Details

analyze239.0ms (4.7%)

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)

sample32.0ms (0.6%)

Algorithm

1×

intervals

Results

23.0ms

256×

body

128

valid

Compiler

Compiled 69 to 45 computations (34.8% saved)

simplify75.0ms (1.5%)

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
▶	0.0b	(+.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)
	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)

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))) (pow.f64 (hypot.f64 a b) 4)) -1)

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)

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 a -3 1)
✓	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)))
✓	1.2b	(.f64 (.f64 b b) (fma.f64 a -3 1))

series62.0ms (1.2%)

Counts

4 → 84

Calls

4 calls:

36.0ms	(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))
14.0ms	(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))
2.0ms	(fma.f64 a -3 1)

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`fma-udef_binary64`

Counts

4 → 53

Calls

4 calls:

5.0ms	(.f64 (.f64 b b) (fma.f64 a -3 1))
0.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
0.0ms	(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))

simplify107.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

786×	`fma-def_binary64`
528×	`fma-neg_binary64`
415×	`associate-+l+_binary64`
313×	`cancel-sign-sub-inv_binary64`
229×	`associate-+r+_binary64`

Counts

137 → 125

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	125	2754
1	318	2352
2	969	2192
3	3184	2169
4	4818	2143
5	4983	2143

prune138.0ms (2.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	123	2	125
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	124	3	127

Error

0.0b

Counts

127 → 3

Alt Table

Status	Error	Program
	9.2b	(+.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (pow.f64 a 3)) (+.f64 (pow.f64 a 4) (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2)))))) -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)
▶	0.2b	(+.f64 (.f64 (sqrt.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))) (sqrt.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 3616 to 2025 computations (44% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
✓	0.2b	(.f64 (sqrt.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))) (sqrt.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))))
	1.2b	(.f64 (.f64 b b) (fma.f64 a -3 1))
✓	10.1b	(sqrt.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)))

series113.0ms (2.2%)

Counts

2 → 48

Calls

2 calls:

75.0ms

(sqrt.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)))

38.0ms

(*.f64 (sqrt.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))) (sqrt.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))))

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
18×	`pow1_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 68

Calls

2 calls:

7.0ms

(*.f64 (sqrt.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))) (sqrt.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))))

1.0ms

(sqrt.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)))

simplify147.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

757×	`times-frac_binary64`
457×	`cancel-sign-sub-inv_binary64`
333×	`fma-def_binary64`
265×	`associate-r_binary64`
256×	`associate-+r+_binary64`

Counts

116 → 132

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	289	5926
1	859	5283
2	3236	4999
3	4570	4940
4	5651	4940

prune543.0ms (10.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	310	2	312
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	311	4	315

Error

Counts

315 → 4

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (.f64 (sqrt.f64 (sqrt.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)))) (pow.f64 (sqrt.f64 (sqrt.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)))) 3)) -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)
✓	0.2b	(+.f64 (.f64 (sqrt.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))) (sqrt.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)
	8.7b	(+.f64 (fma.f64 4 (.f64 a a) (+.f64 (fma.f64 4 (pow.f64 a 3) (pow.f64 a 4)) (fma.f64 (.f64 b b) (+.f64 4 (.f64 2 (.f64 a a))) (.f64 (.f64 b b) (*.f64 a -12))))) -1)

Compiler

Compiled 19898 to 11432 computations (42.5% saved)

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (sqrt.f64 (sqrt.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)))) (pow.f64 (sqrt.f64 (sqrt.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)))) 3))
✓	0.4b	(pow.f64 (sqrt.f64 (sqrt.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)))) 3)
	1.2b	(.f64 (.f64 b b) (fma.f64 a -3 1))
	10.1b	(sqrt.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)))

series390.0ms (7.6%)

Counts

2 → 48

Calls

2 calls:

340.0ms

(pow.f64 (sqrt.f64 (sqrt.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)))) 3)

50.0ms

(*.f64 (sqrt.f64 (sqrt.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)))) (pow.f64 (sqrt.f64 (sqrt.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)))) 3))

rewrite37.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

87×	`sqrt-prod_binary64`
64×	`add-sqr-sqrt_binary64`
27×	`cube-prod_binary64`
27×	`unpow-prod-down_binary64`
24×	`associate-r_binary64`

Counts

2 → 114

Calls

2 calls:

11.0ms

(*.f64 (sqrt.f64 (sqrt.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)))) (pow.f64 (sqrt.f64 (sqrt.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)))) 3))

3.0ms

(pow.f64 (sqrt.f64 (sqrt.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)))) 3)

simplify189.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

441×	`fma-def_binary64`
439×	`associate-r_binary64`
374×	`associate-l_binary64`
313×	`associate-+r+_binary64`
299×	`fma-neg_binary64`

Counts

162 → 170

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	379	10167
1	1142	9189
2	4727	9185
3	4966	9185

prune721.0ms (14.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	344	0	344
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	344	4	348

Error

Counts

348 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (.f64 (sqrt.f64 (sqrt.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)))) (pow.f64 (sqrt.f64 (sqrt.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)))) 3)) -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)
✓	0.2b	(+.f64 (.f64 (sqrt.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))) (sqrt.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)
▶	8.7b	(+.f64 (fma.f64 4 (.f64 a a) (+.f64 (fma.f64 4 (pow.f64 a 3) (pow.f64 a 4)) (fma.f64 (.f64 b b) (+.f64 4 (.f64 2 (.f64 a a))) (.f64 (.f64 b b) (*.f64 a -12))))) -1)

Compiler

Compiled 26080 to 15968 computations (38.8% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 4 (.f64 a a) (+.f64 (fma.f64 4 (pow.f64 a 3) (pow.f64 a 4)) (fma.f64 (.f64 b b) (+.f64 4 (.f64 2 (.f64 a a))) (.f64 (.f64 b b) (*.f64 a -12)))))
✓	0.1b	(fma.f64 4 (pow.f64 a 3) (pow.f64 a 4))
✓	1.3b	(.f64 (.f64 b b) (*.f64 a -12))
✓	2.3b	(fma.f64 (.f64 b b) (+.f64 4 (.f64 2 (.f64 a a))) (.f64 (.f64 b b) (.f64 a -12)))

series72.0ms (1.4%)

Counts

4 → 84

Calls

4 calls:

33.0ms	(fma.f64 4 (.f64 a a) (+.f64 (fma.f64 4 (pow.f64 a 3) (pow.f64 a 4)) (fma.f64 (.f64 b b) (+.f64 4 (.f64 2 (.f64 a a))) (.f64 (.f64 b b) (*.f64 a -12)))))
23.0ms	(fma.f64 (.f64 b b) (+.f64 4 (.f64 2 (.f64 a a))) (.f64 (.f64 b b) (.f64 a -12)))
11.0ms	(.f64 (.f64 b b) (*.f64 a -12))
4.0ms	(fma.f64 4 (pow.f64 a 3) (pow.f64 a 4))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
16×	`pow1_binary64`
8×	`cbrt-unprod_binary64`
8×	`prod-exp_binary64`

Counts

4 → 54

Calls

4 calls:

6.0ms	(.f64 (.f64 b b) (*.f64 a -12))
0.0ms	(fma.f64 (.f64 b b) (+.f64 4 (.f64 2 (.f64 a a))) (.f64 (.f64 b b) (.f64 a -12)))
0.0ms	(fma.f64 4 (pow.f64 a 3) (pow.f64 a 4))
0.0ms	(fma.f64 4 (.f64 a a) (+.f64 (fma.f64 4 (pow.f64 a 3) (pow.f64 a 4)) (fma.f64 (.f64 b b) (+.f64 4 (.f64 2 (.f64 a a))) (.f64 (.f64 b b) (*.f64 a -12)))))

simplify107.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

637×	`fma-def_binary64`
295×	`cancel-sign-sub-inv_binary64`
294×	`*-commutative_binary64`
278×	`fma-neg_binary64`
265×	`exp-sum_binary64`

Counts

138 → 109

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	121	2988
1	276	2552
2	911	2303
3	3011	2244
4	4962	2244
5	4969	2244

prune167.0ms (3.3%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	109	4	113

Error

Counts

113 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (.f64 (sqrt.f64 (sqrt.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)))) (pow.f64 (sqrt.f64 (sqrt.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)))) 3)) -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)
✓	0.2b	(+.f64 (.f64 (sqrt.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))) (sqrt.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)
✓	8.7b	(+.f64 (fma.f64 4 (.f64 a a) (+.f64 (fma.f64 4 (pow.f64 a 3) (pow.f64 a 4)) (fma.f64 (.f64 b b) (+.f64 4 (.f64 2 (.f64 a a))) (.f64 (.f64 b b) (*.f64 a -12))))) -1)

Compiler

Compiled 4314 to 2593 computations (39.9% saved)

regimes757.0ms (14.8%)

Accuracy

Total 0.1b remaining (80.7%)

Threshold costs 0.1b (80.7%)

Counts

124 → 1

Compiler

Compiled 21142 to 14350 computations (32.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	25
1	13	25
2	13	25

end1.0ms (0%)

Compiler: Compiled 20 to 12 computations (40% saved)

sample1.1s (21.7%)

Algorithm

1×

intervals

Results

726.0ms	8000×	body	128	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 219 to 135 computations (38.4% saved)

Details

analyze239.0ms (4.7%)

sample32.0ms (0.6%)

simplify75.0ms (1.5%)

prune5.0ms (0.1%)

localize16.0ms (0.3%)

series62.0ms (1.2%)

rewrite8.0ms (0.2%)

simplify107.0ms (2.1%)

prune138.0ms (2.7%)

localize17.0ms (0.3%)

series113.0ms (2.2%)

rewrite17.0ms (0.3%)

simplify147.0ms (2.9%)

prune543.0ms (10.6%)

localize21.0ms (0.4%)

series390.0ms (7.6%)

rewrite37.0ms (0.7%)

simplify189.0ms (3.7%)

prune721.0ms (14.1%)

localize18.0ms (0.4%)

series72.0ms (1.4%)

rewrite9.0ms (0.2%)

simplify107.0ms (2.1%)

prune167.0ms (3.3%)

regimes757.0ms (14.8%)

simplify2.0ms (0%)

end1.0ms (0%)

sample1.1s (21.7%)

Profiling