Details

analyze2.8s (19.9%)

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
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	87.2%	12.8%	12
0%	81%	19%	13
0%	81%	19%	14

Compiler

Compiled 41 to 30 computations (26.8% saved)

sample3.2s (22.8%)

Results

1.9s	8256×	body	128	valid
1.2s	5117×	body	128	invalid

Compiler

Compiled 81 to 59 computations (27.2% saved)

simplify46.0ms (0.3%)

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

prune5.0ms (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

3.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	3.2b	(/.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 (*.f64 z (sqrt.f64 (+.f64 t a))) t))) x))

Compiler

Compiled 135 to 87 computations (35.6% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 z (sqrt.f64 (+.f64 t a)))
✓	0.4b	(/.f64 2/3 t)
✓	1.8b	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))
✓	4.7b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

series153.0ms (1.1%)

Counts

4 → 88

Calls

4 calls:

71.0ms	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))
47.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
33.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
1.0ms	(/.f64 2/3 t)

rewrite17.0ms (0.1%)

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:

5.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
5.0ms	(*.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))

simplify133.0ms (0.9%)

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

prune223.0ms (1.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	187	2	189
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	187	3	190

Error

0.0b

Counts

190 → 3

Alt Table

Status	Error	Program
✓	3.2b	(/.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 (*.f64 z (sqrt.f64 (+.f64 t a))) t))) x))
	18.7b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 b (-.f64 (/.f64 2/3 t) (+.f64 a 5/6)))) x))
▶	17.9b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))) x))

Compiler

Compiled 6945 to 3507 computations (49.5% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 a 5/6)
✓	0.0b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))) x))
✓	0.1b	(*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))
	0.4b	(/.f64 2/3 t)

series341.0ms (2.4%)

Counts

3 → 108

Calls

3 calls:

322.0ms	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))) x))
16.0ms	(*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))
2.0ms	(+.f64 a 5/6)

rewrite45.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

169×	`*-un-lft-identity_binary64`
117×	`add-sqr-sqrt_binary64`
110×	`add-cube-cbrt_binary64`
104×	`prod-diff_binary64`
100×	`times-frac_binary64`

Counts

3 → 208

Calls

3 calls:

14.0ms	(*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))
3.0ms	(+.f64 a 5/6)
2.0ms	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))) x))

simplify223.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

696×	`associate-/l*_binary64`
513×	`associate-/r*_binary64`
350×	`fma-def_binary64`
282×	`*-commutative_binary64`
122×	`distribute-rgt-in_binary64`

Counts

316 → 301

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	802	14639
1	2254	12117
2	5488	12117

prune477.0ms (3.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	332	2	334
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	333	4	337

Error

Counts

337 → 4

Alt Table

Status	Error	Program
▶	17.9b	(/.f64 1 (/.f64 (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))) x) x))
✓	3.2b	(/.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 (*.f64 z (sqrt.f64 (+.f64 t a))) t))) x))
	18.7b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 b (-.f64 (/.f64 2/3 t) (+.f64 a 5/6)))) x))
	18.5b	(.f64 (sqrt.f64 (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))) x))) (sqrt.f64 (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))) x))))

Compiler

Compiled 15414 to 10147 computations (34.2% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 a 5/6)
✓	0.0b	(/.f64 1 (/.f64 (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))) x) x))
	0.1b	(*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))
	0.4b	(/.f64 2/3 t)

series316.0ms (2.2%)

Counts

1 → 60

Calls

1 calls:

315.0ms

(/.f64 1 (/.f64 (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))) x) x))

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac_binary64`
43×	`*-un-lft-identity_binary64`
43×	`add-sqr-sqrt_binary64`
43×	`add-cube-cbrt_binary64`
13×	`associate-/r*_binary64`

Counts

1 → 78

Calls

1 calls:

4.0ms

(/.f64 1 (/.f64 (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))) x) x))

simplify145.0ms (1%)

Algorithm

1×	egg-herbie

Rules

652×	`associate-/l*_binary64`
521×	`associate-/r*_binary64`
298×	`fma-def_binary64`
244×	`associate-*r/_binary64`
220×	`associate-*l/_binary64`

Counts

138 → 152

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	500	9320
1	1665	9007
2	5028	9007

prune622.0ms (4.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	391	0	391
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	391	4	395

Error

Counts

395 → 4

Alt Table

Status	Error	Program
✓	17.9b	(/.f64 1 (/.f64 (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))) x) x))
✓	3.2b	(/.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 (*.f64 z (sqrt.f64 (+.f64 t a))) t))) x))
	18.7b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 b (-.f64 (/.f64 2/3 t) (+.f64 a 5/6)))) x))
▶	18.5b	(.f64 (sqrt.f64 (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))) x))) (sqrt.f64 (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))) x))))

Compiler

Compiled 18322 to 12351 computations (32.6% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (sqrt.f64 (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))) x))) (sqrt.f64 (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))) x))))
	0.1b	(*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))
	0.4b	(/.f64 2/3 t)
✓	1.7b	(sqrt.f64 (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))) x)))

series968.0ms (6.8%)

Counts

2 → 108

Calls

2 calls:

671.0ms

(sqrt.f64 (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))) x)))

296.0ms

(*.f64 (sqrt.f64 (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))) x))) (sqrt.f64 (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))) x))))

rewrite40.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`add-sqr-sqrt_binary64`
79×	`sqrt-prod_binary64`
58×	`times-frac_binary64`
41×	`*-un-lft-identity_binary64`
41×	`add-cube-cbrt_binary64`

Counts

2 → 122

Calls

2 calls:

14.0ms

(*.f64 (sqrt.f64 (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))) x))) (sqrt.f64 (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))) x))))

2.0ms

(sqrt.f64 (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))) x)))

simplify268.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

917×	`fma-def_binary64`
681×	`associate-/r*_binary64`
444×	`*-commutative_binary64`
221×	`associate-r_binary64`
192×	`+-commutative_binary64`

Counts

230 → 251

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1035	17516
1	3234	16852
2	5988	16852

prune1.7s (12%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	750	0	750
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	750	4	754

Error

Counts

754 → 4

Alt Table

Status	Error	Program
✓	17.9b	(/.f64 1 (/.f64 (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))) x) x))
✓	3.2b	(/.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 (*.f64 z (sqrt.f64 (+.f64 t a))) t))) x))
	18.7b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 b (-.f64 (/.f64 2/3 t) (+.f64 a 5/6)))) x))
✓	18.5b	(.f64 (sqrt.f64 (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))) x))) (sqrt.f64 (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))) x))))

Compiler

Compiled 54397 to 36373 computations (33.1% saved)

regimes2.2s (15.5%)

Accuracy

Total 1.8b remaining (99.8%)

Threshold costs 0b (0%)

Counts

114 → 1

Compiler

Compiled 43430 to 32547 computations (25.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	40
1	31	40
2	42	40
3	46	40
4	48	40
5	47	40

end126.0ms (0.9%)

Compiler: Compiled 196 to 139 computations (29.1% saved)

Details

analyze2.8s (19.9%)

sample3.2s (22.8%)

simplify46.0ms (0.3%)

prune5.0ms (0%)

localize21.0ms (0.1%)

series153.0ms (1.1%)

rewrite17.0ms (0.1%)

simplify133.0ms (0.9%)

prune223.0ms (1.6%)

localize13.0ms (0.1%)

series341.0ms (2.4%)

rewrite45.0ms (0.3%)

simplify223.0ms (1.6%)

prune477.0ms (3.4%)

localize17.0ms (0.1%)

series316.0ms (2.2%)

rewrite15.0ms (0.1%)

simplify145.0ms (1%)

prune622.0ms (4.4%)

localize17.0ms (0.1%)

series968.0ms (6.8%)

rewrite40.0ms (0.3%)

simplify268.0ms (1.9%)

prune1.7s (12%)

regimes2.2s (15.5%)

simplify3.0ms (0%)

end126.0ms (0.9%)

Profiling