Details

analyze1.7s (14.2%)

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
12.5%	87.2%	0.3%	7
12.5%	87.2%	0.3%	8
12.5%	87.2%	0.3%	9
12.5%	87.2%	0.3%	10
18.7%	81%	0.3%	11
28%	71.7%	0.3%	12
31.2%	68.5%	0.3%	13
31.2%	68.5%	0.3%	14

Compiler

Compiled 24 to 16 computations (33.3% saved)

sample2.0s (16.6%)

Results

2.0s

8256×

body

128

valid

Compiler

Compiled 71 to 47 computations (33.8% saved)

simplify18.0ms (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

prune8.0ms (0.1%)

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

14.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	17.2b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))
	19.1b	(/.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)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (*.f64 y z) t))
✓	4.2b	(/.f64 (*.f64 y b) t)
✓	4.6b	(/.f64 (*.f64 y z) t)
✓	14.6b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))

series548.0ms (4.5%)

Counts

4 → 120

Calls

4 calls:

466.0ms	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))
28.0ms	(/.f64 (*.f64 y z) t)
27.0ms	(/.f64 (*.f64 y b) t)
26.0ms	(+.f64 x (/.f64 (*.f64 y z) t))

rewrite63.0ms (0.5%)

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:

22.0ms	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))
8.0ms	(+.f64 x (/.f64 (*.f64 y z) t))
7.0ms	(/.f64 (*.f64 y b) t)
7.0ms	(/.f64 (*.f64 y z) t)

simplify290.0ms (2.4%)

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

prune483.0ms (3.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

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

Error

0.7b

Counts

203 → 10

Alt Table

Status	Error	Program
	33.3b	(.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))
	43.6b	(-.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)))))
	17.5b	(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)))))
	17.2b	(/.f64 (+.f64 x (.f64 (.f64 y z) (/.f64 1 t))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
	19.1b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	41.9b	(/.f64 z b)
	17.8b	(/.f64 (.f64 (cbrt.f64 (+.f64 x (/.f64 (.f64 y z) t))) (cbrt.f64 (+.f64 x (/.f64 (.f64 y z) t)))) (/.f64 (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)) (cbrt.f64 (+.f64 x (/.f64 (*.f64 y z) t)))))
▶	14.5b	(+.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)))))
	17.2b	(.f64 (+.f64 x (/.f64 (.f64 y z) t)) (/.f64 1 (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))))
	17.5b	(/.f64 1 (/.f64 (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)) (+.f64 x (/.f64 (.f64 y z) t))))

Compiler

Compiled 10219 to 4391 computations (57% saved)

localize33.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.2b	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
	4.2b	(/.f64 (*.f64 y b) t)
✓	5.7b	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)
✓	10.6b	(/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))

series488.0ms (4%)

Counts

3 → 152

Calls

3 calls:

253.0ms	(/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))
211.0ms	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
24.0ms	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)

rewrite64.0ms (0.5%)

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:

18.0ms	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)
17.0ms	(/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))
14.0ms	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))

simplify299.0ms (2.4%)

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

prune613.0ms (5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	238	5	243
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	242	11	253

Error

0.5b

Counts

253 → 11

Alt Table

Status	Error	Program
	15.6b	(+.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 t b))))))
	33.3b	(.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))
	43.6b	(-.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)))))
	17.5b	(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)))))
	17.2b	(/.f64 (+.f64 x (.f64 (.f64 y z) (/.f64 1 t))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
	26.1b	(+.f64 (/.f64 z b) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
▶	15.0b	(+.f64 (/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)) (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) (cbrt.f64 x))))
	28.8b	(+.f64 (/.f64 (.f64 y z) (.f64 (sqrt.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))) (.f64 (sqrt.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))) t))) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
	15.6b	(+.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)))))
	17.2b	(.f64 (+.f64 x (/.f64 (.f64 y z) t)) (/.f64 1 (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))))
	17.5b	(/.f64 1 (/.f64 (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)) (+.f64 x (/.f64 (.f64 y z) t))))

Compiler

Compiled 11250 to 4481 computations (60.2% saved)

localize39.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.8b	(/.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) (cbrt.f64 x))
	4.2b	(/.f64 (*.f64 y b) t)
	5.7b	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)
	10.6b	(/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))

series569.0ms (4.7%)

Counts

1 → 60

Calls

1 calls:

569.0ms

(/.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) (cbrt.f64 x))

rewrite29.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 57

Calls

1 calls:

17.0ms

(/.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) (cbrt.f64 x))

simplify210.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

734×	`fma-neg_binary64`
448×	`associate-/l*_binary64`
440×	`associate-*r/_binary64`
398×	`times-frac_binary64`
283×	`*-commutative_binary64`

Counts

117 → 88

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	98	3178
1	215	2836
2	598	2586
3	2049	2582
4	3997	2582
5	5004	2582

prune543.0ms (4.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	265	0	265
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	265	11	276

Error

0.5b

Counts

276 → 11

Alt Table

Status	Error	Program
▶	15.6b	(+.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 t b))))))
	33.3b	(.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))
	43.6b	(-.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)))))
	17.5b	(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)))))
	17.2b	(/.f64 (+.f64 x (.f64 (.f64 y z) (/.f64 1 t))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
	26.1b	(+.f64 (/.f64 z b) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
✓	15.0b	(+.f64 (/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)) (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) (cbrt.f64 x))))
	28.8b	(+.f64 (/.f64 (.f64 y z) (.f64 (sqrt.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))) (.f64 (sqrt.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))) t))) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
	15.6b	(+.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)))))
	17.2b	(.f64 (+.f64 x (/.f64 (.f64 y z) t)) (/.f64 1 (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))))
	17.5b	(/.f64 1 (/.f64 (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)) (+.f64 x (/.f64 (.f64 y z) t))))

Compiler

Compiled 13063 to 4520 computations (65.4% saved)

localize37.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	4.2b	(/.f64 (*.f64 y b) t)
	5.7b	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)
✓	5.9b	(/.f64 y (/.f64 t b))
	10.6b	(/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))

series27.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

27.0ms

(/.f64 y (/.f64 t b))

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac_binary64`
43×	`*-un-lft-identity_binary64`
43×	`add-sqr-sqrt_binary64`
43×	`add-cube-cbrt_binary64`
13×	`associate-/r*_binary64`

Counts

1 → 72

Calls

1 calls:

9.0ms

(/.f64 y (/.f64 t b))

simplify237.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

1089×	`associate-/r/_binary64`
835×	`fma-def_binary64`
611×	`fma-neg_binary64`
460×	`distribute-rgt-in_binary64`
452×	`div-sub_binary64`

Counts

108 → 114

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	149	1514
1	310	1454
2	924	1451
3	2212	1451
4	2356	1451
5	2544	1451
6	2955	1451
7	3895	1451
8	4379	1451
9	5031	1451

prune643.0ms (5.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	263	0	263
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	263	11	274

Error

0.5b

Counts

274 → 11

Alt Table

Status	Error	Program
✓	15.6b	(+.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 t b))))))
	33.3b	(.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))
	43.6b	(-.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)))))
	17.5b	(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)))))
	17.2b	(/.f64 (+.f64 x (.f64 (.f64 y z) (/.f64 1 t))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
	26.1b	(+.f64 (/.f64 z b) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
✓	15.0b	(+.f64 (/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)) (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) (cbrt.f64 x))))
	28.8b	(+.f64 (/.f64 (.f64 y z) (.f64 (sqrt.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))) (.f64 (sqrt.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))) t))) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
	15.6b	(+.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)))))
	17.2b	(.f64 (+.f64 x (/.f64 (.f64 y z) t)) (/.f64 1 (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))))
	17.5b	(/.f64 1 (/.f64 (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)) (+.f64 x (/.f64 (.f64 y z) t))))

Compiler

Compiled 10746 to 4041 computations (62.4% saved)

regimes2.8s (22.9%)

Accuracy

Total 6.5b remaining (92.8%)

Threshold costs 0b (0%)

Counts

101 → 4

Compiler

Compiled 26834 to 15718 computations (41.4% saved)

bsearch13.0ms (0.1%)

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

simplify15.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
8×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-lft-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	204
1	63	204
2	67	204
3	69	204
4	70	204
5	69	204

end355.0ms (2.9%)

Compiler: Compiled 637 to 318 computations (50.1% saved)

Details

analyze1.7s (14.2%)

sample2.0s (16.6%)

simplify18.0ms (0.1%)

prune8.0ms (0.1%)

localize29.0ms (0.2%)

series548.0ms (4.5%)

rewrite63.0ms (0.5%)

simplify290.0ms (2.4%)

prune483.0ms (3.9%)

localize33.0ms (0.3%)

series488.0ms (4%)

rewrite64.0ms (0.5%)

simplify299.0ms (2.4%)

prune613.0ms (5%)

localize39.0ms (0.3%)

series569.0ms (4.7%)

rewrite29.0ms (0.2%)

simplify210.0ms (1.7%)

prune543.0ms (4.4%)

localize37.0ms (0.3%)

series27.0ms (0.2%)

rewrite21.0ms (0.2%)

simplify237.0ms (1.9%)

prune643.0ms (5.3%)

regimes2.8s (22.9%)

bsearch13.0ms (0.1%)

simplify15.0ms (0.1%)

end355.0ms (2.9%)

Profiling