Details

analyze1.3s (14.1%)

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
3.5%	96.2%	0.2%	10
9.2%	90.6%	0.2%	11
13.7%	86%	0.2%	12
22.1%	77.7%	0.2%	13
23%	76.7%	0.2%	14

Compiler

Compiled 19 to 12 computations (36.8% saved)

sample1.5s (16.2%)

Results

920.0ms	7003×	body	128	valid
178.0ms	347×	body	1024	valid
143.0ms	487×	body	512	valid
92.0ms	757×	body	128	invalid
77.0ms	355×	body	256	valid
46.0ms	64×	body	2048	valid

Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify129.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1303×	`div-sub_binary64`
658×	`fma-def_binary64`
640×	`sub-neg_binary64`
569×	`unsub-neg_binary64`
393×	`neg-mul-1_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	23	19
2	58	19
3	143	17
4	344	17
5	967	17
6	2282	17
7	3646	17
8	3700	17
9	4097	17
10	4253	17
11	4543	17
12	4719	17
13	5478	17

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

8.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	10.8b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))
	15.4b	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

Compiler

Compiled 100 to 56 computations (44% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t z) (-.f64 a t))
✓	4.0b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))

series62.0ms (0.7%)

Counts

2 → 96

Calls

2 calls:

41.0ms	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))
20.0ms	(/.f64 (-.f64 t z) (-.f64 a t))

rewrite11.0ms (0.1%)

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

simplify113.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

671×	`times-frac_binary64`
644×	`fma-neg_binary64`
523×	`cancel-sign-sub-inv_binary64`
397×	`sub-neg_binary64`
195×	`div-sub_binary64`

Counts

160 → 137

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	273	4255
1	740	4157
2	2480	3550
3	4430	3531
4	5167	3531

prune125.0ms (1.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	131	6	137
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	133	6	139

Error

0.0b

Counts

139 → 6

Alt Table

Status	Error	Program
	32.7b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
	38.2b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
	25.9b	(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))
	33.9b	(-.f64 (+.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 (.f64 (/.f64 a t) (/.f64 a t)) (-.f64 (/.f64 (.f64 y z) t) y))) (/.f64 (.f64 y a) t))
	29.1b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
▶	14.5b	(-.f64 (+.f64 y (+.f64 (/.f64 (.f64 y t) (-.f64 a t)) x)) (/.f64 (.f64 y z) (-.f64 a t)))

Compiler

Compiled 3630 to 1218 computations (66.4% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 y (+.f64 (/.f64 (.f64 y t) (-.f64 a t)) x)) (/.f64 (.f64 y z) (-.f64 a t)))
✓	2.5b	(+.f64 y (+.f64 (/.f64 (*.f64 y t) (-.f64 a t)) x))
✓	6.4b	(/.f64 (*.f64 y z) (-.f64 a t))
✓	8.9b	(/.f64 (*.f64 y t) (-.f64 a t))

series120.0ms (1.3%)

Counts

4 → 111

Calls

4 calls:

51.0ms	(-.f64 (+.f64 y (+.f64 (/.f64 (.f64 y t) (-.f64 a t)) x)) (/.f64 (.f64 y z) (-.f64 a t)))
28.0ms	(/.f64 (*.f64 y z) (-.f64 a t))
21.0ms	(+.f64 y (+.f64 (/.f64 (*.f64 y t) (-.f64 a t)) x))
20.0ms	(/.f64 (*.f64 y t) (-.f64 a t))

rewrite56.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

127×	`*-un-lft-identity_binary64`
55×	`prod-diff_binary64`
55×	`add-sqr-sqrt_binary64`
42×	`distribute-lft-out_binary64`
40×	`times-frac_binary64`

Counts

4 → 171

Calls

4 calls:

18.0ms	(-.f64 (+.f64 y (+.f64 (/.f64 (.f64 y t) (-.f64 a t)) x)) (/.f64 (.f64 y z) (-.f64 a t)))
10.0ms	(+.f64 y (+.f64 (/.f64 (*.f64 y t) (-.f64 a t)) x))
5.0ms	(/.f64 (*.f64 y t) (-.f64 a t))
5.0ms	(/.f64 (*.f64 y z) (-.f64 a t))

simplify180.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

281×	`fma-neg_binary64`
227×	`associate-/l*_binary64`
195×	`times-frac_binary64`
174×	`+-commutative_binary64`
174×	`associate-l_binary64`

Counts

282 → 289

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	420	11863
1	1136	8436
2	4247	8373
3	4968	8373

prune183.0ms (1.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	289	0	289
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	289	6	295

Error

0.0b

Counts

295 → 6

Alt Table

Status	Error	Program
	32.7b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
	38.2b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
▶	25.9b	(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))
	33.9b	(-.f64 (+.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 (.f64 (/.f64 a t) (/.f64 a t)) (-.f64 (/.f64 (.f64 y z) t) y))) (/.f64 (.f64 y a) t))
	29.1b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
✓	14.5b	(-.f64 (+.f64 y (+.f64 (/.f64 (.f64 y t) (-.f64 a t)) x)) (/.f64 (.f64 y z) (-.f64 a t)))

Compiler

Compiled 10344 to 1976 computations (80.9% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series78.0ms (0.8%)

Counts

3 → 168

Calls

3 calls:

33.0ms	(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))
27.0ms	(+.f64 x (*.f64 (/.f64 y a) (-.f64 t z)))
17.0ms	(*.f64 (/.f64 y a) (-.f64 t z))

rewrite29.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-sqr-sqrt_binary64`
45×	`*-un-lft-identity_binary64`
41×	`add-cube-cbrt_binary64`
36×	`prod-diff_binary64`
27×	`associate-+r+_binary64`

Counts

3 → 127

Calls

3 calls:

8.0ms	(*.f64 (/.f64 y a) (-.f64 t z))
4.0ms	(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))
4.0ms	(+.f64 x (*.f64 (/.f64 y a) (-.f64 t z)))

simplify128.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

502×	`fma-neg_binary64`
501×	`associate-*l/_binary64`
429×	`associate-*r/_binary64`
353×	`associate-/l*_binary64`
215×	`cancel-sign-sub-inv_binary64`

Counts

295 → 213

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	261	4024
1	582	3654
2	2010	3594
3	4890	3594
4	5134	3594

prune126.0ms (1.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	213	0	213
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	213	6	219

Error

0.0b

Counts

219 → 6

Alt Table

Status	Error	Program
	32.7b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
	38.2b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
✓	25.9b	(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))
	33.9b	(-.f64 (+.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 (.f64 (/.f64 a t) (/.f64 a t)) (-.f64 (/.f64 (.f64 y z) t) y))) (/.f64 (.f64 y a) t))
▶	29.1b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
✓	14.5b	(-.f64 (+.f64 y (+.f64 (/.f64 (.f64 y t) (-.f64 a t)) x)) (/.f64 (.f64 y z) (-.f64 a t)))

Compiler

Compiled 4733 to 1143 computations (75.9% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
✓	5.7b	(*.f64 (/.f64 y t) (-.f64 z a))

series47.0ms (0.5%)

Counts

2 → 108

Calls

2 calls:

29.0ms	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
18.0ms	(*.f64 (/.f64 y t) (-.f64 z a))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64`
39×	`add-cube-cbrt_binary64`
36×	`prod-diff_binary64`
26×	`associate-+r+_binary64`

Counts

2 → 108

Calls

2 calls:

7.0ms	(*.f64 (/.f64 y t) (-.f64 z a))
4.0ms	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))

simplify116.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

660×	`fma-def_binary64`
488×	`distribute-rgt-in_binary64`
459×	`distribute-lft-in_binary64`
280×	`fma-neg_binary64`
153×	`exp-prod_binary64`

Counts

216 → 178

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	229	3204
1	473	2592
2	1528	2538
3	4618	2538
4	5000	2538
5	4948	2538

prune152.0ms (1.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	178	6	184

Error

0.0b

Counts

184 → 6

Alt Table

Status	Error	Program
	29.5b	(+.f64 x (/.f64 (neg.f64 y) (/.f64 t (-.f64 a z))))
	33.9b	(-.f64 (+.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 (.f64 (/.f64 a t) (/.f64 a t)) (-.f64 (/.f64 (.f64 y z) t) y))) (/.f64 (.f64 y a) t))
	32.7b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
	38.2b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
✓	25.9b	(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))
✓	14.5b	(-.f64 (+.f64 y (+.f64 (/.f64 (.f64 y t) (-.f64 a t)) x)) (/.f64 (.f64 y z) (-.f64 a t)))

Compiler

Compiled 3648 to 836 computations (77.1% saved)

regimes4.7s (50.3%)

Accuracy

Total 6.7b remaining (99.2%)

Threshold costs 0b (0%)

Counts

230 → 4

Compiler

Compiled 28146 to 16956 computations (39.8% saved)

bsearch7.0ms (0.1%)

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

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

25×	`+-commutative_binary64`
22×	`*-commutative_binary64`
19×	`sub-neg_binary64`
16×	`neg-sub0_binary64`
16×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	182
1	69	182
2	90	182
3	114	182
4	130	182
5	144	182
6	155	182
7	165	182
8	176	182
9	182	182
10	184	182
11	180	182

end101.0ms (1.1%)

Compiler: Compiled 401 to 167 computations (58.4% saved)

Iter	Nodes	Cost
0	44	182
1	69	182
2	90	182
3	114	182
4	130	182
5	144	182
6	155	182
7	165	182
8	176	182
9	182	182
10	184	182
11	180	182

Iter	Nodes	Cost
0	44	182
1	69	182
2	90	182
3	114	182
4	130	182
5	144	182
6	155	182
7	165	182
8	176	182
9	182	182
10	184	182
11	180	182

Details

analyze1.3s (14.1%)

sample1.5s (16.2%)

simplify129.0ms (1.4%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series62.0ms (0.7%)

rewrite11.0ms (0.1%)

simplify113.0ms (1.2%)

prune125.0ms (1.3%)

localize11.0ms (0.1%)

series120.0ms (1.3%)

rewrite56.0ms (0.6%)

simplify180.0ms (1.9%)

prune183.0ms (1.9%)

localize9.0ms (0.1%)

series78.0ms (0.8%)

rewrite29.0ms (0.3%)

simplify128.0ms (1.4%)

prune126.0ms (1.3%)

localize6.0ms (0.1%)

series47.0ms (0.5%)

rewrite20.0ms (0.2%)

simplify116.0ms (1.2%)

prune152.0ms (1.6%)

regimes4.7s (50.3%)

bsearch7.0ms (0.1%)

simplify12.0ms (0.1%)

end101.0ms (1.1%)

Profiling

Iter	Nodes	Cost
0	44	182
1	69	182
2	90	182
3	114	182
4	130	182
5	144	182
6	155	182
7	165	182
8	176	182
9	182	182
10	184	182
11	180	182