Details

analyze1.9s (15.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
1.1%	98.6%	0.3%	12
1.9%	97.8%	0.3%	13
7%	92.7%	0.3%	14

Compiler

Compiled 28 to 17 computations (39.3% saved)

sample1.3s (10.3%)

Results

1.2s	8255×	body	128	valid
0.0ms	1×	body	1024	valid

Compiler

Compiled 83 to 50 computations (39.8% saved)

simplify95.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

765×	`sub-neg_binary64`
731×	`fma-neg_binary64`
652×	`neg-mul-1_binary64`
505×	`fma-def_binary64`
495×	`cancel-sign-sub-inv_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	29
1	37	29
2	85	29
3	194	27
4	486	27
5	1003	27
6	1920	27
7	3406	27
8	4078	27
9	4431	27
10	4919	27
11	5085	27

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

26.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	26.9b	(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))

Compiler

Compiled 96 to 51 computations (46.9% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (+.f64 x y) z (*.f64 t a))
✓	1.5b	(fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))
✓	25.2b	(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))

series166.0ms (1.4%)

Counts

3 → 204

Calls

3 calls:

129.0ms	(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))
23.0ms	(fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))
12.0ms	(fma.f64 (+.f64 x y) z (*.f64 t a))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64`
15×	`times-frac_binary64`
13×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out_binary64`

Counts

3 → 59

Calls

3 calls:

5.0ms	(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))
0.0ms	(fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))
0.0ms	(fma.f64 (+.f64 x y) z (*.f64 t a))

simplify141.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

591×	`associate-/l*_binary64`
378×	`associate-/r*_binary64`
286×	`+-commutative_binary64`
241×	`associate-+r+_binary64`
237×	`associate--l+_binary64`

Counts

263 → 200

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	673	11356
1	1961	11106
2	5078	11106

prune197.0ms (1.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	187	13	200
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	188	13	201

Error

2.9b

Counts

201 → 13

Alt Table

Status	Error	Program
	26.9b	(.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (/.f64 1 (+.f64 x (+.f64 y t))))
	42.9b	a
	43.7b	(.f64 (sqrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 x (+.f64 y t)))) (sqrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))))
	41.2b	(/.f64 (fma.f64 a t (*.f64 z x)) (+.f64 t x))
	27.0b	(/.f64 1 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))))
	42.2b	(*.f64 (/.f64 z (+.f64 (+.f64 t x) y)) (+.f64 x y))
	51.9b	(/.f64 (*.f64 z (+.f64 y x)) (+.f64 y (+.f64 t x)))
	37.8b	(/.f64 (+.f64 (.f64 z (+.f64 x y)) (.f64 y (-.f64 a b))) (+.f64 x (+.f64 y t)))
	27.5b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 x (+.f64 y t))) (cbrt.f64 (+.f64 x (+.f64 y t))))) (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (cbrt.f64 (+.f64 x (+.f64 y t)))))
	42.7b	(/.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (sqrt.f64 (+.f64 x (+.f64 y t)))) (sqrt.f64 (+.f64 x (+.f64 y t))))
	45.4b	z
	45.7b	(.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (.f64 a t))) (-.f64 (*.f64 x x) (pow.f64 (+.f64 t y) 2))) (-.f64 x (+.f64 y t)))
▶	26.9b	(-.f64 (+.f64 a z) b)

Compiler

Compiled 10673 to 3191 computations (70.1% saved)

localize3.0ms (0%)

prune12.0ms (0.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	12	12
Picked	1	1
Done	0	0
Total	13	13

Error

2.9b

Counts

13 → 13

Alt Table

Status	Error	Program
▶	26.9b	(.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (/.f64 1 (+.f64 x (+.f64 y t))))
	42.9b	a
	43.7b	(.f64 (sqrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 x (+.f64 y t)))) (sqrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))))
	41.2b	(/.f64 (fma.f64 a t (*.f64 z x)) (+.f64 t x))
	27.0b	(/.f64 1 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))))
	42.2b	(*.f64 (/.f64 z (+.f64 (+.f64 t x) y)) (+.f64 x y))
	51.9b	(/.f64 (*.f64 z (+.f64 y x)) (+.f64 y (+.f64 t x)))
	37.8b	(/.f64 (+.f64 (.f64 z (+.f64 x y)) (.f64 y (-.f64 a b))) (+.f64 x (+.f64 y t)))
	27.5b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 x (+.f64 y t))) (cbrt.f64 (+.f64 x (+.f64 y t))))) (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (cbrt.f64 (+.f64 x (+.f64 y t)))))
	42.7b	(/.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (sqrt.f64 (+.f64 x (+.f64 y t)))) (sqrt.f64 (+.f64 x (+.f64 y t))))
	45.4b	z
	45.7b	(.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (.f64 a t))) (-.f64 (*.f64 x x) (pow.f64 (+.f64 t y) 2))) (-.f64 x (+.f64 y t)))
✓	26.9b	(-.f64 (+.f64 a z) b)

Compiler

Compiled 607 to 330 computations (45.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 x (+.f64 y t)))
	0.0b	(fma.f64 (+.f64 x y) z (*.f64 t a))
	1.5b	(fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))
✓	25.2b	(.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (/.f64 1 (+.f64 x (+.f64 y t))))

series153.0ms (1.2%)

Counts

2 → 108

Calls

2 calls:

128.0ms	(.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (/.f64 1 (+.f64 x (+.f64 y t))))
25.0ms	(/.f64 1 (+.f64 x (+.f64 y t)))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
29×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`
21×	`distribute-lft-out_binary64`

Counts

2 → 89

Calls

2 calls:

9.0ms	(.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (/.f64 1 (+.f64 x (+.f64 y t))))
5.0ms	(/.f64 1 (+.f64 x (+.f64 y t)))

simplify133.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

671×	`associate-/l*_binary64`
456×	`associate-/r*_binary64`
306×	`+-commutative_binary64`
245×	`associate-+r+_binary64`
176×	`fma-def_binary64`

Counts

197 → 229

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	745	11101
1	2289	10838
2	5016	10838

prune214.0ms (1.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	303	1	304
Fresh	1	10	11
Picked	1	0	1
Done	0	1	1
Total	305	12	317

Error

2.9b

Counts

317 → 12

Alt Table

Status	Error	Program
	43.7b	(.f64 (sqrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 x (+.f64 y t)))) (sqrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))))
	41.2b	(/.f64 (fma.f64 a t (*.f64 z x)) (+.f64 t x))
	42.9b	a
▶	27.0b	(/.f64 1 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))))
	42.2b	(*.f64 (/.f64 z (+.f64 (+.f64 t x) y)) (+.f64 x y))
	51.9b	(/.f64 (*.f64 z (+.f64 y x)) (+.f64 y (+.f64 t x)))
	27.5b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 x (+.f64 y t))) (cbrt.f64 (+.f64 x (+.f64 y t))))) (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (cbrt.f64 (+.f64 x (+.f64 y t)))))
	42.7b	(/.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (sqrt.f64 (+.f64 x (+.f64 y t)))) (sqrt.f64 (+.f64 x (+.f64 y t))))
	37.8b	(.f64 (+.f64 (.f64 z (+.f64 x y)) (*.f64 y (-.f64 a b))) (/.f64 1 (+.f64 x (+.f64 y t))))
	45.4b	z
	45.7b	(.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (.f64 a t))) (-.f64 (*.f64 x x) (pow.f64 (+.f64 t y) 2))) (-.f64 x (+.f64 y t)))
✓	26.9b	(-.f64 (+.f64 a z) b)

Compiler

Compiled 14325 to 4568 computations (68.1% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 (+.f64 x y) z (*.f64 t a))
✓	0.2b	(/.f64 1 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))))
	1.5b	(fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))
✓	25.2b	(/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))))

series1.5s (12.6%)

Counts

2 → 144

Calls

2 calls:

1.4s	(/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))))
124.0ms	(/.f64 1 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))))

rewrite35.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

148×	`*-un-lft-identity_binary64`
132×	`times-frac_binary64`
68×	`add-sqr-sqrt_binary64`
68×	`add-cube-cbrt_binary64`
48×	`distribute-lft-out_binary64`

Counts

2 → 141

Calls

2 calls:

7.0ms	(/.f64 1 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))))
5.0ms	(/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))))

simplify354.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

600×	`associate-/l*_binary64`
436×	`times-frac_binary64`
336×	`fma-def_binary64`
77×	`sub-neg_binary64`
46×	`sqr-pow_binary64`

Counts

285 → 297

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2784	46779
1	5617	46779

prune606.0ms (4.9%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	370	2	372
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	371	13	384

Error

2.9b

Counts

384 → 13

Alt Table

Status	Error	Program
	27.0b	(/.f64 (/.f64 1 (+.f64 x (+.f64 y t))) (/.f64 1 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))))
	41.2b	(/.f64 (fma.f64 a t (*.f64 z x)) (+.f64 t x))
	42.9b	a
✓	27.0b	(/.f64 1 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))))
	42.2b	(*.f64 (/.f64 z (+.f64 (+.f64 t x) y)) (+.f64 x y))
	51.9b	(/.f64 (*.f64 z (+.f64 y x)) (+.f64 y (+.f64 t x)))
	27.5b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 x (+.f64 y t))) (cbrt.f64 (+.f64 x (+.f64 y t))))) (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (cbrt.f64 (+.f64 x (+.f64 y t)))))
	27.0b	(/.f64 1 (/.f64 1 (-.f64 (+.f64 a z) b)))
	42.7b	(/.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (sqrt.f64 (+.f64 x (+.f64 y t)))) (sqrt.f64 (+.f64 x (+.f64 y t))))
	37.8b	(.f64 (+.f64 (.f64 z (+.f64 x y)) (*.f64 y (-.f64 a b))) (/.f64 1 (+.f64 x (+.f64 y t))))
	45.4b	z
	45.7b	(.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (.f64 a t))) (-.f64 (*.f64 x x) (pow.f64 (+.f64 t y) 2))) (-.f64 x (+.f64 y t)))
✓	26.9b	(-.f64 (+.f64 a z) b)

Compiler

Compiled 54438 to 20688 computations (62% saved)

regimes5.3s (42.9%)

Accuracy

Total 4.5b remaining (61.3%)

Threshold costs 0b (0%)

Counts

203 → 3

Compiler

Compiled 47612 to 26368 computations (44.6% saved)

bsearch10.0ms (0.1%)

Compiler: Compiled 27 to 16 computations (40.7% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

17×	`+-commutative_binary64`
11×	`*-commutative_binary64`
7×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	154
1	67	154
2	83	154
3	91	154
4	95	154
5	95	154

end152.0ms (1.2%)

Compiler: Compiled 499 to 245 computations (50.9% saved)

Details

analyze1.9s (15.1%)

sample1.3s (10.3%)

simplify95.0ms (0.8%)

prune3.0ms (0%)

localize11.0ms (0.1%)

series166.0ms (1.4%)

rewrite10.0ms (0.1%)

simplify141.0ms (1.1%)

prune197.0ms (1.6%)

localize3.0ms (0%)

prune12.0ms (0.1%)

localize13.0ms (0.1%)

series153.0ms (1.2%)

rewrite20.0ms (0.2%)

simplify133.0ms (1.1%)

prune214.0ms (1.7%)

localize13.0ms (0.1%)

series1.5s (12.6%)

rewrite35.0ms (0.3%)

simplify354.0ms (2.9%)

prune606.0ms (4.9%)

regimes5.3s (42.9%)

bsearch10.0ms (0.1%)

simplify7.0ms (0.1%)

end152.0ms (1.2%)

Profiling