Details

analyze1.8s (23.4%)

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
5.8%	93.9%	0.3%	11
8.4%	91.3%	0.3%	12
9.7%	90%	0.3%	13
10.7%	89%	0.3%	14

Compiler

Compiled 24 to 16 computations (33.3% saved)

sample65.0ms (0.9%)

Algorithm

1×

intervals

Results

17.0ms	256×	body	128	valid
1.0ms	10×	body	128	invalid

Compiler

Compiled 53 to 37 computations (30.2% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

16×	`fma-def_binary64`
6×	`+-commutative_binary64`
6×	`*-commutative_binary64`
4×	`associate-/l*_binary64`
4×	`associate-/r/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	25
1	29	25
2	41	21
3	51	21
4	61	21
5	65	21
6	64	21

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

13.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	16.9b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))
▶	16.9b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))

Compiler

Compiled 126 to 78 computations (38.1% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	2.4b	(fma.f64 b (/.f64 y t) a)
✓	2.8b	(fma.f64 y (/.f64 z t) x)
✓	12.7b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))

series266.0ms (3.5%)

Counts

3 → 168

Calls

3 calls:

236.0ms	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
17.0ms	(fma.f64 b (/.f64 y t) a)
13.0ms	(fma.f64 y (/.f64 z t) x)

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 55

Calls

3 calls:

4.0ms	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
0.0ms	(fma.f64 b (/.f64 y t) a)
0.0ms	(fma.f64 y (/.f64 z t) x)

simplify129.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

741×	`times-frac_binary64`
527×	`associate-/l*_binary64`
403×	`associate-/r*_binary64`
231×	`fma-def_binary64`
204×	`associate-l_binary64`

Counts

223 → 131

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	430	9216
1	1356	8684
2	4993	8684

prune204.0ms (2.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	120	11	131
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	121	12	133

Error

0.0b

Counts

133 → 12

Alt Table

Status	Error	Program
	37.9b	(-.f64 (fma.f64 (/.f64 y t) (/.f64 z (fma.f64 b (/.f64 y t) 1)) (/.f64 x (fma.f64 b (/.f64 y t) 1))) (fma.f64 (/.f64 a t) (/.f64 (.f64 y z) (pow.f64 (fma.f64 b (/.f64 y t) 1) 2)) (/.f64 (.f64 x a) (pow.f64 (fma.f64 b (/.f64 y t) 1) 2))))
	44.9b	(/.f64 z b)
	17.7b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
▶	15.3b	(+.f64 (/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
	40.8b	(-.f64 (+.f64 (/.f64 z b) (/.f64 (.f64 t x) (.f64 y b))) (+.f64 (/.f64 (.f64 t z) (.f64 y (pow.f64 b 2))) (/.f64 (.f64 a (.f64 t z)) (*.f64 y (pow.f64 b 2)))))
	40.7b	(.f64 (/.f64 (sqrt.f64 (fma.f64 y (/.f64 z t) x)) (.f64 (cbrt.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a))) (cbrt.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a))))) (/.f64 (sqrt.f64 (fma.f64 y (/.f64 z t) x)) (cbrt.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)))))
	48.2b	(/.f64 (.f64 (+.f64 (/.f64 (.f64 y z) t) x) t) (*.f64 y b))
	40.6b	(/.f64 (sqrt.f64 (fma.f64 y (/.f64 z t) x)) (/.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)) (sqrt.f64 (fma.f64 y (/.f64 z t) x))))
	38.9b	(cbrt.f64 (.f64 (.f64 (/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a))) (/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))) (/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))))
	15.8b	(fma.f64 (/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))
✓	16.9b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	40.7b	(-.f64 (fma.f64 (/.f64 t y) (/.f64 x b) (/.f64 z b)) (fma.f64 (/.f64 t y) (/.f64 z (.f64 b b)) (/.f64 (.f64 a (.f64 z t)) (.f64 y (*.f64 b b)))))

Compiler

Compiled 8325 to 3861 computations (53.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.4b	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
✓	5.3b	(/.f64 (*.f64 y b) t)
✓	6.1b	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)
✓	11.4b	(/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))

series303.0ms (4%)

Counts

4 → 152

Calls

4 calls:

135.0ms	(/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))
131.0ms	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
25.0ms	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)
12.0ms	(/.f64 (*.f64 y b) t)

rewrite36.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64`
25×	`add-cbrt-cube_binary64`
25×	`add-exp-log_binary64`
20×	`add-sqr-sqrt_binary64`
19×	`times-frac_binary64`

Counts

4 → 111

Calls

4 calls:

8.0ms	(/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))
7.0ms	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)
6.0ms	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
3.0ms	(/.f64 (*.f64 y b) t)

simplify186.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

687×	`associate-/l*_binary64`
522×	`associate-/r*_binary64`
472×	`fma-def_binary64`
298×	`associate-l_binary64`
156×	`associate-*l/_binary64`

Counts

263 → 241

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	430	10630
1	1368	9571
2	4935	9243
3	5254	9243

prune316.0ms (4.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	263	6	269
Fresh	5	5	10
Picked	1	0	1
Done	1	0	1
Total	270	11	281

Error

0.0b

Counts

281 → 11

Alt Table

Status	Error	Program
	15.7b	(+.f64 (/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)) (/.f64 x (+.f64 1 (+.f64 a (.f64 y (/.f64 b t))))))
	37.9b	(-.f64 (fma.f64 (/.f64 y t) (/.f64 z (fma.f64 b (/.f64 y t) 1)) (/.f64 x (fma.f64 b (/.f64 y t) 1))) (fma.f64 (/.f64 a t) (/.f64 (.f64 y z) (pow.f64 (fma.f64 b (/.f64 y t) 1) 2)) (/.f64 (.f64 x a) (pow.f64 (fma.f64 b (/.f64 y t) 1) 2))))
	15.2b	(+.f64 (/.f64 y (/.f64 (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t) z)) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	26.6b	(+.f64 (/.f64 z b) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
▶	12.6b	(+.f64 (/.f64 (.f64 y z) (fma.f64 y b (fma.f64 a t t))) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
	48.2b	(/.f64 (.f64 (+.f64 (/.f64 (.f64 y z) t) x) t) (*.f64 y b))
	15.3b	(+.f64 (.f64 (.f64 y z) (/.f64 1 (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t))) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	15.8b	(fma.f64 (/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))
	17.7b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
	14.8b	(+.f64 (/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t)) (/.f64 1 (/.f64 (+.f64 1 (fma.f64 (/.f64 y t) b a)) x)))
	40.7b	(-.f64 (fma.f64 (/.f64 t y) (/.f64 x b) (/.f64 z b)) (fma.f64 (/.f64 t y) (/.f64 z (.f64 b b)) (/.f64 (.f64 a (.f64 z t)) (.f64 y (*.f64 b b)))))

Compiler

Compiled 12051 to 4646 computations (61.4% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(fma.f64 y b (fma.f64 a t t))
	3.4b	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
	5.3b	(/.f64 (*.f64 y b) t)
✓	11.4b	(/.f64 (*.f64 y z) (fma.f64 y b (fma.f64 a t t)))

series140.0ms (1.8%)

Counts

2 → 108

Calls

2 calls:

128.0ms	(/.f64 (*.f64 y z) (fma.f64 y b (fma.f64 a t t)))
11.0ms	(fma.f64 y b (fma.f64 a t t))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`

Counts

2 → 33

Calls

2 calls:

3.0ms	(/.f64 (*.f64 y z) (fma.f64 y b (fma.f64 a t t)))
0.0ms	(fma.f64 y b (fma.f64 a t t))

simplify102.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

484×	`times-frac_binary64`
480×	`cancel-sign-sub-inv_binary64`
335×	`associate-/l*_binary64`
238×	`associate-/r*_binary64`
211×	`fma-neg_binary64`

Counts

141 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	232	4826
1	717	4480
2	3716	4438
3	5080	4438

prune269.0ms (3.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	218	5	223
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	224	10	234

Error

0.0b

Counts

234 → 10

Alt Table

Status	Error	Program
▶	11.2b	(+.f64 (/.f64 y (/.f64 (fma.f64 y b (fma.f64 a t t)) z)) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	17.7b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
	37.9b	(-.f64 (fma.f64 (/.f64 y t) (/.f64 z (fma.f64 b (/.f64 y t) 1)) (/.f64 x (fma.f64 b (/.f64 y t) 1))) (fma.f64 (/.f64 a t) (/.f64 (.f64 y z) (pow.f64 (fma.f64 b (/.f64 y t) 1) 2)) (/.f64 (.f64 x a) (pow.f64 (fma.f64 b (/.f64 y t) 1) 2))))
	40.5b	(+.f64 (/.f64 (.f64 y z) (fma.f64 y b (fma.f64 a t t))) (/.f64 (.f64 t x) (*.f64 y b)))
	26.6b	(+.f64 (/.f64 z b) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	12.0b	(+.f64 (/.f64 (.f64 y z) (fma.f64 y b (fma.f64 a t t))) (.f64 x (/.f64 1 (+.f64 1 (fma.f64 (/.f64 y t) b a)))))
	13.0b	(+.f64 (/.f64 (.f64 y z) (fma.f64 y b (fma.f64 a t t))) (/.f64 x (+.f64 1 (+.f64 a (.f64 y (/.f64 b t))))))
	15.8b	(fma.f64 (/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))
	12.6b	(+.f64 (.f64 (.f64 y z) (/.f64 1 (fma.f64 y b (fma.f64 a t t)))) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	40.7b	(-.f64 (fma.f64 (/.f64 t y) (/.f64 x b) (/.f64 z b)) (fma.f64 (/.f64 t y) (/.f64 z (.f64 b b)) (/.f64 (.f64 a (.f64 z t)) (.f64 y (*.f64 b b)))))

Compiler

Compiled 9474 to 3314 computations (65% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	3.4b	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
✓	3.8b	(/.f64 (fma.f64 y b (fma.f64 a t t)) z)
	5.3b	(/.f64 (*.f64 y b) t)
✓	8.0b	(/.f64 y (/.f64 (fma.f64 y b (fma.f64 a t t)) z))

series151.0ms (2%)

Counts

2 → 120

Calls

2 calls:

121.0ms	(/.f64 y (/.f64 (fma.f64 y b (fma.f64 a t t)) z))
29.0ms	(/.f64 (fma.f64 y b (fma.f64 a t t)) z)

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
52×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`

Counts

2 → 101

Calls

2 calls:

6.0ms	(/.f64 y (/.f64 (fma.f64 y b (fma.f64 a t t)) z))
2.0ms	(/.f64 (fma.f64 y b (fma.f64 a t t)) z)

simplify197.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

478×	`times-frac_binary64`
346×	`associate-/l*_binary64`
253×	`associate-/r*_binary64`
237×	`fma-neg_binary64`
198×	`unswap-sqr_binary64`

Counts

221 → 237

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	345	7620
1	934	7228
2	4305	7177
3	4992	7177
4	4995	7177

prune418.0ms (5.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	351	0	351
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	351	10	361

Error

0.0b

Counts

361 → 10

Alt Table

Status	Error	Program
✓	11.2b	(+.f64 (/.f64 y (/.f64 (fma.f64 y b (fma.f64 a t t)) z)) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	17.7b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
	37.9b	(-.f64 (fma.f64 (/.f64 y t) (/.f64 z (fma.f64 b (/.f64 y t) 1)) (/.f64 x (fma.f64 b (/.f64 y t) 1))) (fma.f64 (/.f64 a t) (/.f64 (.f64 y z) (pow.f64 (fma.f64 b (/.f64 y t) 1) 2)) (/.f64 (.f64 x a) (pow.f64 (fma.f64 b (/.f64 y t) 1) 2))))
	40.5b	(+.f64 (/.f64 (.f64 y z) (fma.f64 y b (fma.f64 a t t))) (/.f64 (.f64 t x) (*.f64 y b)))
	26.6b	(+.f64 (/.f64 z b) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	12.0b	(+.f64 (/.f64 (.f64 y z) (fma.f64 y b (fma.f64 a t t))) (.f64 x (/.f64 1 (+.f64 1 (fma.f64 (/.f64 y t) b a)))))
	13.0b	(+.f64 (/.f64 (.f64 y z) (fma.f64 y b (fma.f64 a t t))) (/.f64 x (+.f64 1 (+.f64 a (.f64 y (/.f64 b t))))))
	15.8b	(fma.f64 (/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))
	12.6b	(+.f64 (.f64 (.f64 y z) (/.f64 1 (fma.f64 y b (fma.f64 a t t)))) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	40.7b	(-.f64 (fma.f64 (/.f64 t y) (/.f64 x b) (/.f64 z b)) (fma.f64 (/.f64 t y) (/.f64 z (.f64 b b)) (/.f64 (.f64 a (.f64 z t)) (.f64 y (*.f64 b b)))))

Compiler

Compiled 14025 to 4117 computations (70.6% saved)

regimes1.8s (23.7%)

Accuracy

Total 7.1b remaining (98.4%)

Threshold costs 0b (0%)

Counts

127 → 3

Compiler

Compiled 31639 to 18242 computations (42.3% saved)

bsearch7.0ms (0.1%)

Compiler: Compiled 23 to 15 computations (34.8% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`+-commutative_binary64`
6×	`*-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	43	153
1	63	151
2	71	151
3	76	151
4	78	151
5	77	151

end1.0ms (0%)

Compiler: Compiled 109 to 49 computations (55% saved)

sample1.1s (14.9%)

Algorithm

1×

intervals

Results

552.0ms	8000×	body	128	valid
24.0ms	286×	body	128	invalid

Compiler

Compiled 448 to 247 computations (44.9% saved)

Details

analyze1.8s (23.4%)

sample65.0ms (0.9%)

simplify7.0ms (0.1%)

prune4.0ms (0%)

localize12.0ms (0.2%)

series266.0ms (3.5%)

rewrite7.0ms (0.1%)

simplify129.0ms (1.7%)

prune204.0ms (2.7%)

localize13.0ms (0.2%)

series303.0ms (4%)

rewrite36.0ms (0.5%)

simplify186.0ms (2.4%)

prune316.0ms (4.1%)

localize15.0ms (0.2%)

series140.0ms (1.8%)

rewrite5.0ms (0.1%)

simplify102.0ms (1.3%)

prune269.0ms (3.5%)

localize15.0ms (0.2%)

series151.0ms (2%)

rewrite18.0ms (0.2%)

simplify197.0ms (2.6%)

prune418.0ms (5.5%)

regimes1.8s (23.7%)

bsearch7.0ms (0.1%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.1s (14.9%)

Profiling