Details

analyze1.9s (18%)

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
3.9%	95.8%	0.3%	11
7.4%	92.3%	0.3%	12
8.8%	90.9%	0.3%	13
10.2%	89.5%	0.3%	14

Compiler

Compiled 24 to 16 computations (33.3% saved)

sample1.4s (13.2%)

Results

1.3s	8256×	body	128	valid
40.0ms	299×	body	128	invalid

Compiler

Compiled 71 to 47 computations (33.8% 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

prune5.0ms (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

11.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	17.5b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
▶	14.9b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))

Compiler

Compiled 126 to 78 computations (38.1% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (*.f64 y z) t))
✓	5.1b	(/.f64 (*.f64 y b) t)
✓	5.3b	(/.f64 (*.f64 y z) t)
✓	10.6b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))

series206.0ms (2%)

Counts

4 → 120

Calls

4 calls:

168.0ms	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))
13.0ms	(/.f64 (*.f64 y z) t)
13.0ms	(+.f64 x (/.f64 (*.f64 y z) t))
11.0ms	(/.f64 (*.f64 y b) t)

rewrite26.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`*-un-lft-identity_binary64`
26×	`times-frac_binary64`
22×	`distribute-lft-out_binary64`
20×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`

Counts

4 → 112

Calls

4 calls:

9.0ms	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))
4.0ms	(+.f64 x (/.f64 (*.f64 y z) t))
3.0ms	(/.f64 (*.f64 y b) t)
3.0ms	(/.f64 (*.f64 y z) t)

simplify134.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

897×	`times-frac_binary64`
656×	`associate-/l*_binary64`
274×	`fma-def_binary64`
148×	`+-commutative_binary64`
118×	`distribute-rgt-in_binary64`

Counts

232 → 201

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	521	10152
1	1626	9540
2	5047	9540

prune252.0ms (2.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	192	9	201
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	193	10	203

Error

0.0b

Counts

203 → 10

Alt Table

Status	Error	Program
	42.9b	(-.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)))))
▶	16.9b	(/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 y (/.f64 t b))))
	17.9b	(fma.f64 (/.f64 y (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))) (/.f64 z t) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
	35.3b	(.f64 (/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (fma.f64 (.f64 y b) (-.f64 a 1) (.f64 t (fma.f64 a a -1)))) (*.f64 (-.f64 a 1) t))
	39.6b	(/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))
✓	14.9b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))
	34.9b	(/.f64 (-.f64 (.f64 x x) (.f64 (/.f64 (.f64 y z) t) (/.f64 (.f64 y z) t))) (.f64 (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)) (-.f64 x (/.f64 (*.f64 y z) t))))
	51.5b	(-.f64 (fma.f64 2 (/.f64 (.f64 a (.f64 z (.f64 t t))) (.f64 (.f64 y y) (pow.f64 b 3))) (+.f64 (fma.f64 (.f64 (/.f64 t y) (/.f64 t y)) (/.f64 z (pow.f64 b 3)) (/.f64 z b)) (fma.f64 (/.f64 t y) (/.f64 x b) (/.f64 (.f64 (.f64 z (.f64 t t)) (.f64 a a)) (.f64 (.f64 y y) (pow.f64 b 3)))))) (fma.f64 (/.f64 t y) (/.f64 z (.f64 b b)) (fma.f64 (.f64 (/.f64 t y) (/.f64 t y)) (/.f64 x (.f64 b b)) (fma.f64 (/.f64 a y) (.f64 (/.f64 z b) (/.f64 t b)) (/.f64 (.f64 a (.f64 x (.f64 t t))) (.f64 (.f64 y b) (.f64 y b)))))))
	42.9b	(/.f64 z b)
	17.0b	(/.f64 (+.f64 x (/.f64 y (/.f64 t z))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

Compiler

Compiled 10338 to 4426 computations (57.2% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 x (/.f64 (*.f64 y z) t))
	5.3b	(/.f64 (*.f64 y z) t)
✓	6.0b	(/.f64 y (/.f64 t b))
✓	10.6b	(/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 y (/.f64 t b))))

series174.0ms (1.7%)

Counts

2 → 108

Calls

2 calls:

161.0ms	(/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 y (/.f64 t b))))
13.0ms	(/.f64 y (/.f64 t b))

rewrite29.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

95×	`times-frac_binary64`
92×	`*-un-lft-identity_binary64`
55×	`add-sqr-sqrt_binary64`
55×	`add-cube-cbrt_binary64`
21×	`distribute-lft-out_binary64`

Counts

2 → 121

Calls

2 calls:

16.0ms	(/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 y (/.f64 t b))))
4.0ms	(/.f64 y (/.f64 t b))

simplify150.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

796×	`times-frac_binary64`
608×	`associate-/l*_binary64`
268×	`fma-def_binary64`
198×	`associate-/r/_binary64`
145×	`+-commutative_binary64`

Counts

229 → 233

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	580	10544
1	1723	9789
2	4987	9789

prune307.0ms (3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	277	4	281
Fresh	3	5	8
Picked	1	0	1
Done	1	0	1
Total	282	9	291

Error

0.0b

Counts

291 → 9

Alt Table

Status	Error	Program
	42.9b	(/.f64 z b)
▶	14.5b	(.f64 (+.f64 x (/.f64 (.f64 y z) t)) (/.f64 1 (+.f64 1 (fma.f64 (/.f64 y t) b a))))
	17.9b	(fma.f64 (/.f64 y (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))) (/.f64 z t) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
	18.0b	(/.f64 (+.f64 x (/.f64 y (/.f64 t z))) (+.f64 (+.f64 a 1) (/.f64 y (/.f64 t b))))
	35.3b	(.f64 (/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (fma.f64 (.f64 y b) (-.f64 a 1) (.f64 t (fma.f64 a a -1)))) (*.f64 (-.f64 a 1) t))
	17.3b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (.f64 y (*.f64 (/.f64 1 t) b))))
	42.9b	(-.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)))))
	41.0b	(.f64 (/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (.f64 (+.f64 (pow.f64 a 3) (pow.f64 1 3)) (/.f64 t b)) (.f64 (+.f64 (.f64 a a) (-.f64 (.f64 1 1) (.f64 a 1))) y))) (.f64 (+.f64 (.f64 a a) (-.f64 (.f64 1 1) (*.f64 a 1))) (/.f64 t b)))
	39.6b	(/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))

Compiler

Compiled 12263 to 5037 computations (58.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 1 (+.f64 1 (fma.f64 (/.f64 y t) b a)))
✓	3.1b	(fma.f64 (/.f64 y t) b a)
	5.3b	(/.f64 (*.f64 y z) t)
✓	10.5b	(.f64 (+.f64 x (/.f64 (.f64 y z) t)) (/.f64 1 (+.f64 1 (fma.f64 (/.f64 y t) b a))))

series228.0ms (2.2%)

Counts

3 → 168

Calls

3 calls:

163.0ms	(.f64 (+.f64 x (/.f64 (.f64 y z) t)) (/.f64 1 (+.f64 1 (fma.f64 (/.f64 y t) b a))))
51.0ms	(/.f64 1 (+.f64 1 (fma.f64 (/.f64 y t) b a)))
14.0ms	(fma.f64 (/.f64 y t) b a)

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
28×	`add-sqr-sqrt_binary64`
26×	`times-frac_binary64`
21×	`add-cube-cbrt_binary64`
18×	`associate-r_binary64`

Counts

3 → 97

Calls

3 calls:

11.0ms	(.f64 (+.f64 x (/.f64 (.f64 y z) t)) (/.f64 1 (+.f64 1 (fma.f64 (/.f64 y t) b a))))
3.0ms	(/.f64 1 (+.f64 1 (fma.f64 (/.f64 y t) b a)))
0.0ms	(fma.f64 (/.f64 y t) b a)

simplify170.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

663×	`associate-/l*_binary64`
537×	`associate-/r*_binary64`
290×	`fma-def_binary64`
169×	`+-commutative_binary64`
168×	`associate-*r/_binary64`

Counts

265 → 237

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	531	12981
1	1756	12189
2	5110	12189

prune368.0ms (3.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	263	1	264
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	263	10	273

Error

0.0b

Counts

273 → 10

Alt Table

Status	Error	Program
	42.9b	(/.f64 z b)
✓	14.5b	(.f64 (+.f64 x (/.f64 (.f64 y z) t)) (/.f64 1 (+.f64 1 (fma.f64 (/.f64 y t) b a))))
	17.9b	(fma.f64 (/.f64 y (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))) (/.f64 z t) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
	18.0b	(/.f64 (+.f64 x (/.f64 y (/.f64 t z))) (+.f64 (+.f64 a 1) (/.f64 y (/.f64 t b))))
	35.3b	(.f64 (/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (fma.f64 (.f64 y b) (-.f64 a 1) (.f64 t (fma.f64 a a -1)))) (*.f64 (-.f64 a 1) t))
	39.6b	(/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))
	17.5b	(.f64 (+.f64 x (.f64 y (/.f64 z t))) (/.f64 1 (+.f64 1 (fma.f64 (/.f64 y t) b a))))
▶	17.3b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (.f64 y (*.f64 (/.f64 1 t) b))))
	42.9b	(-.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)))))
	41.0b	(.f64 (/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (.f64 (+.f64 (pow.f64 a 3) (pow.f64 1 3)) (/.f64 t b)) (.f64 (+.f64 (.f64 a a) (-.f64 (.f64 1 1) (.f64 a 1))) y))) (.f64 (+.f64 (.f64 a a) (-.f64 (.f64 1 1) (*.f64 a 1))) (/.f64 t b)))

Compiler

Compiled 12765 to 5768 computations (54.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (/.f64 1 t) b)
	5.3b	(/.f64 (*.f64 y z) t)
✓	6.3b	(.f64 y (.f64 (/.f64 1 t) b))
✓	10.6b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (.f64 y (*.f64 (/.f64 1 t) b))))

series201.0ms (1.9%)

Counts

3 → 132

Calls

3 calls:

181.0ms	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (.f64 y (*.f64 (/.f64 1 t) b))))
13.0ms	(.f64 y (.f64 (/.f64 1 t) b))
5.0ms	(*.f64 (/.f64 1 t) b)

rewrite94.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`*-un-lft-identity_binary64`
29×	`add-exp-log_binary64`
28×	`add-sqr-sqrt_binary64`
23×	`times-frac_binary64`
21×	`add-cube-cbrt_binary64`

Counts

3 → 101

Calls

3 calls:

10.0ms	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (.f64 y (*.f64 (/.f64 1 t) b))))
5.0ms	(.f64 y (.f64 (/.f64 1 t) b))
5.0ms	(*.f64 (/.f64 1 t) b)

simplify210.0ms (2%)

Algorithm

1×	egg-herbie

Rules

762×	`times-frac_binary64`
568×	`associate-/l*_binary64`
427×	`associate-/r*_binary64`
273×	`fma-def_binary64`
150×	`+-commutative_binary64`

Counts

233 → 220

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	517	9633
1	1595	8865
2	4992	8865

prune280.0ms (2.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	246	1	247
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	247	10	257

Error

0.0b

Counts

257 → 10

Alt Table

Status	Error	Program
	42.9b	(/.f64 z b)
✓	14.5b	(.f64 (+.f64 x (/.f64 (.f64 y z) t)) (/.f64 1 (+.f64 1 (fma.f64 (/.f64 y t) b a))))
	18.0b	(/.f64 (+.f64 x (/.f64 y (/.f64 t z))) (+.f64 (+.f64 a 1) (/.f64 y (/.f64 t b))))
	35.3b	(.f64 (/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (fma.f64 (.f64 y b) (-.f64 a 1) (.f64 t (fma.f64 a a -1)))) (*.f64 (-.f64 a 1) t))
	39.6b	(/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))
	17.5b	(.f64 (+.f64 x (.f64 y (/.f64 z t))) (/.f64 1 (+.f64 1 (fma.f64 (/.f64 y t) b a))))
✓	17.3b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (.f64 y (*.f64 (/.f64 1 t) b))))
	17.3b	(fma.f64 (/.f64 y (fma.f64 y (/.f64 b t) (+.f64 1 a))) (/.f64 z t) (/.f64 x (fma.f64 y (/.f64 b t) (+.f64 1 a))))
	42.9b	(-.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)))))
	41.0b	(.f64 (/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (.f64 (+.f64 (pow.f64 a 3) (pow.f64 1 3)) (/.f64 t b)) (.f64 (+.f64 (.f64 a a) (-.f64 (.f64 1 1) (.f64 a 1))) y))) (.f64 (+.f64 (.f64 a a) (-.f64 (.f64 1 1) (*.f64 a 1))) (/.f64 t b)))

Compiler

Compiled 11294 to 5362 computations (52.5% saved)

regimes4.0s (38.9%)

Accuracy

Total 6.8b remaining (97.1%)

Threshold costs 0b (0%)

Counts

185 → 3

Compiler

Compiled 46107 to 28537 computations (38.1% saved)

bsearch8.0ms (0.1%)

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

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
3×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	139
1	48	139
2	47	139

end164.0ms (1.6%)

Compiler: Compiled 479 to 266 computations (44.5% saved)

Details

analyze1.9s (18%)

sample1.4s (13.2%)

simplify7.0ms (0.1%)

prune5.0ms (0%)

localize13.0ms (0.1%)

series206.0ms (2%)

rewrite26.0ms (0.2%)

simplify134.0ms (1.3%)

prune252.0ms (2.4%)

localize12.0ms (0.1%)

series174.0ms (1.7%)

rewrite29.0ms (0.3%)

simplify150.0ms (1.5%)

prune307.0ms (3%)

localize12.0ms (0.1%)

series228.0ms (2.2%)

rewrite21.0ms (0.2%)

simplify170.0ms (1.6%)

prune368.0ms (3.6%)

localize13.0ms (0.1%)

series201.0ms (1.9%)

rewrite94.0ms (0.9%)

simplify210.0ms (2%)

prune280.0ms (2.7%)

regimes4.0s (38.9%)

bsearch8.0ms (0.1%)

simplify5.0ms (0%)

end164.0ms (1.6%)

Profiling