Details

analyze2.3s (25%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
3.1%	96.5%	0.3%	9
4.7%	95%	0.3%	10
4.7%	95%	0.3%	11
5.1%	82.1%	12.8%	12
6.2%	74.7%	19%	13
6.4%	74.5%	19%	14

Compiler

Compiled 41 to 30 computations (26.8% saved)

sample3.3s (36.1%)

Results

2.0s	8256×	body	128	valid
1.1s	5143×	body	128	invalid

Compiler

Compiled 122 to 89 computations (27% saved)

simplify47.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

829×	`fma-neg_binary64`
433×	`exp-sum_binary64`
321×	`distribute-rgt-in_binary64`
303×	`distribute-lft-in_binary64`
279×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	47
1	55	42
2	136	40
3	512	40
4	2106	40
5	4520	40
6	4992	40

prune6.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

4.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	4.6b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))) x))

Compiler

Compiled 135 to 87 computations (35.6% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 z (sqrt.f64 (+.f64 t a)))
✓	0.3b	(/.f64 2/3 t)
✓	2.3b	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))
✓	8.0b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

series127.0ms (1.4%)

Counts

4 → 88

Calls

4 calls:

67.0ms	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))
33.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
23.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
1.0ms	(/.f64 2/3 t)

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`

Counts

4 → 91

Calls

4 calls:

6.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
6.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
2.0ms	(/.f64 2/3 t)
0.0ms	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))

simplify132.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

801×	`times-frac_binary64`
430×	`cancel-sign-sub-inv_binary64`
324×	`fma-neg_binary64`
272×	`sub-neg_binary64`
270×	`fma-def_binary64`

Counts

179 → 189

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	321	4150
1	864	3932
2	2992	3925
3	4865	3924
4	4956	3924

prune200.0ms (2.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	186	3	189
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	187	3	190

Error

0.0b

Counts

190 → 3

Alt Table

Status	Error	Program
	18.7b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))) x))
▶	17.2b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 c (+.f64 a 5/6) (*.f64 b (-.f64 -5/6 a)))) x))
	32.9b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (/.f64 (fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))) t)) x))

Compiler

Compiled 6983 to 3532 computations (49.4% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 -5/6 a)
✓	0.0b	(pow.f64 (exp.f64 2) (fma.f64 c (+.f64 a 5/6) (*.f64 b (-.f64 -5/6 a))))
✓	0.1b	(*.f64 b (-.f64 -5/6 a))
✓	1.1b	(fma.f64 c (+.f64 a 5/6) (*.f64 b (-.f64 -5/6 a)))

series34.0ms (0.4%)

Counts

4 → 108

Calls

4 calls:

18.0ms	(pow.f64 (exp.f64 2) (fma.f64 c (+.f64 a 5/6) (*.f64 b (-.f64 -5/6 a))))
10.0ms	(fma.f64 c (+.f64 a 5/6) (*.f64 b (-.f64 -5/6 a)))
5.0ms	(*.f64 b (-.f64 -5/6 a))
1.0ms	(-.f64 -5/6 a)

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64`
36×	`*-un-lft-identity_binary64`
31×	`add-cube-cbrt_binary64`
27×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

4 → 114

Calls

4 calls:

6.0ms	(*.f64 b (-.f64 -5/6 a))
3.0ms	(-.f64 -5/6 a)
2.0ms	(pow.f64 (exp.f64 2) (fma.f64 c (+.f64 a 5/6) (*.f64 b (-.f64 -5/6 a))))
0.0ms	(fma.f64 c (+.f64 a 5/6) (*.f64 b (-.f64 -5/6 a)))

simplify108.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

491×	`associate-r_binary64`
476×	`cancel-sign-sub-inv_binary64`
409×	`associate-l_binary64`
380×	`unswap-sqr_binary64`
294×	`fma-def_binary64`

Counts

222 → 199

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	330	4240
1	822	3311
2	3355	3218
3	5218	3218

prune212.0ms (2.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	198	1	199
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	199	3	202

Error

Counts

202 → 3

Alt Table

Status	Error	Program
	18.7b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))) x))
▶	16.7b	(/.f64 x (fma.f64 y (log.f64 (exp.f64 (pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b))))) x))
	32.9b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (/.f64 (fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))) t)) x))

Compiler

Compiled 6492 to 3974 computations (38.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (exp.f64 (pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b)))))
✓	0.0b	(+.f64 a 5/6)
✓	0.0b	(pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b)))
✓	0.1b	(*.f64 (+.f64 a 5/6) (-.f64 c b))

series45.0ms (0.5%)

Counts

4 → 120

Calls

4 calls:

19.0ms	(pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b)))
17.0ms	(log.f64 (exp.f64 (pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b)))))
8.0ms	(*.f64 (+.f64 a 5/6) (-.f64 c b))
1.0ms	(+.f64 a 5/6)

rewrite39.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

62×	`*-un-lft-identity_binary64`
58×	`add-sqr-sqrt_binary64`
54×	`prod-diff_binary64`
54×	`add-cube-cbrt_binary64`
52×	`unpow-prod-up_binary64`

Counts

4 → 169

Calls

4 calls:

8.0ms	(*.f64 (+.f64 a 5/6) (-.f64 c b))
7.0ms	(log.f64 (exp.f64 (pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b)))))
5.0ms	(pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b)))
2.0ms	(+.f64 a 5/6)

simplify158.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

517×	`associate-r_binary64`
416×	`associate-l_binary64`
375×	`unswap-sqr_binary64`
282×	`*-commutative_binary64`
268×	`fma-def_binary64`

Counts

289 → 278

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	441	7027
1	954	6476
2	3836	6272
3	5158	6272

prune284.0ms (3.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	278	0	278
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	278	3	281

Error

Counts

281 → 3

Alt Table

Status	Error	Program
▶	18.7b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))) x))
✓	16.7b	(/.f64 x (fma.f64 y (log.f64 (exp.f64 (pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b))))) x))
	32.9b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (/.f64 (fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))) t)) x))

Compiler

Compiled 9404 to 5478 computations (41.7% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1 t))
✓	0.2b	(*.f64 (sqrt.f64 (/.f64 1 t)) z)
	0.3b	(/.f64 2/3 t)
✓	1.8b	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))

series67.0ms (0.7%)

Counts

3 → 51

Calls

3 calls:

51.0ms	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))
12.0ms	(*.f64 (sqrt.f64 (/.f64 1 t)) z)
4.0ms	(sqrt.f64 (/.f64 1 t))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
29×	`sqrt-prod_binary64`
22×	`times-frac_binary64`
21×	`*-un-lft-identity_binary64`
19×	`add-cube-cbrt_binary64`

Counts

3 → 77

Calls

3 calls:

9.0ms	(*.f64 (sqrt.f64 (/.f64 1 t)) z)
2.0ms	(sqrt.f64 (/.f64 1 t))
0.0ms	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))

simplify91.0ms (1%)

Algorithm

1×	egg-herbie

Rules

659×	`distribute-rgt-in_binary64`
617×	`distribute-lft-in_binary64`
462×	`fma-neg_binary64`
279×	`sub-neg_binary64`
268×	`fma-def_binary64`

Counts

128 → 119

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	132	2796
1	292	2685
2	862	2514
3	2230	2438
4	5267	2438

prune147.0ms (1.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	152	3	155

Error

Counts

155 → 3

Alt Table

Status	Error	Program
✓	18.7b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))) x))
✓	16.7b	(/.f64 x (fma.f64 y (log.f64 (exp.f64 (pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b))))) x))
	32.9b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (/.f64 (fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))) t)) x))

Compiler

Compiled 4720 to 2955 computations (37.4% saved)

regimes1.6s (17.2%)

Accuracy

Total 0.9b remaining (88.4%)

Threshold costs 0.9b (88.4%)

Counts

100 → 3

Compiler

Compiled 33659 to 24844 computations (26.2% saved)

bsearch45.0ms (0.5%)

Steps

Iters	Range		Point
4	3.4073320166746997e-282	8.276599410265367e-275	5.914976321355086e-279
1	-1.8216588890627468e-73	-1.1596361154539363e-80	-4.598639463012585e-77

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
5×	`*-commutative_binary64`
4×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	113
1	53	113
2	63	113
3	67	113
4	69	113
5	68	113

end101.0ms (1.1%)

Compiler: Compiled 251 to 166 computations (33.9% saved)

Details

analyze2.3s (25%)

sample3.3s (36.1%)

simplify47.0ms (0.5%)

prune6.0ms (0.1%)

localize20.0ms (0.2%)

series127.0ms (1.4%)

rewrite18.0ms (0.2%)

simplify132.0ms (1.5%)

prune200.0ms (2.2%)

localize15.0ms (0.2%)

series34.0ms (0.4%)

rewrite17.0ms (0.2%)

simplify108.0ms (1.2%)

prune212.0ms (2.3%)

localize13.0ms (0.1%)

series45.0ms (0.5%)

rewrite39.0ms (0.4%)

simplify158.0ms (1.7%)

prune284.0ms (3.1%)

localize18.0ms (0.2%)

series67.0ms (0.7%)

rewrite15.0ms (0.2%)

simplify91.0ms (1%)

prune147.0ms (1.6%)

regimes1.6s (17.2%)

bsearch45.0ms (0.5%)

simplify5.0ms (0.1%)

end101.0ms (1.1%)

Profiling