Details

analyze218.0ms (4.8%)

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
25%	74.9%	0.1%	5
25%	68.7%	6.3%	6
25%	56.2%	18.8%	7
25%	48.4%	26.6%	8
25%	35.1%	39.9%	9
28.1%	18.3%	53.6%	10
31.6%	12.3%	56.1%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 34 to 22 computations (35.3% saved)

sample97.0ms (2.1%)

Algorithm

1×

intervals

Results

39.0ms

256×

body

128

valid

Compiler

Compiled 69 to 45 computations (34.8% saved)

simplify58.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

725×	`fma-def_binary64`
669×	`unsub-neg_binary64`
596×	`cancel-sign-sub-inv_binary64`
340×	`+-commutative_binary64`
277×	`fma-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	20	42
1	63	40
2	170	36
3	542	36
4	1867	32
5	3281	32
6	4881	32
7	4958	32

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
▶	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)

Status

Error

Program

0.2b

(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))))) 1)

▶

0.0b

(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)

Compiler

Compiled 172 to 108 computations (37.2% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
✓	0.0b	(pow.f64 (hypot.f64 a b) 4)
✓	0.1b	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
✓	0.7b	(.f64 (.f64 b b) (fma.f64 a -3 1))

series99.0ms (2.2%)

Counts

4 → 96

Calls

4 calls:

39.0ms	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
36.0ms	(pow.f64 (hypot.f64 a b) 4)
13.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
10.0ms	(.f64 (.f64 b b) (fma.f64 a -3 1))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-exp-log_binary64`
10×	`pow1_binary64`
9×	`add-cbrt-cube_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64`

Counts

4 → 63

Calls

4 calls:

4.0ms	(.f64 (.f64 b b) (fma.f64 a -3 1))
1.0ms	(pow.f64 (hypot.f64 a b) 4)
0.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
0.0ms	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))

simplify116.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

821×	`fma-def_binary64`
417×	`fma-neg_binary64`
408×	`associate-+l+_binary64`
315×	`cancel-sign-sub-inv_binary64`
250×	`exp-prod_binary64`

Counts

159 → 140

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	149	3218
1	364	2814
2	1065	2628
3	3367	2622
4	4754	2618
5	4990	2618

prune185.0ms (4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	138	2	140
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	140	2	142

Error

0.0b

Counts

142 → 2

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4)))) -1)
	12.3b	(+.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (pow.f64 a 3)) (pow.f64 a 4))) -1)

Status

Error

Program

▶

0.0b

(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4)))) -1)

12.3b

(+.f64 (+.f64 (*.f64 4 (pow.f64 a 2)) (+.f64 (*.f64 4 (pow.f64 a 3)) (pow.f64 a 4))) -1)

Compiler

Compiled 4077 to 2250 computations (44.8% saved)

localize22.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))))
	0.1b	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
	0.7b	(.f64 (.f64 b b) (fma.f64 a -3 1))
✓	1.4b	(*.f64 (pow.f64 a 2) (pow.f64 b 2))

series40.0ms (0.9%)

Counts

2 → 24

Calls

2 calls:

27.0ms

(fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))))

13.0ms

(*.f64 (pow.f64 a 2) (pow.f64 b 2))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
16×	`unswap-sqr_binary64`
14×	`unpow-prod-down_binary64`
14×	`add-exp-log_binary64`
10×	`sqr-pow_binary64`

Counts

2 → 63

Calls

2 calls:

7.0ms

(*.f64 (pow.f64 a 2) (pow.f64 b 2))

0.0ms

(fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))))

simplify74.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

746×	`distribute-rgt-in_binary64`
701×	`fma-def_binary64`
420×	`associate-+l+_binary64`
232×	`associate-+r+_binary64`
218×	`*-commutative_binary64`

Counts

87 → 111

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	133	1938
1	297	1757
2	929	1569
3	2990	1514
4	5413	1514

prune251.0ms (5.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	177	0	177
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	177	2	179

Error

0.0b

Counts

179 → 2

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4)))) -1)
▶	12.3b	(+.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (pow.f64 a 3)) (pow.f64 a 4))) -1)

Status

Error

Program

✓

0.0b

(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4)))) -1)

▶

12.3b

(+.f64 (+.f64 (*.f64 4 (pow.f64 a 2)) (+.f64 (*.f64 4 (pow.f64 a 3)) (pow.f64 a 4))) -1)

Compiler

Compiled 6999 to 4401 computations (37.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 4 (pow.f64 a 2))
✓	0.0b	(*.f64 4 (pow.f64 a 3))
✓	0.0b	(+.f64 (*.f64 4 (pow.f64 a 3)) (pow.f64 a 4))
✓	0.0b	(+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (pow.f64 a 3)) (pow.f64 a 4)))

series16.0ms (0.3%)

Counts

4 → 9

Calls

4 calls:

4.0ms	(+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (pow.f64 a 3)) (pow.f64 a 4)))
4.0ms	(+.f64 (*.f64 4 (pow.f64 a 3)) (pow.f64 a 4))
4.0ms	(*.f64 4 (pow.f64 a 2))
3.0ms	(*.f64 4 (pow.f64 a 3))

rewrite27.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
20×	`associate-r_binary64`
14×	`add-exp-log_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

4 → 92

Calls

4 calls:

8.0ms	(+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (pow.f64 a 3)) (pow.f64 a 4)))
6.0ms	(*.f64 4 (pow.f64 a 3))
5.0ms	(+.f64 (*.f64 4 (pow.f64 a 3)) (pow.f64 a 4))
4.0ms	(*.f64 4 (pow.f64 a 2))

simplify116.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

1098×	`fma-neg_binary64`
569×	`fma-def_binary64`
299×	`*-commutative_binary64`
278×	`distribute-rgt-in_binary64`
244×	`distribute-lft-in_binary64`

Counts

101 → 136

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	138	1265
1	334	1117
2	1000	1055
3	3454	1053
4	4438	1053
5	4772	1053
6	4928	1053

prune174.0ms (3.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	136	2	138

Error

Counts

138 → 2

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4)))) -1)
▶	56.7b	(+.f64 (+.f64 (*.f64 4 (pow.f64 a 2)) (/.f64 (fma.f64 64 (pow.f64 a 9) (pow.f64 a 12)) (fma.f64 16 (pow.f64 a 6) (fma.f64 -4 (pow.f64 a 7) (pow.f64 a 8))))) -1)

Status

Error

Program

✓

0.0b

(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4)))) -1)

▶

56.7b

(+.f64 (+.f64 (*.f64 4 (pow.f64 a 2)) (/.f64 (fma.f64 64 (pow.f64 a 9) (pow.f64 a 12)) (fma.f64 16 (pow.f64 a 6) (fma.f64 -4 (pow.f64 a 7) (pow.f64 a 8))))) -1)

Compiler

Compiled 3210 to 2586 computations (19.4% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 4 (pow.f64 a 2)) (/.f64 (fma.f64 64 (pow.f64 a 9) (pow.f64 a 12)) (fma.f64 16 (pow.f64 a 6) (fma.f64 -4 (pow.f64 a 7) (pow.f64 a 8)))))
✓	2.0b	(fma.f64 -4 (pow.f64 a 7) (pow.f64 a 8))
✓	2.2b	(fma.f64 64 (pow.f64 a 9) (pow.f64 a 12))
✓	56.0b	(/.f64 (fma.f64 64 (pow.f64 a 9) (pow.f64 a 12)) (fma.f64 16 (pow.f64 a 6) (fma.f64 -4 (pow.f64 a 7) (pow.f64 a 8))))

series25.0ms (0.6%)

Counts

4 → 48

Calls

4 calls:

9.0ms	(/.f64 (fma.f64 64 (pow.f64 a 9) (pow.f64 a 12)) (fma.f64 16 (pow.f64 a 6) (fma.f64 -4 (pow.f64 a 7) (pow.f64 a 8))))
7.0ms	(+.f64 (*.f64 4 (pow.f64 a 2)) (/.f64 (fma.f64 64 (pow.f64 a 9) (pow.f64 a 12)) (fma.f64 16 (pow.f64 a 6) (fma.f64 -4 (pow.f64 a 7) (pow.f64 a 8)))))
5.0ms	(fma.f64 64 (pow.f64 a 9) (pow.f64 a 12))
4.0ms	(fma.f64 -4 (pow.f64 a 7) (pow.f64 a 8))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
6×	`add-cbrt-cube_binary64`

Counts

4 → 63

Calls

4 calls:

5.0ms	(+.f64 (*.f64 4 (pow.f64 a 2)) (/.f64 (fma.f64 64 (pow.f64 a 9) (pow.f64 a 12)) (fma.f64 16 (pow.f64 a 6) (fma.f64 -4 (pow.f64 a 7) (pow.f64 a 8)))))
2.0ms	(/.f64 (fma.f64 64 (pow.f64 a 9) (pow.f64 a 12)) (fma.f64 16 (pow.f64 a 6) (fma.f64 -4 (pow.f64 a 7) (pow.f64 a 8))))
0.0ms	(fma.f64 -4 (pow.f64 a 7) (pow.f64 a 8))
0.0ms	(fma.f64 64 (pow.f64 a 9) (pow.f64 a 12))

simplify117.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

519×	`times-frac_binary64`
418×	`cancel-sign-sub-inv_binary64`
332×	`unswap-sqr_binary64`
325×	`associate-l_binary64`
288×	`associate-r_binary64`

Counts

111 → 95

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	116	2913
1	265	2745
2	720	2734
3	2606	2734
4	5133	2734

prune121.0ms (2.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	95	2	97

Error

Counts

97 → 2

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4)))) -1)
✓	56.7b	(+.f64 (+.f64 (*.f64 4 (pow.f64 a 2)) (/.f64 (fma.f64 64 (pow.f64 a 9) (pow.f64 a 12)) (fma.f64 16 (pow.f64 a 6) (fma.f64 -4 (pow.f64 a 7) (pow.f64 a 8))))) -1)

Status

Error

Program

✓

0.0b

(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4)))) -1)

✓

56.7b

(+.f64 (+.f64 (*.f64 4 (pow.f64 a 2)) (/.f64 (fma.f64 64 (pow.f64 a 9) (pow.f64 a 12)) (fma.f64 16 (pow.f64 a 6) (fma.f64 -4 (pow.f64 a 7) (pow.f64 a 8))))) -1)

Compiler

Compiled 3935 to 3141 computations (20.2% saved)

regimes1.7s (36.3%)

Accuracy

Total 0.0b remaining (21.1%)

Threshold costs 0.0b (21.1%)

Counts

235 → 1

Compiler

Compiled 32540 to 24256 computations (25.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	50
1	31	50
2	30	50

end2.0ms (0%)

Compiler: Compiled 37 to 26 computations (29.7% saved)

sample1.1s (23.4%)

Algorithm

1×

intervals

Results

736.0ms	8000×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 142 to 102 computations (28.2% saved)

Details

analyze218.0ms (4.8%)

sample97.0ms (2.1%)

simplify58.0ms (1.3%)

prune5.0ms (0.1%)

localize16.0ms (0.3%)

series99.0ms (2.2%)

rewrite9.0ms (0.2%)

simplify116.0ms (2.5%)

prune185.0ms (4%)

localize22.0ms (0.5%)

series40.0ms (0.9%)

rewrite11.0ms (0.2%)

simplify74.0ms (1.6%)

prune251.0ms (5.5%)

localize11.0ms (0.2%)

series16.0ms (0.3%)

rewrite27.0ms (0.6%)

simplify116.0ms (2.5%)

prune174.0ms (3.8%)

localize18.0ms (0.4%)

series25.0ms (0.6%)

rewrite11.0ms (0.2%)

simplify117.0ms (2.6%)

prune121.0ms (2.7%)

regimes1.7s (36.3%)

simplify3.0ms (0.1%)

end2.0ms (0%)

sample1.1s (23.4%)

Profiling