Details

analyze415.0ms (8.3%)

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)

sample137.0ms (2.7%)

Algorithm

1×

intervals

Results

42.0ms	256×	body	128	valid
0.0ms	7×	body	128	invalid

Compiler

Compiled 34 to 20 computations (41.2% saved)

simplify70.0ms (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

0.7b

Counts

3 → 2

Alt Table

Status	Error	Program
	17.5b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
▶	2.8b	(/.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))
✓	2.8b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))

series87.0ms (1.7%)

Counts

2 → 60

Calls

2 calls:

70.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
16.0ms	(/.f64 v (+.f64 t1 u))

rewrite40.0ms (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:

12.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
4.0ms	(/.f64 v (+.f64 t1 u))

simplify228.0ms (4.5%)

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

prune153.0ms (3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	215	4	219
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	215	6	221

Error

0.6b

Counts

221 → 6

Alt Table

Status	Error	Program
	48.2b	(/.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (sqrt.f64 (-.f64 -1 (/.f64 u t1)))) (sqrt.f64 (-.f64 -1 (/.f64 u t1))))
	29.3b	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 t1 u))) (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (sqrt.f64 (+.f64 t1 u)))))
	17.5b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	4.9b	(/.f64 v (*.f64 (-.f64 -1 (/.f64 u t1)) (+.f64 t1 u)))
▶	3.4b	(/.f64 1 (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u))))
✓	2.8b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))

Compiler

Compiled 5523 to 2064 computations (62.6% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 v (+.f64 t1 u))
✓	0.8b	(/.f64 1 (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u))))
✓	2.7b	(/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u)))

series94.0ms (1.9%)

Counts

2 → 72

Calls

2 calls:

69.0ms	(/.f64 1 (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u))))
25.0ms	(/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u)))

rewrite214.0ms (4.3%)

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:

25.0ms	(/.f64 1 (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u))))
17.0ms	(/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u)))

simplify623.0ms (12.4%)

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

prune551.0ms (11%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	767	1	768
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	770	4	774

Error

0.6b

Counts

774 → 4

Alt Table

Status	Error	Program
▶	3.4b	(/.f64 1 (*.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 (+.f64 t1 u) v)))
✓	2.8b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
	48.2b	(/.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (sqrt.f64 (-.f64 -1 (/.f64 u t1)))) (sqrt.f64 (-.f64 -1 (/.f64 u t1))))
	17.5b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))

Compiler

Compiled 23210 to 9663 computations (58.4% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 t1 u) v)
✓	0.8b	(/.f64 1 (*.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 (+.f64 t1 u) v)))
✓	2.6b	(*.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 (+.f64 t1 u) v))

series110.0ms (2.2%)

Counts

3 → 96

Calls

3 calls:

74.0ms	(/.f64 1 (*.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 (+.f64 t1 u) v)))
27.0ms	(*.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 (+.f64 t1 u) v))
9.0ms	(/.f64 (+.f64 t1 u) v)

rewrite37.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`*-un-lft-identity_binary64`
33×	`add-sqr-sqrt_binary64`
31×	`add-exp-log_binary64`
29×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`

Counts

3 → 118

Calls

3 calls:

13.0ms	(*.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 (+.f64 t1 u) v))
12.0ms	(/.f64 1 (*.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 (+.f64 t1 u) v)))
4.0ms	(/.f64 (+.f64 t1 u) v)

simplify157.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

907×	`times-frac_binary64`
409×	`distribute-rgt-in_binary64`
405×	`fma-def_binary64`
219×	`fma-neg_binary64`
107×	`*-commutative_binary64`

Counts

214 → 190

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	230	4279
1	606	3942
2	2043	3713
3	4744	3713
4	4970	3713

prune107.0ms (2.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	190	0	190
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	190	4	194

Error

0.6b

Counts

194 → 4

Alt Table

Status	Error	Program
✓	3.4b	(/.f64 1 (*.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 (+.f64 t1 u) v)))
✓	2.8b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
	48.2b	(/.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (sqrt.f64 (-.f64 -1 (/.f64 u t1)))) (sqrt.f64 (-.f64 -1 (/.f64 u t1))))
▶	17.5b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))

Compiler

Compiled 3965 to 1759 computations (55.6% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 t1 u) (+.f64 t1 u))
✓	17.3b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))

series106.0ms (2.1%)

Counts

2 → 60

Calls

2 calls:

95.0ms	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
11.0ms	(*.f64 (+.f64 t1 u) (+.f64 t1 u))

rewrite162.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
12×	`flip-+_binary64`
12×	`flip3-+_binary64`

Counts

2 → 74

Calls

2 calls:

148.0ms	(*.f64 (+.f64 t1 u) (+.f64 t1 u))
9.0ms	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))

simplify248.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

772×	`fma-def_binary64`
325×	`distribute-frac-neg_binary64`
267×	`distribute-rgt-neg-out_binary64`
259×	`distribute-lft-neg-out_binary64`
220×	`times-frac_binary64`

Counts

134 → 131

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	159	2754
1	495	2362
2	2240	2301
3	4672	2301
4	4992	2301

prune151.0ms (3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	129	2	131
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	130	5	135

Error

Counts

135 → 5

Alt Table

Status	Error	Program
✓	3.4b	(/.f64 1 (*.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 (+.f64 t1 u) v)))
✓	2.8b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
	17.7b	(/.f64 (neg.f64 t1) (/.f64 (pow.f64 (+.f64 t1 u) 2) v))
	48.2b	(/.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (sqrt.f64 (-.f64 -1 (/.f64 u t1)))) (sqrt.f64 (-.f64 -1 (/.f64 u t1))))
	9.7b	(/.f64 (/.f64 (*.f64 (neg.f64 t1) v) (+.f64 t1 u)) (+.f64 t1 u))

Compiler

Compiled 2757 to 826 computations (70% saved)

regimes502.0ms (10%)

Accuracy

Total 1.6b remaining (98.6%)

Threshold costs 0b (0%)

Counts

98 → 3

Compiler

Compiled 7562 to 4754 computations (37.1% saved)

bsearch78.0ms (1.5%)

Steps

Iters	Range		Point
6	2.3884443155416435e+144	2.4964466798547254e+145	2.430746947258446e+144
6	2.7511780142472355e+83	4.327804902687262e+84	1.0610017015882892e+84

Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

15×	`*-commutative_binary64`
12×	`+-commutative_binary64`
11×	`sub-neg_binary64`
11×	`neg-sub0_binary64`
11×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	67
1	40	67
2	60	67
3	81	67
4	96	67
5	104	67
6	106	67
7	105	67

end1.0ms (0%)

Compiler: Compiled 48 to 24 computations (50% saved)

sample713.0ms (14.2%)

Algorithm

1×

intervals

Results

371.0ms	8000×	body	128	valid
12.0ms	245×	body	128	invalid

Compiler

Compiled 147 to 87 computations (40.8% saved)

Details

analyze415.0ms (8.3%)

sample137.0ms (2.7%)

simplify70.0ms (1.4%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

series87.0ms (1.7%)

rewrite40.0ms (0.8%)

simplify228.0ms (4.5%)

prune153.0ms (3%)

localize9.0ms (0.2%)

series94.0ms (1.9%)

rewrite214.0ms (4.3%)

simplify623.0ms (12.4%)

prune551.0ms (11%)

localize8.0ms (0.2%)

series110.0ms (2.2%)

rewrite37.0ms (0.7%)

simplify157.0ms (3.1%)

prune107.0ms (2.1%)

localize10.0ms (0.2%)

series106.0ms (2.1%)

rewrite162.0ms (3.2%)

simplify248.0ms (4.9%)

prune151.0ms (3%)

regimes502.0ms (10%)

bsearch78.0ms (1.5%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample713.0ms (14.2%)

Profiling