Details

analyze1.5s (19.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
1.8%	98%	0.2%	10
7.7%	92.1%	0.2%	11
10.4%	89.4%	0.2%	12
12.1%	87.7%	0.2%	13
21.4%	78.3%	0.4%	14

Compiler

Compiled 19 to 12 computations (36.8% saved)

sample1.7s (22.3%)

Results

940.0ms	6931×	body	128	valid
209.0ms	514×	body	512	valid
182.0ms	1303×	body	128	invalid
152.0ms	389×	body	1024	valid
78.0ms	362×	body	256	valid
27.0ms	60×	body	2048	valid

Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify83.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

930×	`fma-def_binary64`
859×	`div-sub_binary64`
817×	`unsub-neg_binary64`
555×	`neg-mul-1_binary64`
380×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	24	17
2	52	17
3	155	17
4	477	17
5	1268	17
6	3213	17
7	4154	17
8	4434	17
9	4965	17
10	4951	17

prune3.0ms (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

15.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	15.4b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
	15.5b	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

Compiler

Compiled 100 to 54 computations (46% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t x) (-.f64 a z))
✓	15.4b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)

series104.0ms (1.4%)

Counts

2 → 108

Calls

2 calls:

72.0ms	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
31.0ms	(/.f64 (-.f64 t x) (-.f64 a z))

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
38×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out--_binary64`

Counts

2 → 64

Calls

2 calls:

6.0ms	(/.f64 (-.f64 t x) (-.f64 a z))
0.0ms	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)

simplify120.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

523×	`cancel-sign-sub-inv_binary64`
479×	`sub-neg_binary64`
353×	`associate-+r+_binary64`
286×	`+-commutative_binary64`
272×	`associate-+l+_binary64`

Counts

172 → 136

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	356	6269
1	1045	6192
2	3851	6156
3	5233	6156

prune104.0ms (1.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	129	7	136
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	131	7	138

Error

0.6b

Counts

138 → 7

Alt Table

Status	Error	Program
	32.1b	(expm1.f64 (log1p.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)))
	39.0b	(-.f64 (+.f64 (/.f64 (.f64 y x) z) (+.f64 t (/.f64 (.f64 a t) z))) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a x) z)))
	34.4b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
	32.2b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
	46.2b	(*.f64 y (/.f64 (-.f64 t x) (-.f64 a z)))
	20.7b	(-.f64 (+.f64 (/.f64 (.f64 z x) (-.f64 a z)) (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x)) (+.f64 (/.f64 (.f64 y x) (-.f64 a z)) (/.f64 (.f64 t z) (-.f64 a z))))
▶	15.9b	(fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x))) x)

Compiler

Compiled 4724 to 1464 computations (69% saved)

localize15.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 a z) (-.f64 t x))
✓	0.6b	(/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x)))
✓	15.4b	(fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x))) x)

series116.0ms (1.5%)

Counts

3 → 156

Calls

3 calls:

60.0ms	(fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x))) x)
29.0ms	(/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x)))
27.0ms	(/.f64 (-.f64 a z) (-.f64 t x))

rewrite41.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

218×	`times-frac_binary64`
195×	`*-un-lft-identity_binary64`
195×	`add-sqr-sqrt_binary64`
91×	`add-cube-cbrt_binary64`
52×	`distribute-lft-out--_binary64`

Counts

3 → 214

Calls

3 calls:

10.0ms	(/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x)))
6.0ms	(/.f64 (-.f64 a z) (-.f64 t x))
0.0ms	(fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x))) x)

simplify163.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

388×	`associate-+r+_binary64`
313×	`associate-+l+_binary64`
283×	`times-frac_binary64`
266×	`associate-/l*_binary64`
227×	`associate--l+_binary64`

Counts

370 → 317

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	484	11287
1	1347	10818
2	4997	10818

prune211.0ms (2.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	315	2	317
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	316	8	324

Error

0.6b

Counts

324 → 8

Alt Table

Status	Error	Program
	32.1b	(expm1.f64 (log1p.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)))
	39.0b	(-.f64 (+.f64 (/.f64 (.f64 y x) z) (+.f64 t (/.f64 (.f64 a t) z))) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a x) z)))
▶	15.7b	(+.f64 (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))) x)
	46.2b	(*.f64 y (/.f64 (-.f64 t x) (-.f64 a z)))
	16.0b	(fma.f64 (-.f64 y z) (/.f64 1 (-.f64 (/.f64 a (-.f64 t x)) (/.f64 z (-.f64 t x)))) x)
	34.4b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
	32.2b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
	20.7b	(-.f64 (+.f64 (/.f64 (.f64 z x) (-.f64 a z)) (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x)) (+.f64 (/.f64 (.f64 y x) (-.f64 a z)) (/.f64 (.f64 t z) (-.f64 a z))))

Compiler

Compiled 9869 to 3020 computations (69.4% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 a z) (-.f64 t x))
✓	3.8b	(+.f64 (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))) x)
✓	6.2b	(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x)))

series155.0ms (2.1%)

Counts

2 → 120

Calls

2 calls:

87.0ms	(+.f64 (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))) x)
67.0ms	(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x)))

rewrite133.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

585×	`times-frac_binary64`
535×	`*-un-lft-identity_binary64`
533×	`add-sqr-sqrt_binary64`
187×	`add-cube-cbrt_binary64`
173×	`distribute-lft-out--_binary64`

Counts

2 → 386

Calls

2 calls:

43.0ms	(+.f64 (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))) x)
14.0ms	(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x)))

simplify270.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

844×	`times-frac_binary64`
422×	`associate-/r/_binary64`
239×	`associate-/l*_binary64`
214×	`sub-neg_binary64`
206×	`associate-/l/_binary64`

Counts

506 → 437

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	632	14909
1	1921	14784
2	4844	14700
3	5862	14700

prune374.0ms (5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	505	2	507
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	506	9	515

Error

0.6b

Counts

515 → 9

Alt Table

Status	Error	Program
	32.1b	(expm1.f64 (log1p.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)))
	39.0b	(-.f64 (+.f64 (/.f64 (.f64 y x) z) (+.f64 t (/.f64 (.f64 a t) z))) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a x) z)))
✓	15.7b	(+.f64 (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))) x)
	46.2b	(*.f64 y (/.f64 (-.f64 t x) (-.f64 a z)))
	16.0b	(fma.f64 (-.f64 y z) (/.f64 1 (-.f64 (/.f64 a (-.f64 t x)) (/.f64 z (-.f64 t x)))) x)
	34.4b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
	32.2b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
▶	12.7b	(fma.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x) x)
	41.7b	(fma.f64 (/.f64 1 (sqrt.f64 (/.f64 (-.f64 a z) (-.f64 t x)))) (/.f64 (-.f64 y z) (sqrt.f64 (/.f64 (-.f64 a z) (-.f64 t x)))) x)

Compiler

Compiled 17067 to 3700 computations (78.3% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 y z) (-.f64 a z))
✓	2.4b	(fma.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x) x)

series140.0ms (1.9%)

Counts

2 → 96

Calls

2 calls:

120.0ms	(fma.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x) x)
20.0ms	(/.f64 (-.f64 y z) (-.f64 a z))

rewrite56.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
38×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out--_binary64`

Counts

2 → 64

Calls

2 calls:

6.0ms	(/.f64 (-.f64 y z) (-.f64 a z))
0.0ms	(fma.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x) x)

simplify119.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

585×	`cancel-sign-sub-inv_binary64`
534×	`sub-neg_binary64`
343×	`associate-+r+_binary64`
312×	`+-commutative_binary64`
262×	`associate-+l+_binary64`

Counts

160 → 148

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	393	5874
1	1056	5788
2	3960	5728
3	5446	5728

prune138.0ms (1.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	147	1	148
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	148	9	157

Error

0.6b

Counts

157 → 9

Alt Table

Status	Error	Program
	32.1b	(expm1.f64 (log1p.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)))
	39.0b	(-.f64 (+.f64 (/.f64 (.f64 y x) z) (+.f64 t (/.f64 (.f64 a t) z))) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a x) z)))
✓	15.7b	(+.f64 (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))) x)
	46.2b	(*.f64 y (/.f64 (-.f64 t x) (-.f64 a z)))
	32.2b	(*.f64 t (/.f64 (-.f64 y z) (-.f64 a z)))
✓	12.7b	(fma.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x) x)
	16.0b	(fma.f64 (-.f64 y z) (/.f64 1 (-.f64 (/.f64 a (-.f64 t x)) (/.f64 z (-.f64 t x)))) x)
	34.4b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
	41.7b	(fma.f64 (/.f64 1 (sqrt.f64 (/.f64 (-.f64 a z) (-.f64 t x)))) (/.f64 (-.f64 y z) (sqrt.f64 (/.f64 (-.f64 a z) (-.f64 t x)))) x)

Compiler

Compiled 5017 to 1589 computations (68.3% saved)

regimes1.8s (24.5%)

Accuracy

Total 4.0b remaining (82.3%)

Threshold costs 0b (0%)

Counts

159 → 3

Compiler

Compiled 21558 to 12540 computations (41.8% saved)

bsearch7.0ms (0.1%)

Compiler: Compiled 18 to 11 computations (38.9% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

18×	`+-commutative_binary64`
15×	`*-commutative_binary64`
14×	`sub-neg_binary64`
10×	`neg-sub0_binary64`
10×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	104
1	52	104
2	67	104
3	83	104
4	105	104
5	117	104
6	125	104
7	128	104
8	128	104

end123.0ms (1.6%)

Compiler: Compiled 334 to 171 computations (48.8% saved)

Details

analyze1.5s (19.6%)

sample1.7s (22.3%)

simplify83.0ms (1.1%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series104.0ms (1.4%)

rewrite14.0ms (0.2%)

simplify120.0ms (1.6%)

prune104.0ms (1.4%)

localize15.0ms (0.2%)

series116.0ms (1.5%)

rewrite41.0ms (0.5%)

simplify163.0ms (2.2%)

prune211.0ms (2.8%)

localize9.0ms (0.1%)

series155.0ms (2.1%)

rewrite133.0ms (1.8%)

simplify270.0ms (3.6%)

prune374.0ms (5%)

localize9.0ms (0.1%)

series140.0ms (1.9%)

rewrite56.0ms (0.7%)

simplify119.0ms (1.6%)

prune138.0ms (1.8%)

regimes1.8s (24.5%)

bsearch7.0ms (0.1%)

simplify6.0ms (0.1%)

end123.0ms (1.6%)

Profiling