Details

analyze1.8s (17.1%)

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)

sample93.0ms (0.9%)

Algorithm

1×

intervals

Results

19.0ms

256×

body

128

valid

Compiler

Compiled 61 to 39 computations (36.1% saved)

simplify101.0ms (1%)

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

prune4.0ms (0%)

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

28.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	28.7b	(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))
	28.7b	(/.f64 (-.f64 (+.f64 (.f64 (+.f64 x y) z) (.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

Compiler

Compiled 150 to 83 computations (44.7% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(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)))
✓	26.9b	(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))

series171.0ms (1.6%)

Counts

3 → 204

Calls

3 calls:

133.0ms	(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))
25.0ms	(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 (+.f64 x y) z (*.f64 t a))
0.0ms	(fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))

simplify142.0ms (1.3%)

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

prune168.0ms (1.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	190	10	200
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	192	10	202

Error

2.3b

Counts

202 → 10

Alt Table

Status	Error	Program
	42.0b	(*.f64 (/.f64 z (+.f64 (+.f64 t x) y)) (+.f64 x y))
▶	26.0b	(-.f64 (+.f64 a z) b)
	28.8b	(/.f64 1 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))))
	38.7b	(/.f64 (fma.f64 y (-.f64 a b) (+.f64 (.f64 y z) (.f64 z x))) (+.f64 x (+.f64 y t)))
	45.0b	z
	40.7b	a
	45.8b	(/.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))))
	43.1b	(.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)))
	28.8b	(.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (/.f64 1 (+.f64 x (+.f64 y t))))
	52.9b	(/.f64 (*.f64 a t) (+.f64 x (+.f64 y t)))

Compiler

Compiled 10461 to 3099 computations (70.4% saved)

localize3.0ms (0%)

prune12.0ms (0.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	9	9
Picked	1	1
Done	0	0
Total	10	10

Error

2.3b

Counts

10 → 10

Alt Table

Status	Error	Program
	42.0b	(*.f64 (/.f64 z (+.f64 (+.f64 t x) y)) (+.f64 x y))
✓	26.0b	(-.f64 (+.f64 a z) b)
▶	28.8b	(/.f64 1 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))))
	38.7b	(/.f64 (fma.f64 y (-.f64 a b) (+.f64 (.f64 y z) (.f64 z x))) (+.f64 x (+.f64 y t)))
	45.0b	z
	40.7b	a
	45.8b	(/.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))))
	43.1b	(.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)))
	28.8b	(.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (/.f64 1 (+.f64 x (+.f64 y t))))
	52.9b	(/.f64 (*.f64 a t) (+.f64 x (+.f64 y t)))

Compiler

Compiled 395 to 238 computations (39.7% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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)))))
	0.3b	(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)))
✓	26.9b	(/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))))

series1.7s (15.8%)

Counts

2 → 144

Calls

2 calls:

1.5s	(/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))))
132.0ms	(/.f64 1 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))))

rewrite36.0ms (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)))))
6.0ms	(/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))))

simplify391.0ms (3.7%)

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

prune638.0ms (6%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	370	2	372
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	370	12	382

Error

2.2b

Counts

382 → 12

Alt Table

Status	Error	Program
	42.0b	(*.f64 (/.f64 z (+.f64 (+.f64 t x) y)) (+.f64 x y))
✓	26.0b	(-.f64 (+.f64 a z) b)
	29.4b	(/.f64 1 (.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))))) (cbrt.f64 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a)))))) (cbrt.f64 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))))))
	45.8b	(/.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))))
✓	28.8b	(/.f64 1 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))))
	38.7b	(/.f64 (fma.f64 y (-.f64 a b) (+.f64 (.f64 y z) (.f64 z x))) (+.f64 x (+.f64 y t)))
	45.0b	z
	40.7b	a
	38.8b	(/.f64 1 (/.f64 (+.f64 x (+.f64 y t)) (+.f64 (.f64 z (+.f64 x y)) (.f64 y (-.f64 a b)))))
	43.1b	(.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)))
▶	28.8b	(.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (/.f64 1 (+.f64 x (+.f64 y t))))
	52.9b	(/.f64 (*.f64 a t) (+.f64 x (+.f64 y t)))

Compiler

Compiled 54715 to 20811 computations (62% 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)))
	0.3b	(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)))
✓	27.0b	(.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (/.f64 1 (+.f64 x (+.f64 y t))))

series161.0ms (1.5%)

Counts

2 → 108

Calls

2 calls:

135.0ms	(.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (/.f64 1 (+.f64 x (+.f64 y t))))
26.0ms	(/.f64 1 (+.f64 x (+.f64 y t)))

rewrite27.0ms (0.3%)

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)))

simplify145.0ms (1.4%)

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

prune211.0ms (2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	302	2	304
Fresh	2	7	9
Picked	1	0	1
Done	0	2	2
Total	305	11	316

Error

2.2b

Counts

316 → 11

Alt Table

Status	Error	Program
	42.0b	(*.f64 (/.f64 z (+.f64 (+.f64 t x) y)) (+.f64 x y))
✓	26.0b	(-.f64 (+.f64 a z) b)
✓	28.8b	(/.f64 1 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))))
	38.7b	(/.f64 (fma.f64 y (-.f64 a b) (+.f64 (.f64 y z) (.f64 z x))) (+.f64 x (+.f64 y t)))
	45.0b	z
	40.7b	a
	43.2b	(.f64 (.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (/.f64 1 (-.f64 (.f64 x x) (*.f64 (+.f64 y t) (+.f64 y t))))) (-.f64 x (+.f64 y t)))
	45.8b	(/.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))))
	43.1b	(.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)))
	52.9b	(/.f64 (*.f64 a t) (+.f64 x (+.f64 y t)))
	38.8b	(.f64 (+.f64 (.f64 z (+.f64 x y)) (*.f64 y (-.f64 a b))) (/.f64 1 (+.f64 x (+.f64 y t))))

Compiler

Compiled 14008 to 4409 computations (68.5% saved)

regimes3.7s (35.3%)

Accuracy

Total 4.5b remaining (60%)

Threshold costs 0b (0%)

Counts

148 → 3

Compiler

Compiled 26724 to 14909 computations (44.2% saved)

bsearch5.0ms (0%)

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

end1.0ms (0%)

Compiler: Compiled 109 to 38 computations (65.1% saved)

sample990.0ms (9.4%)

Algorithm

1×

intervals

Results

535.0ms

8000×

body

128

valid

Compiler

Compiled 383 to 204 computations (46.7% saved)

Details

analyze1.8s (17.1%)

sample93.0ms (0.9%)

simplify101.0ms (1%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series171.0ms (1.6%)

rewrite10.0ms (0.1%)

simplify142.0ms (1.3%)

prune168.0ms (1.6%)

localize3.0ms (0%)

prune12.0ms (0.1%)

localize13.0ms (0.1%)

series1.7s (15.8%)

rewrite36.0ms (0.3%)

simplify391.0ms (3.7%)

prune638.0ms (6%)

localize13.0ms (0.1%)

series161.0ms (1.5%)

rewrite27.0ms (0.3%)

simplify145.0ms (1.4%)

prune211.0ms (2%)

regimes3.7s (35.3%)

bsearch5.0ms (0%)

simplify7.0ms (0.1%)

end1.0ms (0%)

sample990.0ms (9.4%)

Profiling