Metrics for ln(1 + x)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze1.0ms (0%)

Memory

2.1MiB live, 2.1MiB allocated

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
50%	50%	50%	0%	0%	0%	0%	2
66.7%	50%	25%	0%	0%	25%	0%	3
83.3%	62.5%	12.5%	0%	0%	25%	0%	4
91.7%	68.7%	6.2%	0%	0%	25%	0%	5
95.8%	71.8%	3.1%	0%	0%	25%	0%	6
97.9%	73.4%	1.6%	0%	0%	25%	0%	7
99%	74.2%	0.8%	0%	0%	25%	0%	8
99.5%	74.6%	0.4%	0%	0%	25%	0%	9
99.7%	74.8%	0.2%	0%	0%	25%	0%	10
99.9%	74.9%	0.1%	0%	0%	25%	0%	11
99.9%	74.9%	0%	0%	0%	25%	0%	12

Compiler

Compiled 6 to 4 computations (33.3% saved)

sample422.0ms (11.9%)

Memory

55.3MiB live, 504.9MiB allocated

Samples

249.0ms	8 256×	0	valid
0.0ms	1×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 110.0ms

ival-log1p: 101.0ms (92% of total)

ival-true: 6.0ms (5.5% of total)

ival-assert: 3.0ms (2.7% of total)

Bogosity

explain133.0ms (3.8%)

Memory

-7.0MiB live, 74.3MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`log.f64`	`(log.f64 (+.f64 #s(literal 1 binary64) x))`	sensitivity	180	0

Confusion

	Predicted +	Predicted -
+	180	0
-	0	76

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	180	0	0
-	0	0	76

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	76
1	180

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

106.0ms

512×

valid

Compiler

Compiled 44 to 27 computations (38.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 93.0ms

ival-log1p: 89.0ms (95.5% of total)

ival-add: 3.0ms (3.2% of total)

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

exact: 0.0ms (0% of total)

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

preprocess18.0ms (0.5%)

Memory

-19.3MiB live, 17.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	15	9
2	22	9
3	30	9
4	40	9
5	53	9
6	66	9
7	69	9
0	4	4
0	6	4
1	9	4
0	9	2

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 4 to 4 computations (0% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune1.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	34.9%	(log.f64 (+.f64 #s(literal 1 binary64) x))

Compiler

Compiled 4 to 4 computations (0% saved)

simplify3.0ms (0.1%)

Memory

3.6MiB live, 3.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(+.f64 #s(literal 1 binary64) x)
cost-diff	192	(log.f64 (+.f64 #s(literal 1 binary64) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	9
0	6	9
1	9	9
0	9	7

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize13.0ms (0.4%)

Memory

21.8MiB live, 21.8MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(+.f64 #s(literal 1 binary64) x)
accuracy	41.665435979597646	(log.f64 (+.f64 #s(literal 1 binary64) x))

Samples

9.0ms

256×

valid

Compiler

Compiled 20 to 10 computations (50% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-log1p: 2.0ms (48.3% of total)

ival-add: 1.0ms (24.1% of total)

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

exact: 0.0ms (0% of total)

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

series2.0ms (0.1%)

Memory

2.7MiB live, 2.7MiB allocated

Counts

2 → 24

Calls

Call 1

Inputs
#s(alt (log.f64 (+.f64 #s(literal 1 binary64) x)) (patch (log.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())
#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())

Inputs

#s(alt (log.f64 (+.f64 #s(literal 1 binary64) x)) (patch (log.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())

#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())

Outputs
#s(alt x (taylor 0 x) (#s(alt (log.f64 (+.f64 #s(literal 1 binary64) x)) (patch (log.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/2 x))) (taylor 0 x) (#s(alt (log.f64 (+.f64 #s(literal 1 binary64) x)) (patch (log.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (- (* 1/3 x) 1/2)))) (taylor 0 x) (#s(alt (log.f64 (+.f64 #s(literal 1 binary64) x)) (patch (log.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2)))) (taylor 0 x) (#s(alt (log.f64 (+.f64 #s(literal 1 binary64) x)) (patch (log.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (log (/ 1 x))) (taylor inf x) (#s(alt (log.f64 (+.f64 #s(literal 1 binary64) x)) (patch (log.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (log (/ 1 x))) (/ 1 x)) (taylor inf x) (#s(alt (log.f64 (+.f64 #s(literal 1 binary64) x)) (patch (log.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1 (log (/ 1 x))) (/ 1 x)) (/ 1/2 (pow x 2))) (taylor inf x) (#s(alt (log.f64 (+.f64 #s(literal 1 binary64) x)) (patch (log.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1 (log (/ 1 x))) (+ (/ 1 x) (* 1/3 (/ 1 (pow x 3))))) (/ 1/2 (pow x 2))) (taylor inf x) (#s(alt (log.f64 (+.f64 #s(literal 1 binary64) x)) (patch (log.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (* -1 (log (/ -1 x)))) (taylor -inf x) (#s(alt (log.f64 (+.f64 #s(literal 1 binary64) x)) (patch (log.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (+ (* -1 (log (/ -1 x))) (/ 1 x))) (taylor -inf x) (#s(alt (log.f64 (+.f64 #s(literal 1 binary64) x)) (patch (log.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* 1/2 (/ 1 x)) 1) x)))) (taylor -inf x) (#s(alt (log.f64 (+.f64 #s(literal 1 binary64) x)) (patch (log.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* -1 (/ (- (* 1/3 (/ 1 x)) 1/2) x)) 1) x)))) (taylor -inf x) (#s(alt (log.f64 (+.f64 #s(literal 1 binary64) x)) (patch (log.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())

Calls

3 calls:

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

simplify249.0ms (7%)

Memory

-10.5MiB live, 146.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	169
1	171	155
2	363	150
3	979	148
4	2422	144
5	4452	144
6	5392	144
7	6689	144
8	7472	144
9	7620	144
10	7664	144
11	7666	144
12	7666	144
13	7909	144
0	8006	138

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 21

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
(+ 1 x)
(+ 1 x)
(+ 1 x)
(* -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)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(+ (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))))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))

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

rewrite224.0ms (6.3%)

Memory

-11.8MiB live, 179.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	7
0	6	7
1	22	7
2	131	7
3	984	7
0	8620	5

Stop Event

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

Counts

2 → 344

Calls

Call 1

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

Outputs
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eval63.0ms (1.8%)

Memory: 10.3MiB live, 90.0MiB allocated
Compiler: Compiled 9 099 to 1 130 computations (87.6% saved)

prune6.0ms (0.2%)

Memory

22.3MiB live, 22.3MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	361	4	365
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	362	4	366

Accuracy

100.0%

Counts

366 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(log1p.f64 x)
▶	70.5%	#s(approx (log (+ 1 x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x))
▶	71.5%	#s(approx (log (+ 1 x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x))
▶	70.3%	#s(approx (log (+ 1 x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x))

Compiler

Compiled 32 to 26 computations (18.8% saved)

simplify18.0ms (0.5%)

Memory

-16.3MiB live, 19.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(log1p.f64 x)
cost-diff	0	(fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64))
cost-diff	0	(fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))
cost-diff	0	(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x)
cost-diff	0	#s(approx (log (+ 1 x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x))
cost-diff	0	(fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64))
cost-diff	0	(fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))
cost-diff	0	(*.f64 (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x)
cost-diff	0	#s(approx (log (+ 1 x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x))
cost-diff	0	(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
cost-diff	0	(*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x)
cost-diff	0	#s(approx (log (+ 1 x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	114
0	35	114
1	53	114
2	91	114
3	196	114
4	431	114
5	694	114
6	750	114
0	750	114

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize76.0ms (2.2%)

Memory

-9.5MiB live, 113.0MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0	(log1p.f64 x)
accuracy	0.015625	(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x)
accuracy	0.0234375	(fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))
accuracy	0.0234375	(fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64))
accuracy	18.850108795971593	#s(approx (log (+ 1 x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x))
accuracy	0.0234375	(*.f64 (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x)
accuracy	0.05078125	(fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))
accuracy	0.125	(fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64))
accuracy	18.212112250836174	#s(approx (log (+ 1 x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x))
accuracy	0	(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
accuracy	0.0234375	(*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x)
accuracy	18.999311881022198	#s(approx (log (+ 1 x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x))

Samples

55.0ms

256×

valid

Compiler

Compiled 218 to 41 computations (81.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 43.0ms

ival-mult: 29.0ms (67% of total)

ival-add: 7.0ms (16.2% of total)

const: 4.0ms (9.2% of total)

ival-log1p: 3.0ms (6.9% of total)

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

exact: 0.0ms (0% of total)

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

series15.0ms (0.4%)

Memory

-6.2MiB live, 32.1MiB allocated

Counts

12 → 144

Calls

Call 1

Inputs
#s(alt #s(approx (log (+ 1 x)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x)) (patch #s(approx (log (+ 1 x)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x) (patch (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (log (+ 1 x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x)) (patch #s(approx (log (+ 1 x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) (patch (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (log (+ 1 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x)) (patch #s(approx (log (+ 1 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt (log1p.f64 x) (patch (log1p.f64 x) #<representation binary64>) () ())

Outputs
#s(alt x (taylor 0 x) (#s(alt #s(approx (log (+ 1 x)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x)) (patch #s(approx (log (+ 1 x)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/2 x))) (taylor 0 x) (#s(alt #s(approx (log (+ 1 x)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x)) (patch #s(approx (log (+ 1 x)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (- (* 1/3 x) 1/2)))) (taylor 0 x) (#s(alt #s(approx (log (+ 1 x)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x)) (patch #s(approx (log (+ 1 x)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2)))) (taylor 0 x) (#s(alt #s(approx (log (+ 1 x)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x)) (patch #s(approx (log (+ 1 x)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x) (patch (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/2 x))) (taylor 0 x) (#s(alt (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x) (patch (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/2 x))) (taylor 0 x) (#s(alt (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x) (patch (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/2 x))) (taylor 0 x) (#s(alt (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x) (patch (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 x)) (taylor 0 x) (#s(alt (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 x)) (taylor 0 x) (#s(alt (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 x)) (taylor 0 x) (#s(alt (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt #s(approx (log (+ 1 x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x)) (patch #s(approx (log (+ 1 x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/2 x))) (taylor 0 x) (#s(alt #s(approx (log (+ 1 x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x)) (patch #s(approx (log (+ 1 x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (- (* 1/3 x) 1/2)))) (taylor 0 x) (#s(alt #s(approx (log (+ 1 x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x)) (patch #s(approx (log (+ 1 x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2)))) (taylor 0 x) (#s(alt #s(approx (log (+ 1 x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x)) (patch #s(approx (log (+ 1 x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/2 x))) (taylor 0 x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (- (* 1/3 x) 1/2)))) (taylor 0 x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (- (* 1/3 x) 1/2)))) (taylor 0 x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* (pow x 3) (+ 1/4 (* -1 (/ (- 1/3 (* 1/2 (/ 1 x))) x))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (+ 1/4 (* -1 (/ (+ 1/3 (* -1 (/ (- 1/2 (/ 1 x)) x))) x))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/4 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/3) x)) 1/4)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/3) x)) 1/4)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (* -1 (log (/ -1 x)))) (taylor -inf x) (#s(alt (log1p.f64 x) (patch (log1p.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (+ (* -1 (log (/ -1 x))) (/ 1 x))) (taylor -inf x) (#s(alt (log1p.f64 x) (patch (log1p.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* 1/2 (/ 1 x)) 1) x)))) (taylor -inf x) (#s(alt (log1p.f64 x) (patch (log1p.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* -1 (/ (- (* 1/3 (/ 1 x)) 1/2) x)) 1) x)))) (taylor -inf x) (#s(alt (log1p.f64 x) (patch (log1p.f64 x) #<representation binary64>) () ())) ())

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	((log (+ 1 x)) (* (+ (* -1/2 x) 1) x) (+ (* -1/2 x) 1) (log (+ 1 x)) (* (+ (* (+ (* 1/3 x) -1/2) x) 1) x) (+ (* (+ (* 1/3 x) -1/2) x) 1) (+ (* 1/3 x) -1/2) (log (+ 1 x)) (* (+ (* (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) x) (+ (* (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) (+ (* (+ (* -1/4 x) 1/3) x) -1/2) (log (+ 1 x)))
2.0ms	x	@	-inf	((log (+ 1 x)) (* (+ (* -1/2 x) 1) x) (+ (* -1/2 x) 1) (log (+ 1 x)) (* (+ (* (+ (* 1/3 x) -1/2) x) 1) x) (+ (* (+ (* 1/3 x) -1/2) x) 1) (+ (* 1/3 x) -1/2) (log (+ 1 x)) (* (+ (* (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) x) (+ (* (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) (+ (* (+ (* -1/4 x) 1/3) x) -1/2) (log (+ 1 x)))
1.0ms	x	@	0	((log (+ 1 x)) (* (+ (* -1/2 x) 1) x) (+ (* -1/2 x) 1) (log (+ 1 x)) (* (+ (* (+ (* 1/3 x) -1/2) x) 1) x) (+ (* (+ (* 1/3 x) -1/2) x) 1) (+ (* 1/3 x) -1/2) (log (+ 1 x)) (* (+ (* (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) x) (+ (* (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) (+ (* (+ (* -1/4 x) 1/3) x) -1/2) (log (+ 1 x)))

Time

Variable

Point

Expression

2.0ms

inf

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

2.0ms

-inf

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

1.0ms

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

simplify187.0ms (5.3%)

Memory

21.1MiB live, 178.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	132	1258
1	377	1186
2	1154	1162
3	3986	1130
0	8185	1010

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 137

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

rewrite365.0ms (10.3%)

Memory

9.4MiB live, 199.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	97
0	35	97
1	134	97
2	982	97
0	8480	97

Stop Event

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

Counts

12 → 412

Calls

Call 1

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

Outputs
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eval103.0ms (2.9%)

Memory: -15.6MiB live, 192.8MiB allocated
Compiler: Compiled 11 643 to 1 924 computations (83.5% saved)

prune20.0ms (0.6%)

Memory

12.6MiB live, 49.9MiB allocated

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	546	3	549
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	546	7	553

Accuracy

100.0%

Counts

553 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(log1p.f64 x)
▶	70.3%	#s(approx (log (+ 1 x)) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) x))
✓	70.5%	#s(approx (log (+ 1 x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x))
✓	71.5%	#s(approx (log (+ 1 x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x))
▶	71.5%	#s(approx (log (+ 1 x)) (.f64 (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) x))
✓	70.3%	#s(approx (log (+ 1 x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x))
▶	71.2%	#s(approx (log (+ 1 x)) (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x))

Compiler

Compiled 56 to 45 computations (19.6% saved)

simplify14.0ms (0.4%)

Memory

-7.3MiB live, 29.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) x)
cost-diff	0	#s(approx (log (+ 1 x)) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) x))
cost-diff	0	(fma.f64 (*.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))
cost-diff	0	(.f64 (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) x)
cost-diff	0	#s(approx (log (+ 1 x)) (.f64 (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) x))
cost-diff	320	(fma.f64 x #s(literal -1/2 binary64) (fma.f64 (*.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)))
cost-diff	0	#s(approx (+ (* (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64))
cost-diff	0	(.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x)
cost-diff	0	#s(approx (log (+ 1 x)) (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	127
0	32	127
1	54	127
2	95	127
3	169	127
4	319	127
5	372	127
6	378	127
0	378	106

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize180.0ms (5.1%)

Memory

24.8MiB live, 107.4MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.015625	(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) x)
accuracy	18.999311881022198	#s(approx (log (+ 1 x)) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) x))
accuracy	0.01171875	(fma.f64 x #s(literal -1/2 binary64) (fma.f64 (*.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)))
accuracy	0.0234375	(.f64 (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) x)
accuracy	0.046875	(fma.f64 (*.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))
accuracy	18.212112250836174	#s(approx (log (+ 1 x)) (.f64 (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) x))
accuracy	0.015625	(.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x)
accuracy	18.850108795971593	#s(approx (log (+ 1 x)) (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x))
accuracy	19.407472367631787	#s(approx (+ (* (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64))

Samples

166.0ms

256×

valid

Compiler

Compiled 170 to 37 computations (78.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 155.0ms

ival-add: 134.0ms (86.4% of total)

ival-mult: 14.0ms (9% of total)

const: 4.0ms (2.6% of total)

ival-log1p: 3.0ms (1.9% of total)

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

exact: 0.0ms (0% of total)

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

series51.0ms (1.4%)

Memory

-18.2MiB live, 15.9MiB allocated

Counts

10 → 120

Calls

Call 1

Inputs
#s(alt #s(approx (log (+ 1 x)) (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x)) (patch #s(approx (log (+ 1 x)) (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x)) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) (patch (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (log (+ 1 x)) (.f64 (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) x)) (patch #s(approx (log (+ 1 x)) (.f64 (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) x)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) x) (patch (.f64 (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) x) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (log (+ 1 x)) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) x)) (patch #s(approx (log (+ 1 x)) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) x)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x x) #s(literal -1/2 binary64) x) (patch (fma.f64 (.f64 x x) #s(literal -1/2 binary64) x) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())

Outputs
#s(alt x (taylor 0 x) (#s(alt #s(approx (log (+ 1 x)) (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x)) (patch #s(approx (log (+ 1 x)) (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/2 x))) (taylor 0 x) (#s(alt #s(approx (log (+ 1 x)) (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x)) (patch #s(approx (log (+ 1 x)) (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (- (* 1/3 x) 1/2)))) (taylor 0 x) (#s(alt #s(approx (log (+ 1 x)) (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x)) (patch #s(approx (log (+ 1 x)) (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2)))) (taylor 0 x) (#s(alt #s(approx (log (+ 1 x)) (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x)) (patch #s(approx (log (+ 1 x)) (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/2 x))) (taylor 0 x) (#s(alt (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (- (* 1/3 x) 1/2)))) (taylor 0 x) (#s(alt (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2)))) (taylor 0 x) (#s(alt (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (+ (* (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 x)) (taylor 0 x) (#s(alt #s(approx (+ (* (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* 1/3 x) 1/2))) (taylor 0 x) (#s(alt #s(approx (+ (* (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2))) (taylor 0 x) (#s(alt #s(approx (+ (* (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) (patch (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 x)) (taylor 0 x) (#s(alt (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) (patch (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* 1/3 x) 1/2))) (taylor 0 x) (#s(alt (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) (patch (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
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#s(alt (+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* 1/2 (/ 1 x)) 1) x)))) (taylor -inf x) (#s(alt #s(approx (log (+ 1 x)) (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x)) (patch #s(approx (log (+ 1 x)) (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* -1 (/ (- (* 1/3 (/ 1 x)) 1/2) x)) 1) x)))) (taylor -inf x) (#s(alt #s(approx (log (+ 1 x)) (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x)) (patch #s(approx (log (+ 1 x)) (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1/4 (pow x 4)) (taylor -inf x) (#s(alt (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (* 1/3 (/ 1 x)) 1/4)) (taylor -inf x) (#s(alt (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/3) x)) 1/4)) (taylor -inf x) (#s(alt (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/3) x)) 1/4)) (taylor -inf x) (#s(alt (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1/4 (pow x 3)) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- 1/4 (* 1/3 (/ 1 x))))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (+ 1/4 (* -1 (/ (- 1/3 (* 1/2 (/ 1 x))) x))))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (+ 1/4 (* -1 (/ (+ 1/3 (* -1 (/ (- 1/2 (/ 1 x)) x))) x))))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) (patch (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/3 (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) (patch (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/3 (* -1 (/ (- 1/2 (/ 1 x)) x)))) (taylor -inf x) (#s(alt (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) (patch (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/3 (* -1 (/ (- 1/2 (/ 1 x)) x)))) (taylor -inf x) (#s(alt (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) (patch (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (* -1 (log (/ -1 x)))) (taylor -inf x) (#s(alt #s(approx (log (+ 1 x)) (.f64 (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) x)) (patch #s(approx (log (+ 1 x)) (.f64 (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (+ (* -1 (log (/ -1 x))) (/ 1 x))) (taylor -inf x) (#s(alt #s(approx (log (+ 1 x)) (.f64 (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) x)) (patch #s(approx (log (+ 1 x)) (.f64 (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* 1/2 (/ 1 x)) 1) x)))) (taylor -inf x) (#s(alt #s(approx (log (+ 1 x)) (.f64 (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) x)) (patch #s(approx (log (+ 1 x)) (.f64 (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* -1 (/ (- (* 1/3 (/ 1 x)) 1/2) x)) 1) x)))) (taylor -inf x) (#s(alt #s(approx (log (+ 1 x)) (.f64 (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) x)) (patch #s(approx (log (+ 1 x)) (.f64 (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 (pow x 3)) (taylor -inf x) (#s(alt (.f64 (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) x) (patch (.f64 (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (* 1/2 (/ 1 x)) 1/3))) (taylor -inf x) (#s(alt (.f64 (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) x) (patch (.f64 (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/3))) (taylor -inf x) (#s(alt (.f64 (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) x) (patch (.f64 (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/3))) (taylor -inf x) (#s(alt (.f64 (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) x) (patch (.f64 (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* 1/3 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/3 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/3 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/3 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (* -1 (log (/ -1 x)))) (taylor -inf x) (#s(alt #s(approx (log (+ 1 x)) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) x)) (patch #s(approx (log (+ 1 x)) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (+ (* -1 (log (/ -1 x))) (/ 1 x))) (taylor -inf x) (#s(alt #s(approx (log (+ 1 x)) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) x)) (patch #s(approx (log (+ 1 x)) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* 1/2 (/ 1 x)) 1) x)))) (taylor -inf x) (#s(alt #s(approx (log (+ 1 x)) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) x)) (patch #s(approx (log (+ 1 x)) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* -1 (/ (- (* 1/3 (/ 1 x)) 1/2) x)) 1) x)))) (taylor -inf x) (#s(alt #s(approx (log (+ 1 x)) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) x)) (patch #s(approx (log (+ 1 x)) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/2 binary64) x) (patch (fma.f64 (.f64 x x) #s(literal -1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 x) 1/2)) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/2 binary64) x) (patch (fma.f64 (.f64 x x) #s(literal -1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 x) 1/2)) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/2 binary64) x) (patch (fma.f64 (.f64 x x) #s(literal -1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 x) 1/2)) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/2 binary64) x) (patch (fma.f64 (.f64 x x) #s(literal -1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

45.0ms

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

1.0ms

inf

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

1.0ms

-inf

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

simplify127.0ms (3.6%)

Memory

13.7MiB live, 138.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	124	1037
1	361	980
2	1091	968
3	3644	938
4	7687	938
0	8199	848

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 114

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

Outputs
x
(* x (+ 1 (* -1/2 x)))
(*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x)
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(* 1/3 (pow x 2))
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(* (pow x 2) (- (/ 1 x) 1/2))
(*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x)
(* (pow x 2) (- (/ 1 x) 1/2))
(*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x)
(* (pow x 2) (- (/ 1 x) 1/2))
(*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x)
(pow x 2)
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(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(+ (log -1) (* -1 (log (/ -1 x))))
(+.f64 (log.f64 (neg.f64 x)) (log.f64 #s(literal -1 binary64)))
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(+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* -1 (/ (- (* 1/3 (/ 1 x)) 1/2) x)) 1) x))))
(-.f64 (+.f64 (log.f64 (neg.f64 x)) (log.f64 #s(literal -1 binary64))) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) x) #s(literal 1/2 binary64)) x)) x))
(* -1/4 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64))
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(*.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 4 binary64)))
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(* -1/4 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/4 binary64))
(* -1 (* (pow x 3) (- 1/4 (* 1/3 (/ 1 x)))))
(.f64 (.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x) x)
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(*.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x)
(* -1 (* (pow x 3) (+ 1/4 (* -1 (/ (+ 1/3 (* -1 (/ (- 1/2 (/ 1 x)) x))) x)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(* 1/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/3 binary64))
(* (pow x 2) (- 1/3 (* 1/2 (/ 1 x))))
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(* (pow x 2) (+ 1/3 (* -1 (/ (- 1/2 (/ 1 x)) x))))
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(+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* -1 (/ (- (* 1/3 (/ 1 x)) 1/2) x)) 1) x))))
(-.f64 (+.f64 (log.f64 (neg.f64 x)) (log.f64 #s(literal -1 binary64))) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) x) #s(literal 1/2 binary64)) x)) x))
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(* 1/3 (pow x 2))
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(+ (log -1) (* -1 (log (/ -1 x))))
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(-.f64 (+.f64 (log.f64 (neg.f64 x)) (log.f64 #s(literal -1 binary64))) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) x) #s(literal 1/2 binary64)) x)) x))
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(* (pow x 2) (- (/ 1 x) 1/2))
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(pow x 2)
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(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
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rewrite200.0ms (5.6%)

Memory

-17.6MiB live, 173.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	116
0	32	116
1	138	116
2	1063	116
0	8485	98

Stop Event

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

Counts

10 → 226

Calls

Call 1

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

Outputs
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eval110.0ms (3.1%)

Memory: 14.8MiB live, 86.8MiB allocated
Compiler: Compiled 7 451 to 1 145 computations (84.6% saved)

prune10.0ms (0.3%)

Memory

20.5MiB live, 20.5MiB allocated

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	360	0	360
Fresh	0	0	0
Picked	0	3	3
Done	0	4	4
Total	360	7	367

Accuracy

100.0%

Counts

367 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(log1p.f64 x)
✓	70.3%	#s(approx (log (+ 1 x)) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) x))
✓	70.5%	#s(approx (log (+ 1 x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x))
✓	71.5%	#s(approx (log (+ 1 x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x))
✓	71.5%	#s(approx (log (+ 1 x)) (.f64 (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) x))
✓	70.3%	#s(approx (log (+ 1 x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x))
✓	71.2%	#s(approx (log (+ 1 x)) (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x))

Compiler

Compiled 116 to 75 computations (35.3% saved)

regimes40.0ms (1.1%)

Memory

-48.0MiB live, 13.7MiB allocated

Counts

8 → 1

Calls

Call 1

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

Outputs
(log1p.f64 x)

Calls

3 calls:

35.0ms	x
3.0ms	(+.f64 #s(literal 1 binary64) x)
2.0ms	(log.f64 (+.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 8 to 8 computations (0% saved)

regimes7.0ms (0.2%)

Memory

7.3MiB live, 7.3MiB allocated

Counts

6 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
71.5%	1	`x`
71.5%	1	`(log.f64 (+.f64 #s(literal 1 binary64) x))`
71.5%	1	`(+.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 8 to 8 computations (0% saved)

regimes5.0ms (0.1%)

Memory

10.5MiB live, 10.5MiB allocated

Accuracy

Total -1.0b remaining (-5.2%)

Threshold costs -1b (-5.2%)

Counts

3 → 1

Calls

Call 1

Inputs

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

#s(approx (log (+ 1 x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x))

#s(approx (log (+ 1 x)) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) x))

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

Calls

3 calls:

2.0ms	x
1.0ms	(log.f64 (+.f64 #s(literal 1 binary64) x))
1.0ms	(+.f64 #s(literal 1 binary64) x)

Results

Accuracy	Segments	Branch
71.2%	1	`x`
71.2%	1	`(log.f64 (+.f64 #s(literal 1 binary64) x))`
71.2%	1	`(+.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 8 to 8 computations (0% saved)

simplify24.0ms (0.7%)

Memory

13.6MiB live, 50.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	38
1	26	38

Stop Event

1×

saturated

Calls

Call 1

Inputs

(log1p.f64 x)

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

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

Outputs

(log1p.f64 x)

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

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

soundness767.0ms (21.6%)

Memory

4.5MiB live, 343.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	132	1258
1	377	1186
2	1154	1162
3	3986	1130
0	8185	1010
0	62	169
1	171	155
2	363	150
3	979	148
4	2422	144
5	4452	144
6	5392	144
7	6689	144
8	7472	144
9	7620	144
10	7664	144
11	7666	144
12	7666	144
13	7909	144
0	8006	138
0	4	7
0	6	7
1	22	7
2	131	7
3	984	7
0	8620	5

Stop Event

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

Compiler

Compiled 48 to 37 computations (22.9% saved)

preprocess89.0ms (2.5%)

Memory: 17.1MiB live, 138.7MiB allocated
Compiler: Compiled 80 to 50 computations (37.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze1.0ms (0%)

sample422.0ms (11.9%)

explain133.0ms (3.8%)

preprocess18.0ms (0.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0.1%)

localize13.0ms (0.4%)

series2.0ms (0.1%)

simplify249.0ms (7%)

rewrite224.0ms (6.3%)

eval63.0ms (1.8%)

prune6.0ms (0.2%)

simplify18.0ms (0.5%)

localize76.0ms (2.2%)

series15.0ms (0.4%)

simplify187.0ms (5.3%)

rewrite365.0ms (10.3%)

eval103.0ms (2.9%)

prune20.0ms (0.6%)

simplify14.0ms (0.4%)

localize180.0ms (5.1%)

series51.0ms (1.4%)

simplify127.0ms (3.6%)

rewrite200.0ms (5.6%)

eval110.0ms (3.1%)

prune10.0ms (0.3%)

regimes40.0ms (1.1%)

regimes7.0ms (0.2%)

regimes5.0ms (0.1%)

simplify24.0ms (0.7%)

soundness767.0ms (21.6%)

preprocess89.0ms (2.5%)

end0.0ms (0%)

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