Details

analyze2.5s (34.1%)

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
0.3%	86.9%	12.8%	12
0.3%	80.7%	19%	13
0.4%	80.6%	19%	14

Compiler

Compiled 41 to 30 computations (26.8% saved)

sample2.8s (39.2%)

Results

1.8s	8256×	body	128	valid
1.1s	5150×	body	128	invalid

Compiler

Compiled 82 to 60 computations (26.8% saved)

preprocess45.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

417×	`fma-def_binary64`
285×	`associate-r_binary64`
266×	`associate-l_binary64`
250×	`associate--r+_binary64`
208×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	263	1034
1	602	924
2	1793	880
0	7	7

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 40 to 29 computations (27.5% saved)

simplify23.0ms (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

2.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	4.0b	(/.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))))))))))
▶	2.5b	(/.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

4.0b

(/.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))))))))))

▶

2.5b

(/.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)

localize19.0ms (0.3%)

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)
✓	2.7b	(fma.f64 z (/.f64 (sqrt.f64 (+.f64 t a)) t) (*.f64 (-.f64 b c) (-.f64 (/.f64 2/3 t) (+.f64 a 5/6))))

series114.0ms (1.6%)

Counts

4 → 104

Calls

36 calls:

7.0ms	(fma.f64 z (/.f64 (sqrt.f64 (+.f64 t a)) t) (*.f64 (-.f64 b c) (-.f64 (/.f64 2/3 t) (+.f64 a 5/6))))	b	0
6.0ms	(fma.f64 z (/.f64 (sqrt.f64 (+.f64 t a)) t) (*.f64 (-.f64 b c) (-.f64 (/.f64 2/3 t) (+.f64 a 5/6))))	z	inf
5.0ms	(/.f64 (sqrt.f64 (+.f64 t a)) t)	t	-inf
5.0ms	(/.f64 (sqrt.f64 (+.f64 t a)) t)	a	0
5.0ms	(fma.f64 z (/.f64 (sqrt.f64 (+.f64 t a)) t) (*.f64 (-.f64 b c) (-.f64 (/.f64 2/3 t) (+.f64 a 5/6))))	b	-inf

rewrite37.0ms (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

simplify61.0ms (0.8%)

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

prune150.0ms (2.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	144	2	146

Error

Counts

146 → 2

Alt Table

Status	Error	Program
✓	2.5b	(/.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))
▶	32.1b	(/.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))

Status

Error

Program

✓

2.5b

(/.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))

▶

32.1b

(/.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 5246 to 2811 computations (46.4% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))
✓	0.1b	(fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3)))
✓	0.3b	(*.f64 c -2/3)
✓	1.0b	(/.f64 (fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))) t)

series79.0ms (1.1%)

Counts

4 → 123

Calls

39 calls:

7.0ms	(/.f64 (fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))) t)	t	inf
6.0ms	(/.f64 (fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))) t)	b	inf
4.0ms	(fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3)))	a	-inf
4.0ms	(/.f64 (fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))) t)	t	-inf
3.0ms	(/.f64 (fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))) t)	a	-inf

rewrite58.0ms (0.8%)

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

simplify81.0ms (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

prune122.0ms (1.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	138	2	140

Error

Counts

140 → 2

Alt Table

Status	Error	Program
✓	2.5b	(/.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))
✓	32.1b	(/.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))

Status

Error

Program

✓

2.5b

(/.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))

✓

32.1b

(/.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 3515 to 2084 computations (40.7% saved)

regimes1.0s (13.9%)

Accuracy

Total 1.7b remaining (86.4%)

Threshold costs 0b (0%)

Counts

65 → 2

Compiler

Compiled 24309 to 17651 computations (27.4% saved)

bsearch31.0ms (0.4%)

Algorithm

1×	binary-search

Calls

1 calls:

28.0ms

Steps

Iters	Point		Range
1.4047430456158109e-278	∈ [	2.9324814831291963e-281	,	2.2385460131555342e-278	]

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`+-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	79
1	47	79
2	60	79
3	67	79
4	71	79
5	72	79

Stop Event

1×

saturated

end82.0ms (1.1%)

Stop Event

1×

done

Compiler

Compiled 181 to 122 computations (32.6% saved)

Details

analyze2.5s (34.1%)

sample2.8s (39.2%)

preprocess45.0ms (0.6%)

simplify23.0ms (0.3%)

prune5.0ms (0.1%)

localize19.0ms (0.3%)

series114.0ms (1.6%)

rewrite37.0ms (0.5%)

simplify61.0ms (0.8%)

prune150.0ms (2.1%)

localize15.0ms (0.2%)

series79.0ms (1.1%)

rewrite58.0ms (0.8%)

simplify81.0ms (1.1%)

prune122.0ms (1.7%)

regimes1.0s (13.9%)

bsearch31.0ms (0.4%)

simplify4.0ms (0.1%)

end82.0ms (1.1%)

Profiling