Details

analyze2.9s (17.4%)

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
18.7%	81%	0.3%	6
18.7%	81%	0.3%	7
18.7%	81%	0.3%	8
18.7%	81%	0.3%	9
18.7%	81%	0.3%	10
18.7%	81%	0.3%	11
18.8%	68.4%	12.8%	12
22.3%	58.7%	19%	13
22.3%	58.6%	19%	14

Compiler

Compiled 41 to 30 computations (26.8% saved)

sample4.6s (27.7%)

Results

2.5s	8256×	body	128	valid
1.8s	5158×	body	128	invalid

Compiler

Compiled 122 to 89 computations (27% saved)

simplify88.0ms (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%)

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

2.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	2.4b	(/.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)

localize37.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.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))
✓	4.0b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

series335.0ms (2%)

Counts

4 → 88

Calls

4 calls:

115.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
113.0ms	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))
103.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
3.0ms	(/.f64 2/3 t)

rewrite52.0ms (0.3%)

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:

22.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
15.0ms	(/.f64 2/3 t)
7.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
1.0ms	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))

simplify262.0ms (1.6%)

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

prune559.0ms (3.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	186	3	189
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	186	4	190

Error

0.0b

Counts

190 → 4

Alt Table

Status	Error	Program
✓	2.4b	(/.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))
▶	10.5b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (+.f64 (.f64 c (+.f64 a 5/6)) (fma.f64 2/3 (/.f64 b t) (fma.f64 b (-.f64 -5/6 a) (.f64 (/.f64 c t) -2/3))))) x))
	20.0b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 c (+.f64 a 5/6) (*.f64 b (-.f64 -5/6 a)))) x))
	15.2b	(/.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))

Compiler

Compiled 7035 to 3567 computations (49.3% saved)

localize56.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 c (+.f64 a 5/6))
✓	0.2b	(*.f64 (/.f64 c t) -2/3)
✓	1.6b	(+.f64 (.f64 c (+.f64 a 5/6)) (fma.f64 2/3 (/.f64 b t) (fma.f64 b (-.f64 -5/6 a) (.f64 (/.f64 c t) -2/3))))
✓	1.8b	(fma.f64 2/3 (/.f64 b t) (fma.f64 b (-.f64 -5/6 a) (*.f64 (/.f64 c t) -2/3)))

series206.0ms (1.3%)

Counts

4 → 144

Calls

4 calls:

93.0ms	(+.f64 (.f64 c (+.f64 a 5/6)) (fma.f64 2/3 (/.f64 b t) (fma.f64 b (-.f64 -5/6 a) (.f64 (/.f64 c t) -2/3))))
82.0ms	(fma.f64 2/3 (/.f64 b t) (fma.f64 b (-.f64 -5/6 a) (*.f64 (/.f64 c t) -2/3)))
22.0ms	(*.f64 (/.f64 c t) -2/3)
8.0ms	(*.f64 c (+.f64 a 5/6))

rewrite35.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
16×	`associate-l_binary64`
16×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
11×	`add-cbrt-cube_binary64`

Counts

4 → 86

Calls

4 calls:

10.0ms	(*.f64 (/.f64 c t) -2/3)
9.0ms	(+.f64 (.f64 c (+.f64 a 5/6)) (fma.f64 2/3 (/.f64 b t) (fma.f64 b (-.f64 -5/6 a) (.f64 (/.f64 c t) -2/3))))
8.0ms	(*.f64 c (+.f64 a 5/6))
1.0ms	(fma.f64 2/3 (/.f64 b t) (fma.f64 b (-.f64 -5/6 a) (*.f64 (/.f64 c t) -2/3)))

simplify197.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

722×	`distribute-rgt-in_binary64`
702×	`distribute-lft-in_binary64`
602×	`fma-def_binary64`
152×	`fma-neg_binary64`
120×	`associate-l_binary64`

Counts

230 → 166

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	193	4088
1	502	3749
2	1515	3749
3	4997	3749

prune430.0ms (2.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	164	2	166
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	167	3	170

Error

0.0b

Counts

170 → 3

Alt Table

Status	Error	Program
✓	2.4b	(/.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))
	19.8b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b))) x))
▶	12.1b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (+.f64 (.f64 c (+.f64 a 5/6)) (+.f64 (/.f64 2/3 (/.f64 t (-.f64 b c))) (.f64 b -5/6)))) x))

Compiler

Compiled 5850 to 3304 computations (43.5% saved)

localize37.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 c (+.f64 a 5/6))
✓	0.2b	(*.f64 b -5/6)
✓	0.5b	(/.f64 2/3 (/.f64 t (-.f64 b c)))
✓	1.4b	(+.f64 (.f64 c (+.f64 a 5/6)) (+.f64 (/.f64 2/3 (/.f64 t (-.f64 b c))) (.f64 b -5/6)))

series64.0ms (0.4%)

Counts

3 → 96

Calls

3 calls:

41.0ms	(+.f64 (.f64 c (+.f64 a 5/6)) (+.f64 (/.f64 2/3 (/.f64 t (-.f64 b c))) (.f64 b -5/6)))
19.0ms	(/.f64 2/3 (/.f64 t (-.f64 b c)))
2.0ms	(*.f64 b -5/6)

rewrite78.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

123×	`times-frac_binary64`
89×	`add-sqr-sqrt_binary64`
87×	`*-un-lft-identity_binary64`
63×	`add-cube-cbrt_binary64`
21×	`associate-/r*_binary64`

Counts

3 → 146

Calls

3 calls:

52.0ms	(+.f64 (.f64 c (+.f64 a 5/6)) (+.f64 (/.f64 2/3 (/.f64 t (-.f64 b c))) (.f64 b -5/6)))
10.0ms	(/.f64 2/3 (/.f64 t (-.f64 b c)))
3.0ms	(*.f64 b -5/6)

simplify336.0ms (2%)

Algorithm

1×	egg-herbie

Rules

314×	`fma-neg_binary64`
293×	`associate-/l/_binary64`
252×	`times-frac_binary64`
226×	`cancel-sign-sub-inv_binary64`
208×	`*-commutative_binary64`

Counts

242 → 236

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	353	5061
1	909	4783
2	3311	4580
3	4818	4576
4	4997	4576
5	4959	4576

prune579.0ms (3.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	269	0	269
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	269	3	272

Error

0.0b

Counts

272 → 3

Alt Table

Status	Error	Program
✓	2.4b	(/.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))
▶	19.8b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b))) x))
✓	12.1b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (+.f64 (.f64 c (+.f64 a 5/6)) (+.f64 (/.f64 2/3 (/.f64 t (-.f64 b c))) (.f64 b -5/6)))) x))

Compiler

Compiled 9484 to 5224 computations (44.9% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b)))
✓	0.0b	(fma.f64 y (pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b))) x)
✓	0.0b	(+.f64 a 5/6)
✓	0.2b	(*.f64 (+.f64 a 5/6) (-.f64 c b))

series281.0ms (1.7%)

Counts

4 → 144

Calls

4 calls:

227.0ms	(fma.f64 y (pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b))) x)
33.0ms	(pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b)))
16.0ms	(*.f64 (+.f64 a 5/6) (-.f64 c b))
4.0ms	(+.f64 a 5/6)

rewrite27.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`*-un-lft-identity_binary64`
41×	`add-sqr-sqrt_binary64`
37×	`add-cube-cbrt_binary64`
36×	`prod-diff_binary64`
26×	`unpow-prod-up_binary64`

Counts

4 → 131

Calls

4 calls:

8.0ms	(*.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)
0.0ms	(fma.f64 y (pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b))) x)

simplify452.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

546×	`fma-def_binary64`
509×	`*-commutative_binary64`
305×	`associate-+r+_binary64`
262×	`+-commutative_binary64`
238×	`fma-neg_binary64`

Counts

275 → 257

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	542	7158
1	1519	6600
2	4157	6408
3	4937	6408
4	4966	6408

prune751.0ms (4.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	256	1	257
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	256	4	260

Error

Counts

260 → 4

Alt Table

Status	Error	Program
✓	2.4b	(/.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))
✓	19.8b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b))) x))
	20.4b	(/.f64 x (.f64 (.f64 (cbrt.f64 (fma.f64 y (pow.f64 (exp.f64 2) (.f64 (+.f64 a 5/6) (-.f64 c b))) x)) (cbrt.f64 (fma.f64 y (pow.f64 (exp.f64 2) (.f64 (+.f64 a 5/6) (-.f64 c b))) x))) (cbrt.f64 (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b))) x))))
✓	12.1b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (+.f64 (.f64 c (+.f64 a 5/6)) (+.f64 (/.f64 2/3 (/.f64 t (-.f64 b c))) (.f64 b -5/6)))) x))

Compiler

Compiled 9143 to 5330 computations (41.7% saved)

regimes3.8s (23.3%)

Accuracy

Total 2.1b remaining (97.2%)

Threshold costs 0b (0%)

Counts

115 → 2

Compiler

Compiled 40694 to 29788 computations (26.8% saved)

bsearch14.0ms (0.1%)

Compiler: Compiled 31 to 23 computations (25.8% saved)

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

16×	`+-commutative_binary64`
15×	`sub-neg_binary64`
13×	`*-commutative_binary64`
12×	`cancel-sign-sub-inv_binary64`
11×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	101
1	64	101
2	94	101
3	117	101
4	147	101
5	158	101
6	161	101
7	162	101
8	153	101

end281.0ms (1.7%)

Compiler: Compiled 291 to 189 computations (35.1% saved)

Iter	Nodes	Cost
0	45	101
1	64	101
2	94	101
3	117	101
4	147	101
5	158	101
6	161	101
7	162	101
8	153	101

Iter	Nodes	Cost
0	45	101
1	64	101
2	94	101
3	117	101
4	147	101
5	158	101
6	161	101
7	162	101
8	153	101

Details

analyze2.9s (17.4%)

sample4.6s (27.7%)

simplify88.0ms (0.5%)

prune6.0ms (0%)

localize37.0ms (0.2%)

series335.0ms (2%)

rewrite52.0ms (0.3%)

simplify262.0ms (1.6%)

prune559.0ms (3.4%)

localize56.0ms (0.3%)

series206.0ms (1.3%)

rewrite35.0ms (0.2%)

simplify197.0ms (1.2%)

prune430.0ms (2.6%)

localize37.0ms (0.2%)

series64.0ms (0.4%)

rewrite78.0ms (0.5%)

simplify336.0ms (2%)

prune579.0ms (3.5%)

localize22.0ms (0.1%)

series281.0ms (1.7%)

rewrite27.0ms (0.2%)

simplify452.0ms (2.7%)

prune751.0ms (4.6%)

regimes3.8s (23.3%)

bsearch14.0ms (0.1%)

simplify13.0ms (0.1%)

end281.0ms (1.7%)

Profiling

Iter	Nodes	Cost
0	45	101
1	64	101
2	94	101
3	117	101
4	147	101
5	158	101
6	161	101
7	162	101
8	153	101