Details

analyze2.2s (27.7%)

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)

sample2.9s (36.1%)

Results

1.7s	8256×	body	128	valid
1.1s	5285×	body	128	invalid

Compiler

Compiled 122 to 89 computations (27% saved)

simplify27.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

433×	`exp-sum_binary64`
311×	`distribute-rgt-in_binary64`
293×	`distribute-lft-in_binary64`
250×	`fma-neg_binary64`
202×	`exp-prod_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	47
1	55	42
2	138	40
3	631	40
4	3487	40

Stop Event

1×	node limit

Counts

1 → 2

prune5.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

1.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	2.5b	(/.f64 x (+.f64 x (.f64 y (exp.f64 (.f64 2 (-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3))))))))))
▶	2.0b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 z (/.f64 (sqrt.f64 (+.f64 t a)) t) (*.f64 (-.f64 b c) (-.f64 (/.f64 2/3 t) (+.f64 a 5/6))))) x))

Status

Error

Program

2.5b

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

▶

2.0b

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

Compiler

Compiled 215 to 146 computations (32.1% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (-.f64 b c) (-.f64 (/.f64 2/3 t) (+.f64 a 5/6)))
✓	0.2b	(/.f64 (sqrt.f64 (+.f64 t a)) t)
✓	0.4b	(/.f64 2/3 t)
✓	2.0b	(fma.f64 z (/.f64 (sqrt.f64 (+.f64 t a)) t) (*.f64 (-.f64 b c) (-.f64 (/.f64 2/3 t) (+.f64 a 5/6))))

series106.0ms (1.3%)

Counts

4 → 104

Calls

4 calls:

61.0ms	(fma.f64 z (/.f64 (sqrt.f64 (+.f64 t a)) t) (*.f64 (-.f64 b c) (-.f64 (/.f64 2/3 t) (+.f64 a 5/6))))
22.0ms	(*.f64 (-.f64 b c) (-.f64 (/.f64 2/3 t) (+.f64 a 5/6)))
21.0ms	(/.f64 (sqrt.f64 (+.f64 t a)) t)
1.0ms	(/.f64 2/3 t)

rewrite40.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

201×	`add-sqr-sqrt_binary64`
194×	`log1p-expm1-u_binary64`
194×	`expm1-log1p-u_binary64`
193×	`add-cbrt-cube_binary64`
188×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	57
1	393	57

Stop Event

1×	node limit

Counts

4 → 88

Calls

4 calls:

38.0ms	(*.f64 (-.f64 b c) (-.f64 (/.f64 2/3 t) (+.f64 a 5/6)))
38.0ms	(/.f64 (sqrt.f64 (+.f64 t a)) t)
38.0ms	(/.f64 2/3 t)
38.0ms	(fma.f64 z (/.f64 (sqrt.f64 (+.f64 t a)) t) (*.f64 (-.f64 b c) (-.f64 (/.f64 2/3 t) (+.f64 a 5/6))))

simplify70.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

584×	`associate--r+_binary64`
319×	`associate-l_binary64`
289×	`cancel-sign-sub-inv_binary64`
272×	`associate-r_binary64`
242×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	174	3452
1	588	3366
2	2040	3337

Stop Event

1×	node limit

Counts

192 → 144

prune206.0ms (2.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	143	3	146

Error

Counts

146 → 3

Alt Table

Status	Error	Program
▶	2.5b	(/.f64 x (+.f64 x (.f64 y (exp.f64 (.f64 2 (-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3))))))))))
✓	2.0b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 z (/.f64 (sqrt.f64 (+.f64 t a)) t) (*.f64 (-.f64 b c) (-.f64 (/.f64 2/3 t) (+.f64 a 5/6))))) x))
	26.5b	(/.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 5326 to 2869 computations (46.1% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 z (sqrt.f64 (+.f64 t a)))
✓	0.2b	(/.f64 2 (*.f64 t 3))
✓	1.3b	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3)))))
✓	4.2b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

series135.0ms (1.7%)

Counts

4 → 100

Calls

4 calls:

75.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3)))))
33.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
24.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
1.0ms	(/.f64 2 (*.f64 t 3))

rewrite46.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

257×	`add-sqr-sqrt_binary64`
252×	`log1p-expm1-u_binary64`
252×	`expm1-log1p-u_binary64`
249×	`add-cbrt-cube_binary64`
242×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	61
1	515	61

Stop Event

1×	node limit

Counts

4 → 85

Calls

4 calls:

44.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
44.0ms	(/.f64 2 (*.f64 t 3))
44.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3)))))
44.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

simplify62.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

583×	`associate--r+_binary64`
467×	`associate-r_binary64`
432×	`associate-l_binary64`
416×	`cancel-sign-sub-inv_binary64`
254×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	183	2775
1	621	2727
2	2215	2706

Stop Event

1×	node limit

Counts

185 → 159

prune232.0ms (2.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	159	3	162

Error

Counts

162 → 3

Alt Table

Status	Error	Program
✓	2.5b	(/.f64 x (+.f64 x (.f64 y (exp.f64 (.f64 2 (-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3))))))))))
✓	2.0b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 z (/.f64 (sqrt.f64 (+.f64 t a)) t) (*.f64 (-.f64 b c) (-.f64 (/.f64 2/3 t) (+.f64 a 5/6))))) x))
▶	26.5b	(/.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 7038 to 4129 computations (41.3% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3)))
✓	0.1b	(fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))
✓	0.4b	(*.f64 c -2/3)
✓	1.0b	(/.f64 (fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))) t)

series80.0ms (1%)

Counts

4 → 123

Calls

4 calls:

43.0ms	(/.f64 (fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))) t)
24.0ms	(fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3)))
11.0ms	(fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))
1.0ms	(*.f64 c -2/3)

rewrite59.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

595×	`log-prod_binary64`
233×	`expm1-udef_binary64`
233×	`log1p-udef_binary64`
211×	`log-pow_binary64`
203×	`prod-diff_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	45
1	264	45
2	3133	45

Stop Event

1×	node limit

Counts

4 → 111

Calls

4 calls:

57.0ms	(fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3)))
57.0ms	(fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))
57.0ms	(*.f64 c -2/3)
57.0ms	(/.f64 (fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))) t)

simplify89.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1287×	`fma-neg_binary64`
622×	`fma-def_binary64`
364×	`cancel-sign-sub-inv_binary64`
186×	`div-sub_binary64`
173×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	34	1707
1	84	1535
2	201	1508
3	406	1391
4	983	1391
5	2076	1391
6	4057	1391
7	4988	1391

Stop Event

1×	node limit

Counts

234 → 138

prune150.0ms (1.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	138	3	141

Error

Counts

141 → 3

Alt Table

Status	Error	Program
✓	2.5b	(/.f64 x (+.f64 x (.f64 y (exp.f64 (.f64 2 (-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3))))))))))
✓	2.0b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 z (/.f64 (sqrt.f64 (+.f64 t a)) t) (*.f64 (-.f64 b c) (-.f64 (/.f64 2/3 t) (+.f64 a 5/6))))) x))
✓	26.5b	(/.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 3564 to 2119 computations (40.5% saved)

regimes1.4s (17.2%)

Accuracy

Total 2.3b remaining (94.8%)

Threshold costs 0b (0%)

Counts

88 → 2

Compiler

Compiled 33773 to 24619 computations (27.1% saved)

bsearch50.0ms (0.6%)

Steps

Iters	Range		Point
7	-2.830656375953118e-308	6.328255161692309e-307	6.2302169661545616e-307

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	76
1	48	76
2	60	76
3	67	76
4	71	76
5	72	76

Stop Event

1×

saturated

end98.0ms (1.2%)

Compiler: Compiled 217 to 151 computations (30.4% saved)

Details

analyze2.2s (27.7%)

sample2.9s (36.1%)

simplify27.0ms (0.3%)

prune5.0ms (0.1%)

localize20.0ms (0.2%)

series106.0ms (1.3%)

rewrite40.0ms (0.5%)

simplify70.0ms (0.9%)

prune206.0ms (2.6%)

localize23.0ms (0.3%)

series135.0ms (1.7%)

rewrite46.0ms (0.6%)

simplify62.0ms (0.8%)

prune232.0ms (2.9%)

localize15.0ms (0.2%)

series80.0ms (1%)

rewrite59.0ms (0.7%)

simplify89.0ms (1.1%)

prune150.0ms (1.9%)

regimes1.4s (17.2%)

bsearch50.0ms (0.6%)

simplify4.0ms (0.1%)

end98.0ms (1.2%)

Profiling