal 2 binary64) x)
(*.f64 x x)
(*.f64 (+.f64 x #s(literal 2 binary64)) x)

Outputs
(*.f64 (+.f64 x #s(literal 2 binary64)) x)

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
100.0%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

2 → 3

Calls

Call 1

Inputs
(*.f64 #s(literal 2 binary64) x)
(*.f64 x x)

Outputs
(*.f64 x x)
(*.f64 #s(literal 2 binary64) x)
(*.f64 x x)

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
98.6%	3	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(*.f64 #s(literal 2 binary64) x)

Outputs
(*.f64 #s(literal 2 binary64) x)

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
51.0%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

bsearch26.0ms (0.8%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
13.0ms	5.553070242342735e-8	943.0873923284815
11.0ms	-1139.4333277093995	-4.2103990395837493e-7

Results

15.0ms

304×

valid

Compiler

Compiled 204 to 141 computations (30.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-mult: 4.0ms (55.2% of total)

ival-sub: 2.0ms (27.6% of total)

ival-add: 2.0ms (27.6% of total)

const: 0.0ms (0% of total)

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

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
6×	`+-commutative_binary64`
2×	`1-exp_binary64`
2×	`if-if-or-not_binary32`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	30
1	27	30

Stop Event

1×

saturated

Calls

Call 1

Inputs
(+.f64 (*.f64 x (+.f64 x #s(literal 1 binary64))) x)
(*.f64 (+.f64 x #s(literal 2 binary64)) x)
(if (<=.f64 x #s(literal -2 binary64)) (.f64 x x) (if (<=.f64 x #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) x) (*.f64 x x)))
(*.f64 #s(literal 2 binary64) x)

Outputs
(+.f64 (*.f64 x (+.f64 x #s(literal 1 binary64))) x)
(+.f64 x (*.f64 x (+.f64 x #s(literal 1 binary64))))
(*.f64 (+.f64 x #s(literal 2 binary64)) x)
(*.f64 x (+.f64 x #s(literal 2 binary64)))
(if (<=.f64 x #s(literal -2 binary64)) (.f64 x x) (if (<=.f64 x #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) x) (*.f64 x x)))
(if (<=.f64 x #s(literal -2 binary64)) (.f64 x x) (if (<=.f64 x #s(literal 2 binary64)) (.f64 x #s(literal 2 binary64)) (*.f64 x x)))
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))

soundness775.0ms (22.5%)

Rules

4948×	`-lowering-.f32`
4948×	`-lowering-.f64`
3690×	`-lowering-.f32`
3690×	`-lowering-.f64`
3314×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	23	6
2	61	5
3	367	5
4	1235	5
5	2717	5
6	6625	5
0	8378	5
0	21	232
1	67	219
2	160	219
3	365	219
4	749	219
5	2686	219
6	4973	219
7	6018	219
8	6716	219
9	7618	219
0	8021	219
0	8	20
1	64	20
2	516	20
0	8493	20

Stop Event

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

Compiler

Compiled 83 to 48 computations (42.2% saved)

preprocess24.0ms (0.7%)

Compiler: Compiled 86 to 40 computations (53.5% saved)

Expanding a square

analyze0.0ms (0%)

sample822.0ms (23.8%)

preprocess285.0ms (8.3%)

explain83.0ms (2.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify163.0ms (4.7%)

localize56.0ms (1.6%)

series3.0ms (0.1%)

rewrite243.0ms (7.1%)

simplify207.0ms (6%)

eval85.0ms (2.5%)

prune77.0ms (2.2%)

simplify6.0ms (0.2%)

localize43.0ms (1.2%)

series3.0ms (0.1%)

rewrite300.0ms (8.7%)

simplify168.0ms (4.9%)

eval26.0ms (0.7%)

prune33.0ms (1%)

regimes10.0ms (0.3%)

regimes2.0ms (0.1%)

regimes2.0ms (0%)

regimes1.0ms (0%)

bsearch26.0ms (0.8%)

simplify7.0ms (0.2%)

soundness775.0ms (22.5%)

preprocess24.0ms (0.7%)

end0.0ms (0%)

Profiling