Details

analyze159.0ms (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%	50%	25.1%	6
25%	31.2%	43.8%	7
25%	21.9%	53.2%	8
25%	14%	61%	9
28.1%	10.9%	61%	10
31.6%	7.4%	61%	11
33.4%	5.7%	61%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 20 to 13 computations (35% saved)

sample26.0ms (0.8%)

Algorithm

1×

intervals

Results

18.0ms

256×

body

128

valid

Compiler

Compiled 41 to 27 computations (34.1% saved)

simplify47.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

770×	`unswap-sqr_binary64`
631×	`associate-l_binary64`
623×	`fma-def_binary64`
311×	`fma-neg_binary64`
283×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	30	21
2	60	21
3	159	21
4	518	17
5	1687	17
6	3597	17
7	5026	17

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

0.0b

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 b b))) 1)
▶	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 97 to 64 computations (34% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
✓	0.0b	(hypot.f64 a b)
✓	0.0b	(pow.f64 (hypot.f64 a b) 4)

series97.0ms (3%)

Counts

3 → 72

Calls

3 calls:

41.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
38.0ms	(pow.f64 (hypot.f64 a b) 4)
17.0ms	(hypot.f64 a b)

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
7×	`fma-def_binary64`
7×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
6×	`unpow-prod-down_binary64`

Counts

3 → 52

Calls

3 calls:

4.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
2.0ms	(pow.f64 (hypot.f64 a b) 4)
0.0ms	(hypot.f64 a b)

simplify101.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

785×	`fma-neg_binary64`
421×	`fma-def_binary64`
280×	`associate-r_binary64`
276×	`associate-l_binary64`
184×	`times-frac_binary64`

Counts

124 → 114

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	130	2123
1	343	2010
2	979	1901
3	4070	1899
4	4922	1899
5	4944	1899

prune120.0ms (3.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	110	4	114
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	112	4	116

Error

Counts

116 → 4

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (pow.f64 a 4) (+.f64 -1 (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4))))
	0.1b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (.f64 a a))) (pow.f64 a 4)) (fma.f64 b (.f64 b 4) -1))
	16.2b	(/.f64 (fma.f64 (fma.f64 b (.f64 b 4) -1) (fma.f64 (.f64 b b) -4 1) (pow.f64 (hypot.f64 a b) 8)) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)))
	19.6b	(+.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3)) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 2454 to 1577 computations (35.7% saved)

localize11.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

series50.0ms (1.5%)

Counts

2 → 48

Calls

2 calls:

27.0ms	(+.f64 (pow.f64 a 4) (+.f64 -1 (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4))))
22.0ms	(fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4))

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
7×	`fma-def_binary64`
7×	`add-log-exp_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`

Counts

2 → 34

Calls

2 calls:

6.0ms	(+.f64 (pow.f64 a 4) (+.f64 -1 (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4))))
0.0ms	(fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4))

simplify92.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

596×	`fma-neg_binary64`
438×	`distribute-rgt-in_binary64`
418×	`distribute-lft-in_binary64`
352×	`fma-def_binary64`
268×	`exp-prod_binary64`

Counts

82 → 72

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	71	1965
1	183	1651
2	572	1645
3	3252	1645
4	4823	1645
5	4957	1645

prune83.0ms (2.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	72	4	76

Error

Counts

76 → 4

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (pow.f64 a 4) (+.f64 -1 (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4))))
▶	0.1b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (.f64 a a))) (pow.f64 a 4)) (fma.f64 b (.f64 b 4) -1))
	16.2b	(/.f64 (fma.f64 (fma.f64 b (.f64 b 4) -1) (fma.f64 (.f64 b b) -4 1) (pow.f64 (hypot.f64 a b) 8)) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)))
	19.6b	(+.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3)) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 2026 to 1268 computations (37.4% saved)

localize12.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (.f64 a a))
✓	0.0b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (.f64 a a))) (pow.f64 a 4)) (fma.f64 b (.f64 b 4) -1))
✓	0.2b	(fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (*.f64 a a))) (pow.f64 a 4))

series41.0ms (1.3%)

Counts

3 → 60

Calls

3 calls:

22.0ms	(+.f64 (fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (.f64 a a))) (pow.f64 a 4)) (fma.f64 b (.f64 b 4) -1))
16.0ms	(fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (*.f64 a a))) (pow.f64 a 4))
2.0ms	(.f64 2 (.f64 a a))

rewrite9.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 50

Calls

3 calls:

4.0ms	(.f64 2 (.f64 a a))
2.0ms	(+.f64 (fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (.f64 a a))) (pow.f64 a 4)) (fma.f64 b (.f64 b 4) -1))
0.0ms	(fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (*.f64 a a))) (pow.f64 a 4))

simplify96.0ms (3%)

Algorithm

1×	egg-herbie

Rules

752×	`fma-neg_binary64`
418×	`cancel-sign-sub-inv_binary64`
343×	`fma-def_binary64`
325×	`distribute-rgt-in_binary64`
317×	`distribute-lft-in_binary64`

Counts

110 → 92

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	100	2244
1	230	2091
2	647	1947
3	2964	1941
4	4527	1941
5	4946	1941

prune95.0ms (2.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	92	4	96

Error

Counts

96 → 4

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (pow.f64 a 4) (+.f64 -1 (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4))))
✓	0.1b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (.f64 a a))) (pow.f64 a 4)) (fma.f64 b (.f64 b 4) -1))
▶	16.2b	(/.f64 (fma.f64 (fma.f64 b (.f64 b 4) -1) (fma.f64 (.f64 b b) -4 1) (pow.f64 (hypot.f64 a b) 8)) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)))
	19.6b	(+.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3)) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 2800 to 1598 computations (42.9% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (hypot.f64 a b) 8)
✓	0.0b	(fma.f64 (fma.f64 b (.f64 b 4) -1) (fma.f64 (.f64 b b) -4 1) (pow.f64 (hypot.f64 a b) 8))
	0.0b	(pow.f64 (hypot.f64 a b) 4)
✓	15.0b	(/.f64 (fma.f64 (fma.f64 b (.f64 b 4) -1) (fma.f64 (.f64 b b) -4 1) (pow.f64 (hypot.f64 a b) 8)) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)))

series312.0ms (9.7%)

Counts

3 → 72

Calls

3 calls:

249.0ms

(/.f64 (fma.f64 (fma.f64 b (*.f64 b 4) -1) (fma.f64 (*.f64 b b) -4 1) (pow.f64 (hypot.f64 a b) 8)) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)))

34.0ms

(fma.f64 (fma.f64 b (*.f64 b 4) -1) (fma.f64 (*.f64 b b) -4 1) (pow.f64 (hypot.f64 a b) 8))

29.0ms

(pow.f64 (hypot.f64 a b) 8)

rewrite17.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
21×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
12×	`difference-of-squares_binary64`

Counts

3 → 77

Calls

3 calls:

6.0ms

(/.f64 (fma.f64 (fma.f64 b (*.f64 b 4) -1) (fma.f64 (*.f64 b b) -4 1) (pow.f64 (hypot.f64 a b) 8)) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)))

1.0ms

(pow.f64 (hypot.f64 a b) 8)

0.0ms

(fma.f64 (fma.f64 b (*.f64 b 4) -1) (fma.f64 (*.f64 b b) -4 1) (pow.f64 (hypot.f64 a b) 8))

simplify136.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

509×	`fma-def_binary64`
356×	`associate-+l+_binary64`
326×	`times-frac_binary64`
315×	`associate-/l*_binary64`
221×	`associate-/r*_binary64`

Counts

149 → 175

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	492	8911
1	1484	8554
2	5206	8554

prune323.0ms (10%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	209	0	209
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	209	4	213

Error

Counts

213 → 4

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (pow.f64 a 4) (+.f64 -1 (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4))))
✓	0.1b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (.f64 a a))) (pow.f64 a 4)) (fma.f64 b (.f64 b 4) -1))
✓	16.2b	(/.f64 (fma.f64 (fma.f64 b (.f64 b 4) -1) (fma.f64 (.f64 b b) -4 1) (pow.f64 (hypot.f64 a b) 8)) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)))
	19.6b	(+.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3)) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 13332 to 8936 computations (33% saved)

regimes553.0ms (17.2%)

Accuracy

Total 0.0b remaining (60.3%)

Threshold costs 0.0b (60.3%)

Counts

96 → 1

Compiler

Compiled 10498 to 7660 computations (27% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	27
1	16	27
2	16	27

end1.0ms (0%)

Compiler: Compiled 21 to 15 computations (28.6% saved)

sample790.0ms (24.6%)

Algorithm

1×

intervals

Results

472.0ms	8000×	body	128	valid
0.0ms	5×	body	128	invalid

Compiler

Compiled 138 to 95 computations (31.2% saved)

Details

analyze159.0ms (5%)

sample26.0ms (0.8%)

simplify47.0ms (1.5%)

prune4.0ms (0.1%)

localize7.0ms (0.2%)

series97.0ms (3%)

rewrite8.0ms (0.2%)

simplify101.0ms (3.1%)

prune120.0ms (3.7%)

localize11.0ms (0.3%)

series50.0ms (1.5%)

rewrite8.0ms (0.2%)

simplify92.0ms (2.9%)

prune83.0ms (2.6%)

localize12.0ms (0.4%)

series41.0ms (1.3%)

rewrite9.0ms (0.3%)

simplify96.0ms (3%)

prune95.0ms (2.9%)

localize14.0ms (0.4%)

series312.0ms (9.7%)

rewrite17.0ms (0.5%)

simplify136.0ms (4.2%)

prune323.0ms (10%)

regimes553.0ms (17.2%)

simplify2.0ms (0.1%)

end1.0ms (0%)

sample790.0ms (24.6%)

Profiling