Details

analyze219.0ms (6.5%)

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)

sample1.3s (38.6%)

Results

1.2s	8256×	body	128	valid
1.0ms	8×	body	128	invalid

Compiler

Compiled 101 to 65 computations (35.6% saved)

simplify58.0ms (1.7%)

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 (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (hypot.f64 a b) 4)
✓	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))
✓	0.1b	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
✓	0.3b	(.f64 (.f64 b b) (fma.f64 a -3 1))

series87.0ms (2.6%)

Counts

4 → 96

Calls

4 calls:

34.0ms	(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))
32.0ms	(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)))
9.0ms	(.f64 (.f64 b b) (fma.f64 a -3 1))

rewrite10.0ms (0.3%)

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:

5.0ms	(.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))

simplify111.0ms (3.3%)

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

prune200.0ms (5.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	137	3	140
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	138	4	142

Error

Counts

142 → 4

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (.f64 (.f64 b b) (+.f64 (fma.f64 2 (.f64 a a) 4) (fma.f64 b b (.f64 a -12))))) (pow.f64 a 4)) -1)
	12.2b	(+.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (pow.f64 a 3)) (pow.f64 a 4))) -1)
	13.0b	(+.f64 (*.f64 (pow.f64 a 3) (+.f64 4 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 4084 to 2262 computations (44.6% saved)

localize18.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 b b (*.f64 a -12))
✓	0.0b	(+.f64 (fma.f64 2 (.f64 a a) 4) (fma.f64 b b (.f64 a -12)))
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (.f64 (.f64 b b) (+.f64 (fma.f64 2 (.f64 a a) 4) (fma.f64 b b (.f64 a -12))))) (pow.f64 a 4))
✓	1.1b	(.f64 (.f64 b b) (+.f64 (fma.f64 2 (.f64 a a) 4) (fma.f64 b b (.f64 a -12))))

series63.0ms (1.9%)

Counts

4 → 96

Calls

4 calls:

26.0ms	(+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (.f64 (.f64 b b) (+.f64 (fma.f64 2 (.f64 a a) 4) (fma.f64 b b (.f64 a -12))))) (pow.f64 a 4))
21.0ms	(.f64 (.f64 b b) (+.f64 (fma.f64 2 (.f64 a a) 4) (fma.f64 b b (.f64 a -12))))
11.0ms	(+.f64 (fma.f64 2 (.f64 a a) 4) (fma.f64 b b (.f64 a -12)))
5.0ms	(fma.f64 b b (*.f64 a -12))

rewrite17.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

7.0ms	(.f64 (.f64 b b) (+.f64 (fma.f64 2 (.f64 a a) 4) (fma.f64 b b (.f64 a -12))))
3.0ms	(+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (.f64 (.f64 b b) (+.f64 (fma.f64 2 (.f64 a a) 4) (fma.f64 b b (.f64 a -12))))) (pow.f64 a 4))
2.0ms	(+.f64 (fma.f64 2 (.f64 a a) 4) (fma.f64 b b (.f64 a -12)))
0.0ms	(fma.f64 b b (*.f64 a -12))

simplify135.0ms (4%)

Algorithm

1×	egg-herbie

Rules

730×	`fma-neg_binary64`
604×	`associate-+l+_binary64`
375×	`associate-+r+_binary64`
325×	`*-commutative_binary64`
318×	`exp-sum_binary64`

Counts

169 → 155

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	154	4340
1	445	3654
2	1518	3480
3	3650	3272
4	4988	3272
5	4871	3272

prune213.0ms (6.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	155	4	159

Error

Counts

159 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (.f64 (.f64 b b) (+.f64 (fma.f64 2 (.f64 a a) 4) (fma.f64 b b (.f64 a -12))))) (pow.f64 a 4)) -1)
▶	12.2b	(+.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (pow.f64 a 3)) (pow.f64 a 4))) -1)
	13.0b	(+.f64 (*.f64 (pow.f64 a 3) (+.f64 4 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 6085 to 3817 computations (37.3% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series14.0ms (0.4%)

Counts

4 → 9

Calls

4 calls:

5.0ms	(+.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))
3.0ms	(*.f64 4 (pow.f64 a 3))
2.0ms	(*.f64 4 (pow.f64 a 2))

rewrite25.0ms (0.7%)

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

simplify102.0ms (3%)

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 → 138

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	138	1290
1	334	1117
2	1000	1055
3	3454	1053
4	4438	1053
5	4772	1053
6	4928	1053

prune153.0ms (4.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	138	4	142

Error

Counts

142 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (.f64 (.f64 b b) (+.f64 (fma.f64 2 (.f64 a a) 4) (fma.f64 b b (.f64 a -12))))) (pow.f64 a 4)) -1)
✓	12.2b	(+.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (pow.f64 a 3)) (pow.f64 a 4))) -1)
▶	13.0b	(+.f64 (*.f64 (pow.f64 a 3) (+.f64 4 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 3250 to 2610 computations (19.7% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (pow.f64 a 3) (+.f64 4 a))

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(*.f64 (pow.f64 a 3) (+.f64 4 a))

rewrite9.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`associate-l_binary64`
12×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64`
6×	`add-exp-log_binary64`
5×	`add-cube-cbrt_binary64`

Counts

1 → 38

Calls

1 calls:

6.0ms

(*.f64 (pow.f64 a 3) (+.f64 4 a))

simplify61.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

971×	`fma-def_binary64`
348×	`sqr-pow_binary64`
340×	`*-commutative_binary64`
308×	`associate-+l+_binary64`
297×	`associate-+r+_binary64`

Counts

50 → 47

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	69	623
1	178	591
2	818	591
3	2091	567
4	4420	567
5	5174	567

prune47.0ms (1.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	47	0	47
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	47	4	51

Error

Counts

51 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (.f64 (.f64 b b) (+.f64 (fma.f64 2 (.f64 a a) 4) (fma.f64 b b (.f64 a -12))))) (pow.f64 a 4)) -1)
✓	12.2b	(+.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (pow.f64 a 3)) (pow.f64 a 4))) -1)
✓	13.0b	(+.f64 (*.f64 (pow.f64 a 3) (+.f64 4 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 795 to 606 computations (23.8% saved)

regimes409.0ms (12%)

Accuracy

Total 0.0b remaining (52.1%)

Threshold costs 0.0b (52.1%)

Counts

79 → 1

Compiler

Compiled 8981 to 6437 computations (28.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	32
1	20	32
2	19	32

end94.0ms (2.8%)

Compiler: Compiled 138 to 95 computations (31.2% saved)

Details

analyze219.0ms (6.5%)

sample1.3s (38.6%)

simplify58.0ms (1.7%)

prune5.0ms (0.1%)

localize16.0ms (0.5%)

series87.0ms (2.6%)

rewrite10.0ms (0.3%)

simplify111.0ms (3.3%)

prune200.0ms (5.9%)

localize18.0ms (0.5%)

series63.0ms (1.9%)

rewrite17.0ms (0.5%)

simplify135.0ms (4%)

prune213.0ms (6.3%)

localize9.0ms (0.3%)

series14.0ms (0.4%)

rewrite25.0ms (0.7%)

simplify102.0ms (3%)

prune153.0ms (4.5%)

localize5.0ms (0.1%)

series3.0ms (0.1%)

rewrite9.0ms (0.3%)

simplify61.0ms (1.8%)

prune47.0ms (1.4%)

regimes409.0ms (12%)

simplify2.0ms (0.1%)

end94.0ms (2.8%)

Profiling