Details

analyze500.0ms (10.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
12.5%	87.4%	0.1%	6
28.1%	71.8%	0.1%	7
42.1%	57.7%	0.1%	8
43.7%	56.2%	0.1%	9
64.4%	35.5%	0.1%	10
71.6%	28.3%	0.1%	11
72.2%	27.7%	0.1%	12
81.6%	18.2%	0.2%	13
84.9%	14.9%	0.2%	14

Compiler

Compiled 16 to 9 computations (43.8% saved)

sample1.1s (22.2%)

Results

874.0ms	8256×	body	128	valid
118.0ms	229×	body	128	invalid

Compiler

Compiled 47 to 26 computations (44.7% saved)

simplify72.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

669×	`fma-def_binary64`
505×	`times-frac_binary64`
497×	`div-sub_binary64`
469×	`neg-mul-1_binary64`
463×	`neg-sub0_binary64`

Counts

1 → 2

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	30	18
2	83	18
3	193	18
4	334	18
5	435	18
6	600	18
7	871	18
8	1369	16
9	3594	16
10	4298	16
11	4856	16

prune4.0ms (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

0.8b

Counts

3 → 2

Alt Table

Status	Error	Program
	18.5b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
▶	2.0b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))

Compiler

Compiled 84 to 47 computations (44% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 v (+.f64 t1 u))
✓	1.9b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))

series86.0ms (1.7%)

Counts

2 → 60

Calls

2 calls:

68.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
17.0ms	(/.f64 v (+.f64 t1 u))

rewrite39.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

223×	`times-frac_binary64`
181×	`add-sqr-sqrt_binary64`
174×	`*-un-lft-identity_binary64`
86×	`add-cube-cbrt_binary64`
38×	`difference-of-squares_binary64`

Counts

2 → 186

Calls

2 calls:

11.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
3.0ms	(/.f64 v (+.f64 t1 u))

simplify178.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

795×	`times-frac_binary64`
383×	`fma-def_binary64`
336×	`fma-neg_binary64`
293×	`associate-/l/_binary64`
286×	`distribute-rgt-in_binary64`

Counts

246 → 219

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	326	7288
1	848	7129
2	2435	7053
3	4601	7053
4	5003	7053

prune146.0ms (2.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	214	5	219
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	215	6	221

Error

0.4b

Counts

221 → 6

Alt Table

Status	Error	Program
	2.7b	(.f64 (.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (cbrt.f64 (/.f64 v (+.f64 t1 u)))) (/.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1))))
✓	2.0b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
	4.0b	(/.f64 v (*.f64 (-.f64 -1 (/.f64 u t1)) (+.f64 t1 u)))
▶	2.0b	(*.f64 (/.f64 v (+.f64 t1 u)) (/.f64 1 (-.f64 -1 (/.f64 u t1))))
	2.5b	(/.f64 1 (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u))))
	38.3b	(-.f64 (.f64 2 (/.f64 (.f64 (pow.f64 t1 2) v) (pow.f64 u 3))) (/.f64 (*.f64 t1 v) (pow.f64 u 2)))

Compiler

Compiled 5539 to 2072 computations (62.6% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 v (+.f64 t1 u))
✓	0.5b	(/.f64 1 (-.f64 -1 (/.f64 u t1)))
✓	1.9b	(*.f64 (/.f64 v (+.f64 t1 u)) (/.f64 1 (-.f64 -1 (/.f64 u t1))))

series76.0ms (1.5%)

Counts

2 → 60

Calls

2 calls:

66.0ms	(*.f64 (/.f64 v (+.f64 t1 u)) (/.f64 1 (-.f64 -1 (/.f64 u t1))))
10.0ms	(/.f64 1 (-.f64 -1 (/.f64 u t1)))

rewrite34.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

83×	`add-sqr-sqrt_binary64`
62×	`times-frac_binary64`
53×	`*-un-lft-identity_binary64`
31×	`add-cube-cbrt_binary64`
28×	`add-exp-log_binary64`

Counts

2 → 122

Calls

2 calls:

16.0ms	(*.f64 (/.f64 v (+.f64 t1 u)) (/.f64 1 (-.f64 -1 (/.f64 u t1))))
7.0ms	(/.f64 1 (-.f64 -1 (/.f64 u t1)))

simplify113.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

766×	`associate-/l*_binary64`
478×	`associate-*l/_binary64`
442×	`associate-/r*_binary64`
294×	`fma-neg_binary64`
258×	`fma-def_binary64`

Counts

182 → 202

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	214	3921
1	576	3621
2	1776	3532
3	4978	3523
4	5138	3523

prune199.0ms (4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	250	1	251
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	252	5	257

Error

0.4b

Counts

257 → 5

Alt Table

Status	Error	Program
✓	2.0b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
	4.0b	(/.f64 v (*.f64 (-.f64 -1 (/.f64 u t1)) (+.f64 t1 u)))
▶	2.5b	(/.f64 1 (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u))))
	26.3b	(*.f64 (/.f64 v (+.f64 t1 u)) (neg.f64 (/.f64 t1 u)))
	38.3b	(-.f64 (.f64 2 (/.f64 (.f64 (pow.f64 t1 2) v) (pow.f64 u 3))) (/.f64 (*.f64 t1 v) (pow.f64 u 2)))

Compiler

Compiled 5704 to 2592 computations (54.6% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 v (+.f64 t1 u))
✓	0.7b	(/.f64 1 (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u))))
✓	1.8b	(/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u)))

series93.0ms (1.9%)

Counts

2 → 72

Calls

2 calls:

68.0ms	(/.f64 1 (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u))))
24.0ms	(/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u)))

rewrite218.0ms (4.4%)

Algorithm

1×	rewrite-expression-head

Rules

1342×	`times-frac_binary64`
914×	`add-sqr-sqrt_binary64`
827×	`*-un-lft-identity_binary64`
459×	`add-cube-cbrt_binary64`
182×	`difference-of-squares_binary64`

Counts

2 → 634

Calls

2 calls:

31.0ms	(/.f64 1 (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u))))
13.0ms	(/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u)))

simplify938.0ms (18.9%)

Algorithm

1×	egg-herbie

Rules

589×	`associate-/r/_binary64`
484×	`fma-def_binary64`
320×	`associate-*l/_binary64`
313×	`*-commutative_binary64`
244×	`associate-*r/_binary64`

Counts

706 → 719

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	491	24821
1	1250	23497
2	4397	23441
3	4990	23441
4	4969	23441

prune550.0ms (11.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	768	0	768
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	768	5	773

Error

0.4b

Counts

773 → 5

Alt Table

Status	Error	Program
✓	2.0b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
▶	4.0b	(/.f64 v (*.f64 (-.f64 -1 (/.f64 u t1)) (+.f64 t1 u)))
✓	2.5b	(/.f64 1 (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u))))
	26.3b	(*.f64 (/.f64 v (+.f64 t1 u)) (neg.f64 (/.f64 t1 u)))
	38.3b	(-.f64 (.f64 2 (/.f64 (.f64 (pow.f64 t1 2) v) (pow.f64 u 3))) (/.f64 (*.f64 t1 v) (pow.f64 u 2)))

Compiler

Compiled 23218 to 9674 computations (58.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 -1 (/.f64 u t1)) (+.f64 t1 u))
✓	4.0b	(/.f64 v (*.f64 (-.f64 -1 (/.f64 u t1)) (+.f64 t1 u)))

series77.0ms (1.6%)

Counts

2 → 60

Calls

2 calls:

69.0ms	(/.f64 v (*.f64 (-.f64 -1 (/.f64 u t1)) (+.f64 t1 u)))
7.0ms	(*.f64 (-.f64 -1 (/.f64 u t1)) (+.f64 t1 u))

rewrite26.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
8×	`associate-/r/_binary64`

Counts

2 → 65

Calls

2 calls:

11.0ms	(/.f64 v (*.f64 (-.f64 -1 (/.f64 u t1)) (+.f64 t1 u)))
9.0ms	(*.f64 (-.f64 -1 (/.f64 u t1)) (+.f64 t1 u))

simplify91.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

872×	`times-frac_binary64`
537×	`associate-/l*_binary64`
512×	`fma-def_binary64`
278×	`fma-neg_binary64`
136×	`distribute-rgt-in_binary64`

Counts

125 → 128

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	182	2784
1	540	2563
2	1977	2500
3	4860	2500
4	5034	2500

prune83.0ms (1.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	128	5	133

Error

0.4b

Counts

133 → 5

Alt Table

Status	Error	Program
✓	2.0b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
✓	4.0b	(/.f64 v (*.f64 (-.f64 -1 (/.f64 u t1)) (+.f64 t1 u)))
✓	2.5b	(/.f64 1 (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u))))
	26.3b	(*.f64 (/.f64 v (+.f64 t1 u)) (neg.f64 (/.f64 t1 u)))
	38.3b	(-.f64 (.f64 2 (/.f64 (.f64 (pow.f64 t1 2) v) (pow.f64 u 3))) (/.f64 (*.f64 t1 v) (pow.f64 u 2)))

Compiler

Compiled 2769 to 1242 computations (55.1% saved)

regimes207.0ms (4.2%)

Accuracy

Total 1.2b remaining (87.6%)

Threshold costs 0b (0%)

Counts

60 → 1

Compiler

Compiled 4070 to 2554 computations (37.2% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`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	10	16
1	13	16
2	19	16
3	23	16
4	26	16
5	27	16
6	27	16

end98.0ms (2%)

Compiler: Compiled 107 to 71 computations (33.6% saved)

Details

analyze500.0ms (10.1%)

sample1.1s (22.2%)

simplify72.0ms (1.4%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

series86.0ms (1.7%)

rewrite39.0ms (0.8%)

simplify178.0ms (3.6%)

prune146.0ms (2.9%)

localize8.0ms (0.2%)

series76.0ms (1.5%)

rewrite34.0ms (0.7%)

simplify113.0ms (2.3%)

prune199.0ms (4%)

localize8.0ms (0.2%)

series93.0ms (1.9%)

rewrite218.0ms (4.4%)

simplify938.0ms (18.9%)

prune550.0ms (11.1%)

localize7.0ms (0.1%)

series77.0ms (1.6%)

rewrite26.0ms (0.5%)

simplify91.0ms (1.8%)

prune83.0ms (1.7%)

regimes207.0ms (4.2%)

simplify3.0ms (0.1%)

end98.0ms (2%)

Profiling