Details

analyze1.9s (29%)

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)

sample2.7s (42.5%)

Infinites

0% of outputs are infinite.

Results

1.7s	8256×	body	128	valid
965.0ms	5164×	body	128	invalid

Compiler

Compiled 122 to 89 computations (27% saved)

simplify46.0ms (0.7%)

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

prune4.0ms (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

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)

localize20.0ms (0.3%)

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)
✓	0.9b	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))
✓	5.9b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

series131.0ms (2%)

Counts

4 → 88

Calls

4 calls:

58.0ms	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))
40.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
31.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
1.0ms	(/.f64 2/3 t)

rewrite19.0ms (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:

7.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
6.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
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))

simplify122.0ms (1.9%)

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

prune200.0ms (3.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	188	1	189
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	188	2	190

Error

0.0b

Counts

190 → 2

Alt Table

Status	Error	Program
▶	9.9b	(/.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))
✓	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))

Status

Error

Program

▶

9.9b

(/.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))

✓

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 6921 to 3485 computations (49.6% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (/.f64 c t) -2/3)
✓	0.3b	(fma.f64 b (-.f64 -5/6 a) (*.f64 (/.f64 c t) -2/3))
✓	2.0b	(+.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))))
✓	2.6b	(fma.f64 2/3 (/.f64 b t) (fma.f64 b (-.f64 -5/6 a) (*.f64 (/.f64 c t) -2/3)))

series86.0ms (1.3%)

Counts

4 → 168

Calls

4 calls:

33.0ms	(+.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))))
26.0ms	(fma.f64 2/3 (/.f64 b t) (fma.f64 b (-.f64 -5/6 a) (*.f64 (/.f64 c t) -2/3)))
21.0ms	(fma.f64 b (-.f64 -5/6 a) (*.f64 (/.f64 c t) -2/3))
6.0ms	(*.f64 (/.f64 c t) -2/3)

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

5.0ms	(+.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))))
4.0ms	(*.f64 (/.f64 c t) -2/3)
0.0ms	(fma.f64 2/3 (/.f64 b t) (fma.f64 b (-.f64 -5/6 a) (*.f64 (/.f64 c t) -2/3)))
0.0ms	(fma.f64 b (-.f64 -5/6 a) (*.f64 (/.f64 c t) -2/3))

simplify155.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

615×	`distribute-rgt-in_binary64`
596×	`distribute-lft-in_binary64`
437×	`fma-def_binary64`
191×	`associate-*l/_binary64`
165×	`associate-*r/_binary64`

Counts

239 → 153

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	174	4599
1	440	4117
2	1271	4115
3	4873	4008
4	5000	4008
5	4968	4008

prune187.0ms (2.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	153	2	155

Error

0.0b

Counts

155 → 2

Alt Table

Status	Error	Program
✓	9.9b	(/.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))
✓	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))

Status

Error

Program

✓

9.9b

(/.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))

✓

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 5354 to 3063 computations (42.8% saved)

regimes755.0ms (11.7%)

Accuracy

Total 1.5b remaining (74.2%)

Threshold costs 0b (0%)

Counts

52 → 1

Compiler

Compiled 20941 to 15049 computations (28.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	40
1	30	40
2	41	40
3	45	40
4	47	40
5	46	40

end75.0ms (1.2%)

Compiler: Compiled 138 to 94 computations (31.9% saved)

Details

analyze1.9s (29%)

sample2.7s (42.5%)

simplify46.0ms (0.7%)

prune4.0ms (0.1%)

localize20.0ms (0.3%)

series131.0ms (2%)

rewrite19.0ms (0.3%)

simplify122.0ms (1.9%)

prune200.0ms (3.1%)

localize22.0ms (0.3%)

series86.0ms (1.3%)

rewrite12.0ms (0.2%)

simplify155.0ms (2.4%)

prune187.0ms (2.9%)

regimes755.0ms (11.7%)

simplify3.0ms (0%)

end75.0ms (1.2%)

Profiling