Details

analyze1.6s (21.4%)

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)

sample1.8s (23.4%)

Results

1.0s	6913×	body	128	valid
198.0ms	500×	body	512	valid
169.0ms	1272×	body	128	invalid
159.0ms	405×	body	1024	valid
81.0ms	372×	body	256	valid
40.0ms	66×	body	2048	valid

Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify82.0ms (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

14.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	14.5b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
▶	14.5b	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

Compiler

Compiled 100 to 54 computations (46% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t x) (-.f64 a z))
✓	3.4b	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))
✓	5.5b	(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))

series170.0ms (2.3%)

Counts

3 → 168

Calls

3 calls:

85.0ms	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))
60.0ms	(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))
24.0ms	(/.f64 (-.f64 t x) (-.f64 a z))

rewrite89.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

284×	`expm1-udef_binary64`
284×	`log1p-udef_binary64`
154×	`add-sqr-sqrt_binary64`
149×	`log1p-expm1-u_binary64`
149×	`expm1-log1p-u_binary64`

Counts

3 → 116

Calls

3 calls:

83.0ms	(/.f64 (-.f64 t x) (-.f64 a z))
83.0ms	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))
83.0ms	(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	45
1	287	43
2	4401	43
3	5270	43
0	0	0
1	0	0

simplify175.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

685×	`sub-neg_binary64`
594×	`associate-+r+_binary64`
460×	`associate-+l+_binary64`
404×	`+-commutative_binary64`
311×	`fma-neg_binary64`

Counts

284 → 225

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	362	8872
1	1158	8872
2	4458	8158
3	5440	8158

prune187.0ms (2.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	215	10	225
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	216	11	227

Error

0.3b

Counts

227 → 11

Alt Table

Status	Error	Program
	34.4b	(+.f64 x (.f64 (-.f64 y z) (.f64 (/.f64 (-.f64 t x) (-.f64 (.f64 a a) (.f64 z z))) (+.f64 z a))))
	38.5b	(-.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)))
	34.3b	(expm1.f64 (log1p.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)))
	42.2b	(*.f64 y (-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z))))
	26.9b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
	36.5b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
	42.0b	(+.f64 x (.f64 (-.f64 y z) (.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 t x)) 2) (sqrt.f64 (-.f64 a z))) (/.f64 (cbrt.f64 (-.f64 t x)) (sqrt.f64 (-.f64 a z))))))
▶	14.5b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
	14.6b	(+.f64 x (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))))
	28.7b	(*.f64 t (/.f64 (-.f64 y z) (-.f64 a z)))
	40.7b	(-.f64 (+.f64 t (+.f64 (/.f64 (.f64 (pow.f64 a 2) t) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 y (.f64 a x)) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 a t) z))))) (+.f64 (/.f64 (.f64 (pow.f64 a 2) x) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 a x) z) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a (.f64 y t)) (pow.f64 z 2))))))

Compiler

Compiled 8383 to 2717 computations (67.6% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 t x) (-.f64 a z))
✓	14.4b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)

series71.0ms (0.9%)

Counts

1 → 60

Calls

1 calls:

71.0ms

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

rewrite64.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

514×	`fma-def_binary64`
264×	`fma-neg_binary64`
254×	`expm1-udef_binary64`
254×	`log1p-udef_binary64`
138×	`add-sqr-sqrt_binary64`

Counts

1 → 24

Calls

1 calls:

63.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	257	17
2	3776	17
3	5340	17
0	0	0
1	0	0

simplify80.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

987×	`times-frac_binary64`
353×	`cancel-sign-sub-inv_binary64`
328×	`sub-neg_binary64`
320×	`associate-+r+_binary64`
233×	`distribute-neg-in_binary64`

Counts

84 → 74

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	212	3549
1	675	3549
2	2692	3513
3	5009	3513

prune118.0ms (1.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	128	2	130
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	131	10	141

Error

0.3b

Counts

141 → 10

Alt Table

Status	Error	Program
	34.3b	(expm1.f64 (log1p.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)))
	42.2b	(*.f64 y (-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z))))
	26.9b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
	36.5b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
	38.5b	(-.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)))
▶	14.6b	(+.f64 x (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))))
	42.0b	(fma.f64 (-.f64 y z) (*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 t x)) 2) (sqrt.f64 (-.f64 a z))) (/.f64 (cbrt.f64 (-.f64 t x)) (sqrt.f64 (-.f64 a z)))) x)
	34.4b	(fma.f64 (-.f64 y z) (.f64 (/.f64 (-.f64 t x) (-.f64 (.f64 a a) (*.f64 z z))) (+.f64 z a)) x)
	28.7b	(*.f64 t (/.f64 (-.f64 y z) (-.f64 a z)))
	40.7b	(-.f64 (+.f64 t (+.f64 (/.f64 (.f64 (pow.f64 a 2) t) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 y (.f64 a x)) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 a t) z))))) (+.f64 (/.f64 (.f64 (pow.f64 a 2) x) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 a x) z) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a (.f64 y t)) (pow.f64 z 2))))))

Compiler

Compiled 4663 to 1572 computations (66.3% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 a z) (-.f64 t x))
✓	3.4b	(+.f64 x (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))))
✓	5.6b	(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x)))

series220.0ms (2.9%)

Counts

3 → 168

Calls

3 calls:

108.0ms	(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x)))
86.0ms	(+.f64 x (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))))
26.0ms	(/.f64 (-.f64 a z) (-.f64 t x))

rewrite92.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

294×	`log1p-udef_binary64`
160×	`add-sqr-sqrt_binary64`
155×	`log1p-expm1-u_binary64`
155×	`expm1-log1p-u_binary64`
149×	`add-log-exp_binary64`

Counts

3 → 124

Calls

3 calls:

81.0ms	(/.f64 (-.f64 a z) (-.f64 t x))
81.0ms	(+.f64 x (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))))
81.0ms	(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	45
1	296	43
2	4767	43
3	5265	43
0	0	0
1	0	0

simplify178.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

595×	`associate-+r+_binary64`
461×	`associate-+l+_binary64`
408×	`+-commutative_binary64`
333×	`fma-neg_binary64`
293×	`associate--l+_binary64`

Counts

292 → 233

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	379	8872
1	1200	8755
2	4639	8149
3	4987	8149

prune191.0ms (2.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	230	3	233
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	233	10	243

Error

0.3b

Counts

243 → 10

Alt Table

Status	Error	Program
	34.3b	(expm1.f64 (log1p.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)))
	42.2b	(*.f64 y (-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z))))
	26.9b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
	36.5b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
▶	10.7b	(fma.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x) x)
	11.6b	(-.f64 (/.f64 y (/.f64 (-.f64 a z) (-.f64 t x))) (-.f64 (/.f64 z (/.f64 (-.f64 a z) (-.f64 t x))) x))
	34.4b	(fma.f64 (-.f64 y z) (.f64 (/.f64 (-.f64 t x) (-.f64 (.f64 a a) (*.f64 z z))) (+.f64 z a)) x)
	38.5b	(-.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)))
	14.5b	(*.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x) 1)
	40.7b	(-.f64 (+.f64 t (+.f64 (/.f64 (.f64 (pow.f64 a 2) t) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 y (.f64 a x)) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 a t) z))))) (+.f64 (/.f64 (.f64 (pow.f64 a 2) x) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 a x) z) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a (.f64 y t)) (pow.f64 z 2))))))

Compiler

Compiled 8487 to 2701 computations (68.2% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 y z) (-.f64 a z))
✓	2.7b	(fma.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x) x)

series77.0ms (1%)

Counts

2 → 96

Calls

2 calls:

59.0ms	(fma.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x) x)
17.0ms	(/.f64 (-.f64 y z) (-.f64 a z))

rewrite67.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

516×	`fma-def_binary64`
264×	`fma-neg_binary64`
254×	`expm1-udef_binary64`
254×	`log1p-udef_binary64`
138×	`add-sqr-sqrt_binary64`

Counts

2 → 76

Calls

2 calls:

65.0ms	(/.f64 (-.f64 y z) (-.f64 a z))
65.0ms	(fma.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	27
1	257	27
2	3780	27
3	5347	27
0	0	0
1	0	0

simplify112.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

574×	`cancel-sign-sub-inv_binary64`
500×	`sub-neg_binary64`
341×	`associate-+r+_binary64`
297×	`+-commutative_binary64`
288×	`distribute-neg-in_binary64`

Counts

172 → 160

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	298	4642
1	835	4633
2	3385	4573
3	5205	4573

prune134.0ms (1.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	159	1	160
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	160	10	170

Error

0.3b

Counts

170 → 10

Alt Table

Status	Error	Program
	34.3b	(expm1.f64 (log1p.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)))
	42.2b	(*.f64 y (-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z))))
	26.9b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
	36.5b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
✓	10.7b	(fma.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x) x)
	38.5b	(-.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)))
	11.1b	(fma.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 y z) (-.f64 a z))) 3) (-.f64 t x) x)
	14.5b	(*.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x) 1)
	11.6b	(-.f64 (/.f64 y (/.f64 (-.f64 a z) (-.f64 t x))) (-.f64 (/.f64 z (/.f64 (-.f64 a z) (-.f64 t x))) x))
	40.7b	(-.f64 (+.f64 t (+.f64 (/.f64 (.f64 (pow.f64 a 2) t) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 y (.f64 a x)) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 a t) z))))) (+.f64 (/.f64 (.f64 (pow.f64 a 2) x) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 a x) z) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a (.f64 y t)) (pow.f64 z 2))))))

Compiler

Compiled 5227 to 1687 computations (67.7% saved)

regimes1.8s (23.4%)

Accuracy

Total 5.2b remaining (83.5%)

Threshold costs 0b (0%)

Counts

103 → 3

Compiler

Compiled 12660 to 7626 computations (39.8% saved)

bsearch3.0ms (0%)

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

simplify31.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

106×	`distribute-rgt-neg-in_binary64`
103×	`cancel-sign-sub-inv_binary64`
73×	`neg-sub0_binary64`
73×	`neg-mul-1_binary64`
72×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	133
1	57	133
2	79	133
3	107	133
4	146	133
5	176	133
6	211	133
7	245	133
8	279	133
9	325	133
10	370	133
11	417	133
12	445	133
13	478	133
14	511	133
15	538	133
16	556	133
17	570	133
18	589	133
19	609	133
20	620	133
21	622	133
22	618	133

end223.0ms (2.9%)

Compiler: Compiled 447 to 222 computations (50.3% saved)

Iter	Nodes	Cost
0	38	133
1	57	133
2	79	133
3	107	133
4	146	133
5	176	133
6	211	133
7	245	133
8	279	133
9	325	133
10	370	133
11	417	133
12	445	133
13	478	133
14	511	133
15	538	133
16	556	133
17	570	133
18	589	133
19	609	133
20	620	133
21	622	133
22	618	133

Iter	Nodes	Cost
0	38	133
1	57	133
2	79	133
3	107	133
4	146	133
5	176	133
6	211	133
7	245	133
8	279	133
9	325	133
10	370	133
11	417	133
12	445	133
13	478	133
14	511	133
15	538	133
16	556	133
17	570	133
18	589	133
19	609	133
20	620	133
21	622	133
22	618	133

Details

analyze1.6s (21.4%)

sample1.8s (23.4%)

simplify82.0ms (1.1%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series170.0ms (2.3%)

rewrite89.0ms (1.2%)

simplify175.0ms (2.3%)

prune187.0ms (2.5%)

localize10.0ms (0.1%)

series71.0ms (0.9%)

rewrite64.0ms (0.8%)

simplify80.0ms (1.1%)

prune118.0ms (1.6%)

localize10.0ms (0.1%)

series220.0ms (2.9%)

rewrite92.0ms (1.2%)

simplify178.0ms (2.4%)

prune191.0ms (2.5%)

localize8.0ms (0.1%)

series77.0ms (1%)

rewrite67.0ms (0.9%)

simplify112.0ms (1.5%)

prune134.0ms (1.8%)

regimes1.8s (23.4%)

bsearch3.0ms (0%)

simplify31.0ms (0.4%)

end223.0ms (2.9%)

Profiling

Iter	Nodes	Cost
0	38	133
1	57	133
2	79	133
3	107	133
4	146	133
5	176	133
6	211	133
7	245	133
8	279	133
9	325	133
10	370	133
11	417	133
12	445	133
13	478	133
14	511	133
15	538	133
16	556	133
17	570	133
18	589	133
19	609	133
20	620	133
21	622	133
22	618	133