Details

analyze1.7s (20.6%)

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)

sample1.5s (18.4%)

Results

1.4s	8256×	body	128	valid
37.0ms	276×	body	128	invalid

Compiler

Compiled 71 to 47 computations (33.8% saved)

simplify10.0ms (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

9.8b

Counts

3 → 2

Alt Table

Status	Error	Program
	15.9b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
▶	13.7b	(/.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)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))
✓	3.5b	(/.f64 (*.f64 y z) t)
✓	4.9b	(/.f64 (*.f64 y b) t)
✓	9.5b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))

series258.0ms (3.2%)

Counts

4 → 120

Calls

4 calls:

219.0ms	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))
15.0ms	(+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))
12.0ms	(/.f64 (*.f64 y b) t)
11.0ms	(/.f64 (*.f64 y z) t)

rewrite29.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

9.0ms	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))
8.0ms	(+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))
3.0ms	(/.f64 (*.f64 y z) t)
3.0ms	(/.f64 (*.f64 y b) t)

simplify140.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

897×	`times-frac_binary64`
657×	`associate-/l*_binary64`
275×	`fma-def_binary64`
148×	`+-commutative_binary64`
124×	`distribute-rgt-in_binary64`

Counts

238 → 218

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	527	10471
1	1638	9815
2	5071	9815

prune272.0ms (3.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	209	9	218
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	210	10	220

Error

0.0b

Counts

220 → 10

Alt Table

Status	Error	Program
	15.9b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	26.8b	(-.f64 (+.f64 (/.f64 x (+.f64 1 a)) (/.f64 (.f64 y z) (.f64 (+.f64 1 a) t))) (/.f64 (.f64 y (.f64 b x)) (*.f64 (pow.f64 (+.f64 1 a) 2) t)))
	47.5b	(-.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)))))
	35.7b	(.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))
	47.9b	(/.f64 z b)
	13.8b	(.f64 (+.f64 x (/.f64 (.f64 y z) t)) (/.f64 1 (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))))
	13.8b	(/.f64 1 (/.f64 (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)) (+.f64 x (/.f64 (.f64 y z) t))))
	16.0b	(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)))))
	16.3b	(/.f64 (+.f64 x (/.f64 y (/.f64 t z))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
▶	13.7b	(/.f64 (+.f64 x (.f64 (.f64 y z) (/.f64 1 t))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

Compiler

Compiled 10635 to 4586 computations (56.9% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))
✓	3.6b	(.f64 (.f64 y z) (/.f64 1 t))
	4.9b	(/.f64 (*.f64 y b) t)
✓	9.5b	(/.f64 (+.f64 x (.f64 (.f64 y z) (/.f64 1 t))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

series227.0ms (2.8%)

Counts

2 → 108

Calls

2 calls:

214.0ms	(/.f64 (+.f64 x (.f64 (.f64 y z) (/.f64 1 t))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
12.0ms	(.f64 (.f64 y z) (/.f64 1 t))

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`*-un-lft-identity_binary64`
26×	`add-exp-log_binary64`
24×	`times-frac_binary64`
19×	`add-sqr-sqrt_binary64`
19×	`add-cube-cbrt_binary64`

Counts

2 → 83

Calls

2 calls:

11.0ms	(.f64 (.f64 y z) (/.f64 1 t))
9.0ms	(/.f64 (+.f64 x (.f64 (.f64 y z) (/.f64 1 t))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

simplify131.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

862×	`times-frac_binary64`
604×	`associate-/l*_binary64`
431×	`associate-/r*_binary64`
274×	`fma-def_binary64`
149×	`+-commutative_binary64`

Counts

191 → 182

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	498	9573
1	1578	8726
2	5228	8726

prune313.0ms (3.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	245	1	246
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	246	10	256

Error

0.0b

Counts

256 → 10

Alt Table

Status	Error	Program
▶	12.5b	(+.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)))))
	47.5b	(-.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)))))
	35.7b	(.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))
	47.9b	(/.f64 z b)
	15.9b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	13.8b	(.f64 (+.f64 x (/.f64 (.f64 y z) t)) (/.f64 1 (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))))
	13.8b	(/.f64 1 (/.f64 (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)) (+.f64 x (/.f64 (.f64 y z) t))))
	16.0b	(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)))))
	16.3b	(/.f64 (+.f64 x (/.f64 y (/.f64 t z))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
✓	13.7b	(/.f64 (+.f64 x (.f64 (.f64 y z) (/.f64 1 t))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

Compiler

Compiled 11575 to 5468 computations (52.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.8b	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
✓	3.8b	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)
	4.9b	(/.f64 (*.f64 y b) t)
✓	9.2b	(/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))

series273.0ms (3.4%)

Counts

3 → 152

Calls

3 calls:

137.0ms	(/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))
115.0ms	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
19.0ms	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)

rewrite33.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`*-un-lft-identity_binary64`
19×	`add-cbrt-cube_binary64`
19×	`add-exp-log_binary64`
17×	`add-sqr-sqrt_binary64`
16×	`times-frac_binary64`

Counts

3 → 88

Calls

3 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))))

simplify137.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

938×	`times-frac_binary64`
627×	`associate-/l*_binary64`
490×	`associate-/r*_binary64`
153×	`fma-def_binary64`
91×	`*-commutative_binary64`

Counts

240 → 187

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	395	10369
1	1285	9529
2	5042	9529

prune307.0ms (3.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	238	3	241
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	241	10	251

Error

0.0b

Counts

251 → 10

Alt Table

Status	Error	Program
▶	12.7b	(+.f64 (/.f64 (.f64 (/.f64 y (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))) z) t) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	13.2b	(+.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)))))
	32.5b	(+.f64 (/.f64 z b) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	47.5b	(-.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)))))
	35.7b	(.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))
	15.9b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	13.8b	(.f64 (+.f64 x (/.f64 (.f64 y z) t)) (/.f64 1 (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))))
	13.8b	(/.f64 1 (/.f64 (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)) (+.f64 x (/.f64 (.f64 y z) t))))
	16.3b	(/.f64 (+.f64 x (/.f64 y (/.f64 t z))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
✓	13.7b	(/.f64 (+.f64 x (.f64 (.f64 y z) (/.f64 1 t))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

Compiler

Compiled 11025 to 4376 computations (60.3% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.9b	(/.f64 y (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
✓	4.8b	(/.f64 (.f64 (/.f64 y (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))) z) t)
	4.9b	(/.f64 (*.f64 y b) t)
✓	5.4b	(.f64 (/.f64 y (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))) z)

series328.0ms (4.1%)

Counts

3 → 168

Calls

3 calls:

125.0ms	(.f64 (/.f64 y (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))) z)
122.0ms	(/.f64 (.f64 (/.f64 y (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))) z) t)
80.0ms	(/.f64 y (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))

rewrite34.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`*-un-lft-identity_binary64`
34×	`times-frac_binary64`
30×	`add-sqr-sqrt_binary64`
25×	`add-cube-cbrt_binary64`
21×	`distribute-lft-out_binary64`

Counts

3 → 107

Calls

3 calls:

10.0ms	(/.f64 (.f64 (/.f64 y (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))) z) t)
9.0ms	(.f64 (/.f64 y (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))) z)
6.0ms	(/.f64 y (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))

simplify235.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

737×	`associate-/l*_binary64`
529×	`associate-/r*_binary64`
495×	`fma-def_binary64`
210×	`associate-*l/_binary64`
175×	`associate-*r/_binary64`

Counts

275 → 270

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	495	13906
1	1561	13049
2	4890	12608
3	5201	12608

prune393.0ms (4.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	324	0	324
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	324	10	334

Error

0.0b

Counts

334 → 10

Alt Table

Status	Error	Program
✓	12.7b	(+.f64 (/.f64 (.f64 (/.f64 y (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))) z) t) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	13.2b	(+.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)))))
	32.5b	(+.f64 (/.f64 z b) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	47.5b	(-.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)))))
	35.7b	(.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))
	15.9b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	13.8b	(.f64 (+.f64 x (/.f64 (.f64 y z) t)) (/.f64 1 (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))))
	13.8b	(/.f64 1 (/.f64 (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)) (+.f64 x (/.f64 (.f64 y z) t))))
	16.3b	(/.f64 (+.f64 x (/.f64 y (/.f64 t z))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
✓	13.7b	(/.f64 (+.f64 x (.f64 (.f64 y z) (/.f64 1 t))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

Compiler

Compiled 14988 to 6256 computations (58.3% saved)

regimes1.5s (18.8%)

Accuracy

Total 6.2b remaining (97.1%)

Threshold costs 0b (0%)

Counts

96 → 3

Compiler

Compiled 21851 to 13723 computations (37.2% saved)

bsearch4.0ms (0%)

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

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
4×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	159
1	53	159
2	52	159

end198.0ms (2.5%)

Compiler: Compiled 500 to 266 computations (46.8% saved)

Details

analyze1.7s (20.6%)

sample1.5s (18.4%)

simplify10.0ms (0.1%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series258.0ms (3.2%)

rewrite29.0ms (0.4%)

simplify140.0ms (1.7%)

prune272.0ms (3.4%)

localize14.0ms (0.2%)

series227.0ms (2.8%)

rewrite26.0ms (0.3%)

simplify131.0ms (1.6%)

prune313.0ms (3.9%)

localize12.0ms (0.1%)

series273.0ms (3.4%)

rewrite33.0ms (0.4%)

simplify137.0ms (1.7%)

prune307.0ms (3.8%)

localize13.0ms (0.2%)

series328.0ms (4.1%)

rewrite34.0ms (0.4%)

simplify235.0ms (2.9%)

prune393.0ms (4.9%)

regimes1.5s (18.8%)

bsearch4.0ms (0%)

simplify9.0ms (0.1%)

end198.0ms (2.5%)

Profiling