Details

analyze634.0ms (9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	74.9%	25.1%	5
0%	74.9%	25.1%	6
0%	74.9%	25.1%	7
6.2%	56.2%	37.6%	8
7.8%	53%	39.2%	9
10.9%	45.6%	43.4%	10
18.3%	31.4%	50.3%	11
19.1%	29.5%	51.3%	12
21.4%	24.8%	53.8%	13
25.8%	16.7%	57.5%	14

Compiler

Compiled 28 to 21 computations (25% saved)

sample139.0ms (2%)

Algorithm

1×

intervals

Results

27.0ms	256×	body	128	valid
3.0ms	31×	body	128	invalid
2.0ms	28×	body	128	nan

Compiler

Compiled 58 to 44 computations (24.1% saved)

simplify75.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

703×	`fma-def_binary64`
691×	`associate-/l*_binary64`
673×	`sub-neg_binary64`
568×	`fma-neg_binary64`
439×	`div-sub_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	21	32
1	43	32
2	99	31
3	223	30
4	529	30
5	1016	30
6	1917	30
7	3001	30
8	3396	30
9	4830	30
10	5110	30

prune4.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

6.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	6.1b	(+.f64 (+.f64 (-.f64 (.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (/.f64 (+.f64 (.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))

Status

Error

Program

▶

6.1b

(+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))

Compiler

Compiled 102 to 73 computations (28.4% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000)
✓	0.1b	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
✓	0.2b	(*.f64 (-.f64 x 1/2) (log.f64 x))
✓	5.7b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x)

series95.0ms (1.4%)

Counts

4 → 72

Calls

4 calls:

60.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x)
14.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000)
13.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
8.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))

rewrite36.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`*-un-lft-identity_binary64`
29×	`add-sqr-sqrt_binary64`
25×	`add-cube-cbrt_binary64`
18×	`log-prod_binary64`
13×	`associate-+l+_binary64`

Counts

4 → 120

Calls

4 calls:

11.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000)
9.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x)
6.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
5.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))

simplify154.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

654×	`fma-neg_binary64`
646×	`times-frac_binary64`
406×	`cancel-sign-sub-inv_binary64`
197×	`exp-prod_binary64`
171×	`associate-l_binary64`

Counts

192 → 237

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	284	3766
1	654	3445
2	2312	3267
3	4222	3261
4	4970	3261
5	4899	3261

prune382.0ms (5.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	225	12	237
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	226	12	238

Error

1.5b

Counts

238 → 12

Alt Table

Status	Error	Program
	6.1b	(+.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) (-.f64 x 1/2)) (fma.f64 (+.f64 x -1/2) (log.f64 (sqrt.f64 x)) (-.f64 91893853320467/100000000000000 x))) (/.f64 (+.f64 (.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))
	30.7b	(+.f64 (+.f64 (-.f64 (.f64 (.f64 (sqrt.f64 (-.f64 x 1/2)) (sqrt.f64 (log.f64 x))) (.f64 (sqrt.f64 (-.f64 x 1/2)) (sqrt.f64 (log.f64 x)))) x) 91893853320467/100000000000000) (/.f64 (+.f64 (.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))
	30.6b	(+.f64 (+.f64 (-.f64 (.f64 (sqrt.f64 (-.f64 x 1/2)) (.f64 (sqrt.f64 (-.f64 x 1/2)) (log.f64 x))) x) 91893853320467/100000000000000) (/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))
	12.3b	(+.f64 (+.f64 (-.f64 (.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (/.f64 (-.f64 (.f64 (.f64 (-.f64 (.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) (.f64 (-.f64 (.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z)) (.f64 83333333333333/1000000000000000 83333333333333/1000000000000000)) (.f64 x (-.f64 (.f64 (-.f64 (.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000))))
▶	5.3b	(+.f64 (+.f64 (-.f64 (.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (fma.f64 7936500793651/10000000000000000 (/.f64 (.f64 z z) x) (+.f64 (/.f64 83333333333333/1000000000000000 x) (fma.f64 z (/.f64 (.f64 z y) x) (.f64 z (/.f64 -13888888888889/5000000000000000 x))))))
	6.1b	(+.f64 (.f64 1 (fma.f64 (log.f64 x) (+.f64 x -1/2) (-.f64 91893853320467/100000000000000 x))) (/.f64 (+.f64 (.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))
	6.2b	(+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (/.f64 (/.f64 (fma.f64 z (fma.f64 z (+.f64 7936500793651/10000000000000000 y) -13888888888889/5000000000000000) 83333333333333/1000000000000000) (sqrt.f64 x)) (sqrt.f64 x)))
	9.7b	(+.f64 (+.f64 (-.f64 (.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (.f64 (/.f64 (sqrt.f64 (fma.f64 z (fma.f64 z (+.f64 7936500793651/10000000000000000 y) -13888888888889/5000000000000000) 83333333333333/1000000000000000)) (sqrt.f64 x)) (/.f64 (sqrt.f64 (fma.f64 z (fma.f64 z (+.f64 7936500793651/10000000000000000 y) -13888888888889/5000000000000000) 83333333333333/1000000000000000)) (sqrt.f64 x))))
	9.6b	(+.f64 (+.f64 (-.f64 (.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (-.f64 (/.f64 83333333333333/1000000000000000 x) (.f64 13888888888889/5000000000000000 (/.f64 z x))))
	6.5b	(+.f64 (+.f64 (-.f64 (.f64 (.f64 (-.f64 x 1/2) (.f64 (cbrt.f64 (log.f64 x)) (cbrt.f64 (log.f64 x)))) (cbrt.f64 (log.f64 x))) x) 91893853320467/100000000000000) (/.f64 (+.f64 (.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))
	9.6b	(+.f64 (+.f64 (-.f64 (.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (/.f64 (sqrt.f64 (+.f64 (.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000)) (/.f64 x (sqrt.f64 (fma.f64 z (fma.f64 z (+.f64 7936500793651/10000000000000000 y) -13888888888889/5000000000000000) 83333333333333/1000000000000000)))))
	6.1b	(+.f64 (+.f64 (-.f64 (+.f64 (.f64 (+.f64 x -1/2) (.f64 2 (log.f64 (cbrt.f64 x)))) (.f64 (+.f64 x -1/2) (log.f64 (cbrt.f64 x)))) x) 91893853320467/100000000000000) (/.f64 (+.f64 (.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))

Compiler

Compiled 8507 to 5612 computations (34% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 83333333333333/1000000000000000 x)
✓	1.0b	(fma.f64 z (/.f64 (.f64 z y) x) (.f64 z (/.f64 -13888888888889/5000000000000000 x)))
✓	4.7b	(/.f64 (*.f64 z y) x)
✓	8.6b	(/.f64 (*.f64 z z) x)

series45.0ms (0.6%)

Counts

4 → 96

Calls

4 calls:

21.0ms	(fma.f64 z (/.f64 (.f64 z y) x) (.f64 z (/.f64 -13888888888889/5000000000000000 x)))
12.0ms	(/.f64 (*.f64 z z) x)
11.0ms	(/.f64 (*.f64 z y) x)
1.0ms	(/.f64 83333333333333/1000000000000000 x)

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
16×	`add-cube-cbrt_binary64`
16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`

Counts

4 → 85

Calls

4 calls:

3.0ms	(/.f64 (*.f64 z z) x)
3.0ms	(/.f64 (*.f64 z y) x)
2.0ms	(/.f64 83333333333333/1000000000000000 x)
0.0ms	(fma.f64 z (/.f64 (.f64 z y) x) (.f64 z (/.f64 -13888888888889/5000000000000000 x)))

simplify95.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

567×	`associate-/l*_binary64`
448×	`times-frac_binary64`
327×	`associate-/l/_binary64`
292×	`associate-*l/_binary64`
223×	`fma-def_binary64`

Counts

181 → 116

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	154	1995
1	316	1762
2	841	1722
3	3236	1642
4	4963	1642
5	4959	1642

prune250.0ms (3.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	111	5	116
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	115	13	128

Error

0.5b

Counts

128 → 13

Alt Table

Status	Error	Program
	6.1b	(+.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) (-.f64 x 1/2)) (fma.f64 (+.f64 x -1/2) (log.f64 (sqrt.f64 x)) (-.f64 91893853320467/100000000000000 x))) (/.f64 (+.f64 (.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))
	30.7b	(+.f64 (+.f64 (-.f64 (.f64 (.f64 (sqrt.f64 (-.f64 x 1/2)) (sqrt.f64 (log.f64 x))) (.f64 (sqrt.f64 (-.f64 x 1/2)) (sqrt.f64 (log.f64 x)))) x) 91893853320467/100000000000000) (/.f64 (+.f64 (.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))
▶	2.3b	(+.f64 (+.f64 (-.f64 (.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (fma.f64 7936500793651/10000000000000000 (.f64 z (/.f64 z x)) (+.f64 (/.f64 83333333333333/1000000000000000 x) (fma.f64 z (/.f64 (.f64 z y) x) (.f64 z (/.f64 -13888888888889/5000000000000000 x))))))
	6.5b	(+.f64 (+.f64 (-.f64 (.f64 (.f64 (-.f64 x 1/2) (.f64 (cbrt.f64 (log.f64 x)) (cbrt.f64 (log.f64 x)))) (cbrt.f64 (log.f64 x))) x) 91893853320467/100000000000000) (/.f64 (+.f64 (.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))
	30.6b	(+.f64 (+.f64 (-.f64 (.f64 (sqrt.f64 (-.f64 x 1/2)) (.f64 (sqrt.f64 (-.f64 x 1/2)) (log.f64 x))) x) 91893853320467/100000000000000) (/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))
	12.3b	(+.f64 (+.f64 (-.f64 (.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (/.f64 (-.f64 (.f64 (.f64 (-.f64 (.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) (.f64 (-.f64 (.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z)) (.f64 83333333333333/1000000000000000 83333333333333/1000000000000000)) (.f64 x (-.f64 (.f64 (-.f64 (.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000))))
	5.3b	(+.f64 (+.f64 (-.f64 (.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (fma.f64 7936500793651/10000000000000000 (/.f64 (.f64 z z) x) (+.f64 (/.f64 (sqrt.f64 83333333333333/1000000000000000) (/.f64 x (sqrt.f64 83333333333333/1000000000000000))) (fma.f64 z (/.f64 (.f64 z y) x) (.f64 z (/.f64 -13888888888889/5000000000000000 x))))))
	4.3b	(+.f64 (+.f64 (-.f64 (.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (fma.f64 7936500793651/10000000000000000 (/.f64 (.f64 z z) x) (+.f64 (/.f64 83333333333333/1000000000000000 x) (*.f64 (/.f64 z x) (fma.f64 z y -13888888888889/5000000000000000)))))
	6.1b	(+.f64 (+.f64 (-.f64 (+.f64 (.f64 (+.f64 x -1/2) (.f64 2 (log.f64 (cbrt.f64 x)))) (.f64 (+.f64 x -1/2) (log.f64 (cbrt.f64 x)))) x) 91893853320467/100000000000000) (/.f64 (+.f64 (.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))
	6.1b	(+.f64 (.f64 1 (fma.f64 (log.f64 x) (+.f64 x -1/2) (-.f64 91893853320467/100000000000000 x))) (/.f64 (+.f64 (.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))
	9.6b	(+.f64 (+.f64 (-.f64 (.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (-.f64 (/.f64 83333333333333/1000000000000000 x) (.f64 13888888888889/5000000000000000 (/.f64 z x))))
	2.3b	(+.f64 (+.f64 (-.f64 (.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (fma.f64 7936500793651/10000000000000000 (.f64 (/.f64 z (sqrt.f64 x)) (/.f64 z (sqrt.f64 x))) (+.f64 (/.f64 83333333333333/1000000000000000 x) (fma.f64 z (/.f64 (.f64 z y) x) (.f64 z (/.f64 -13888888888889/5000000000000000 x))))))
	6.7b	(+.f64 (+.f64 (-.f64 (.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (fma.f64 7936500793651/10000000000000000 (/.f64 (.f64 z z) x) (+.f64 (/.f64 83333333333333/1000000000000000 x) (/.f64 (*.f64 y (pow.f64 z 2)) x))))

Compiler

Compiled 5386 to 2855 computations (47% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (-.f64 x 1/2) (log.f64 x))
	0.3b	(/.f64 83333333333333/1000000000000000 x)
	1.0b	(fma.f64 z (/.f64 (.f64 z y) x) (.f64 z (/.f64 -13888888888889/5000000000000000 x)))
	4.7b	(/.f64 (*.f64 z y) x)

prune298.0ms (4.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	139	5	144
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	145	12	157

Error

0.0b

Counts

157 → 12

Alt Table

Status	Error	Program
	6.1b	(+.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) (-.f64 x 1/2)) (fma.f64 (+.f64 x -1/2) (log.f64 (sqrt.f64 x)) (-.f64 91893853320467/100000000000000 x))) (/.f64 (+.f64 (.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))
	30.7b	(+.f64 (+.f64 (-.f64 (.f64 (.f64 (sqrt.f64 (-.f64 x 1/2)) (sqrt.f64 (log.f64 x))) (.f64 (sqrt.f64 (-.f64 x 1/2)) (sqrt.f64 (log.f64 x)))) x) 91893853320467/100000000000000) (/.f64 (+.f64 (.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))
	2.4b	(+.f64 (+.f64 (-.f64 (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 1/2)) (.f64 (log.f64 x) (-.f64 (sqrt.f64 x) (sqrt.f64 1/2)))) x) 91893853320467/100000000000000) (fma.f64 7936500793651/10000000000000000 (.f64 z (/.f64 z x)) (+.f64 (/.f64 83333333333333/1000000000000000 x) (fma.f64 z (/.f64 (.f64 z y) x) (*.f64 z (/.f64 -13888888888889/5000000000000000 x))))))
▶	1.3b	(+.f64 (+.f64 (-.f64 (.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (fma.f64 7936500793651/10000000000000000 (.f64 z (/.f64 z x)) (+.f64 (/.f64 83333333333333/1000000000000000 x) (*.f64 (/.f64 z x) (fma.f64 z y -13888888888889/5000000000000000)))))
	5.3b	(+.f64 (+.f64 (-.f64 (.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (fma.f64 7936500793651/10000000000000000 (/.f64 (.f64 z z) x) (+.f64 (/.f64 (sqrt.f64 83333333333333/1000000000000000) (/.f64 x (sqrt.f64 83333333333333/1000000000000000))) (fma.f64 z (/.f64 (.f64 z y) x) (.f64 z (/.f64 -13888888888889/5000000000000000 x))))))
	6.1b	(+.f64 (+.f64 (-.f64 (+.f64 (.f64 (+.f64 x -1/2) (.f64 2 (log.f64 (cbrt.f64 x)))) (.f64 (+.f64 x -1/2) (log.f64 (cbrt.f64 x)))) x) 91893853320467/100000000000000) (/.f64 (+.f64 (.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))
	6.1b	(+.f64 (.f64 1 (fma.f64 (log.f64 x) (+.f64 x -1/2) (-.f64 91893853320467/100000000000000 x))) (/.f64 (+.f64 (.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))
	2.8b	(+.f64 (+.f64 (-.f64 (.f64 (.f64 (+.f64 x -1/2) (.f64 (cbrt.f64 (log.f64 x)) (cbrt.f64 (log.f64 x)))) (cbrt.f64 (log.f64 x))) x) 91893853320467/100000000000000) (fma.f64 7936500793651/10000000000000000 (.f64 z (/.f64 z x)) (+.f64 (/.f64 83333333333333/1000000000000000 x) (fma.f64 z (/.f64 (.f64 z y) x) (.f64 z (/.f64 -13888888888889/5000000000000000 x))))))
	6.3b	(+.f64 (+.f64 (-.f64 (.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (fma.f64 7936500793651/10000000000000000 (.f64 z (/.f64 z x)) (+.f64 (/.f64 83333333333333/1000000000000000 x) (/.f64 (-.f64 (.f64 y (pow.f64 z 2)) (.f64 13888888888889/5000000000000000 z)) x))))
	2.3b	(+.f64 (+.f64 (-.f64 (.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (fma.f64 7936500793651/10000000000000000 (.f64 (/.f64 z (sqrt.f64 x)) (/.f64 z (sqrt.f64 x))) (+.f64 (/.f64 83333333333333/1000000000000000 x) (fma.f64 z (/.f64 (.f64 z y) x) (.f64 z (/.f64 -13888888888889/5000000000000000 x))))))
	12.3b	(+.f64 (+.f64 (-.f64 (.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (/.f64 (-.f64 (.f64 (.f64 (-.f64 (.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) (.f64 (-.f64 (.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z)) (.f64 83333333333333/1000000000000000 83333333333333/1000000000000000)) (.f64 x (-.f64 (.f64 (-.f64 (.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000))))
	5.1b	(+.f64 (+.f64 (-.f64 (.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (fma.f64 7936500793651/10000000000000000 (.f64 z (/.f64 z x)) (+.f64 (/.f64 83333333333333/1000000000000000 x) (fma.f64 z (/.f64 z (/.f64 x y)) (*.f64 z (/.f64 -13888888888889/5000000000000000 x))))))

Compiler

Compiled 6586 to 3472 computations (47.3% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
	0.2b	(*.f64 (-.f64 x 1/2) (log.f64 x))
	0.3b	(/.f64 83333333333333/1000000000000000 x)
✓	1.7b	(*.f64 (/.f64 z x) (fma.f64 z y -13888888888889/5000000000000000))

series20.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

20.0ms

(*.f64 (/.f64 z x) (fma.f64 z y -13888888888889/5000000000000000))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
13×	`associate-l_binary64`
10×	`times-frac_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`

Counts

1 → 36

Calls

1 calls:

4.0ms

(*.f64 (/.f64 z x) (fma.f64 z y -13888888888889/5000000000000000))

simplify73.0ms (1%)

Algorithm

1×	egg-herbie

Rules

596×	`fma-def_binary64`
386×	`associate-/r*_binary64`
335×	`associate-/l/_binary64`
319×	`associate-/r/_binary64`
310×	`associate-l_binary64`

Counts

72 → 65

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	94	1132
1	219	895
2	625	895
3	2227	895
4	4654	895
5	5106	895

prune370.0ms (5.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	200	6	206
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	206	12	218

Error

0.0b

Counts

218 → 12

Alt Table

Status	Error	Program
	30.7b	(+.f64 (+.f64 (-.f64 (.f64 (.f64 (sqrt.f64 (-.f64 x 1/2)) (sqrt.f64 (log.f64 x))) (.f64 (sqrt.f64 (-.f64 x 1/2)) (sqrt.f64 (log.f64 x)))) x) 91893853320467/100000000000000) (/.f64 (+.f64 (.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))
	1.8b	(+.f64 (+.f64 (-.f64 (.f64 (.f64 (+.f64 x -1/2) (.f64 (cbrt.f64 (log.f64 x)) (cbrt.f64 (log.f64 x)))) (cbrt.f64 (log.f64 x))) x) 91893853320467/100000000000000) (fma.f64 7936500793651/10000000000000000 (.f64 z (/.f64 z x)) (+.f64 (/.f64 83333333333333/1000000000000000 x) (*.f64 (/.f64 z x) (fma.f64 z y -13888888888889/5000000000000000)))))
	6.3b	(+.f64 (+.f64 (-.f64 (.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (fma.f64 7936500793651/10000000000000000 (.f64 z (/.f64 z x)) (+.f64 (/.f64 83333333333333/1000000000000000 x) (/.f64 (-.f64 (.f64 y (pow.f64 z 2)) (.f64 13888888888889/5000000000000000 z)) x))))
	1.3b	(+.f64 (+.f64 (-.f64 (.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (fma.f64 7936500793651/10000000000000000 (.f64 z (/.f64 z x)) (+.f64 (/.f64 (sqrt.f64 83333333333333/1000000000000000) (/.f64 x (sqrt.f64 83333333333333/1000000000000000))) (*.f64 (/.f64 z x) (fma.f64 z y -13888888888889/5000000000000000)))))
	1.3b	(+.f64 (+.f64 (-.f64 (.f64 (log.f64 x) x) (+.f64 (.f64 1/2 (log.f64 x)) x)) 91893853320467/100000000000000) (fma.f64 7936500793651/10000000000000000 (.f64 z (/.f64 z x)) (+.f64 (/.f64 83333333333333/1000000000000000 x) (.f64 (/.f64 z x) (fma.f64 z y -13888888888889/5000000000000000)))))
	12.3b	(+.f64 (+.f64 (-.f64 (.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (/.f64 (-.f64 (.f64 (.f64 (-.f64 (.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) (.f64 (-.f64 (.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z)) (.f64 83333333333333/1000000000000000 83333333333333/1000000000000000)) (.f64 x (-.f64 (.f64 (-.f64 (.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000))))
	5.1b	(+.f64 (+.f64 (-.f64 (.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (fma.f64 7936500793651/10000000000000000 (.f64 z (/.f64 z x)) (+.f64 (/.f64 83333333333333/1000000000000000 x) (fma.f64 z (/.f64 z (/.f64 x y)) (*.f64 z (/.f64 -13888888888889/5000000000000000 x))))))
	1.3b	(+.f64 (+.f64 (+.f64 (.f64 (-.f64 x 1/2) (log.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)))) (-.f64 (.f64 (+.f64 x -1/2) (log.f64 (cbrt.f64 x))) x)) 91893853320467/100000000000000) (fma.f64 7936500793651/10000000000000000 (.f64 z (/.f64 z x)) (+.f64 (/.f64 83333333333333/1000000000000000 x) (*.f64 (/.f64 z x) (fma.f64 z y -13888888888889/5000000000000000)))))
	1.4b	(+.f64 (+.f64 (-.f64 (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 1/2)) (.f64 (log.f64 x) (-.f64 (sqrt.f64 x) (sqrt.f64 1/2)))) x) 91893853320467/100000000000000) (fma.f64 7936500793651/10000000000000000 (.f64 z (/.f64 z x)) (+.f64 (/.f64 83333333333333/1000000000000000 x) (.f64 (/.f64 z x) (fma.f64 z y -13888888888889/5000000000000000)))))
	6.1b	(+.f64 (+.f64 (-.f64 (+.f64 (.f64 (+.f64 x -1/2) (.f64 2 (log.f64 (cbrt.f64 x)))) (.f64 (+.f64 x -1/2) (log.f64 (cbrt.f64 x)))) x) 91893853320467/100000000000000) (/.f64 (+.f64 (.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))
	1.4b	(+.f64 (+.f64 (+.f64 (.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) (-.f64 (.f64 (+.f64 x -1/2) (log.f64 (sqrt.f64 x))) x)) 91893853320467/100000000000000) (fma.f64 7936500793651/10000000000000000 (.f64 z (/.f64 z x)) (+.f64 (/.f64 83333333333333/1000000000000000 x) (.f64 (/.f64 z x) (fma.f64 z y -13888888888889/5000000000000000)))))
	2.3b	(+.f64 (+.f64 (-.f64 (.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (fma.f64 7936500793651/10000000000000000 (.f64 (/.f64 z (sqrt.f64 x)) (/.f64 z (sqrt.f64 x))) (+.f64 (/.f64 83333333333333/1000000000000000 x) (fma.f64 z (/.f64 (.f64 z y) x) (.f64 z (/.f64 -13888888888889/5000000000000000 x))))))

Compiler

Compiled 8071 to 4266 computations (47.1% saved)

regimes2.8s (39.1%)

Accuracy

Total 1.2b remaining (92.6%)

Threshold costs 0b (0%)

Counts

222 → 1

Compiler

Compiled 61863 to 42711 computations (31% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
3×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	51
1	35	51
2	41	51
3	43	51
4	44	51
5	43	51

end1.0ms (0%)

Compiler: Compiled 37 to 25 computations (32.4% saved)

sample1.5s (21.5%)

Algorithm

1×

intervals

Results

738.0ms	8000×	body	128	valid
105.0ms	1185×	body	128	invalid
64.0ms	763×	body	128	nan

Compiler

Compiled 552 to 367 computations (33.5% saved)

Details

analyze634.0ms (9%)

sample139.0ms (2%)

simplify75.0ms (1.1%)

prune4.0ms (0.1%)

localize19.0ms (0.3%)

series95.0ms (1.4%)

rewrite36.0ms (0.5%)

simplify154.0ms (2.2%)

prune382.0ms (5.4%)

localize20.0ms (0.3%)

series45.0ms (0.6%)

rewrite11.0ms (0.2%)

simplify95.0ms (1.4%)

prune250.0ms (3.6%)

localize21.0ms (0.3%)

prune298.0ms (4.2%)

localize17.0ms (0.2%)

series20.0ms (0.3%)

rewrite7.0ms (0.1%)

simplify73.0ms (1%)

prune370.0ms (5.3%)

regimes2.8s (39.1%)

simplify3.0ms (0%)

end1.0ms (0%)

sample1.5s (21.5%)

Profiling