Details

analyze1.6s (18.2%)

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
0%	99.8%	0.2%	10
0%	99.8%	0.2%	11
0%	99.8%	0.2%	12
0%	99.8%	0.2%	13
0%	99.8%	0.2%	14

Compiler

Compiled 19 to 12 computations (36.8% saved)

sample1.9s (21.2%)

Results

976.0ms	6991×	body	128	valid
280.0ms	401×	body	8192	exit
264.0ms	387×	body	1024	valid
157.0ms	476×	body	512	valid
104.0ms	341×	body	256	valid
49.0ms	361×	body	128	invalid
33.0ms	61×	body	2048	valid

Compiler

Compiled 37 to 23 computations (37.8% saved)

simplify134.0ms (1.5%)

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

9.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	15.5b	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
▶	10.5b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))

Compiler

Compiled 100 to 56 computations (44% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t z) (-.f64 a t))
✓	3.3b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))

series66.0ms (0.7%)

Counts

2 → 96

Calls

2 calls:

43.0ms	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))
22.0ms	(/.f64 (-.f64 t z) (-.f64 a t))

rewrite13.0ms (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:

7.0ms	(/.f64 (-.f64 t z) (-.f64 a t))
0.0ms	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))

simplify121.0ms (1.3%)

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

prune155.0ms (1.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	127	10	137
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	129	10	139

Error

0.0b

Counts

139 → 10

Alt Table

Status	Error	Program
	31.2b	(-.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))
	40.3b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
	34.6b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))) (sqrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))))
	29.0b	(+.f64 (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t)) (-.f64 x (/.f64 (*.f64 y a) t)))
	25.3b	(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))
▶	10.7b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z))) (/.f64 (cbrt.f64 (-.f64 t z)) (-.f64 a t))) (+.f64 x y))
	14.0b	(-.f64 (+.f64 y (+.f64 (/.f64 (.f64 y t) (-.f64 a t)) x)) (/.f64 (.f64 y z) (-.f64 a t)))
	46.2b	(cbrt.f64 (.f64 (.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y)) (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))) (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))))
	30.9b	(-.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))))
	25.8b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))

Compiler

Compiled 3886 to 1324 computations (65.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z))) (/.f64 (cbrt.f64 (-.f64 t z)) (-.f64 a t)))
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z)))
✓	0.6b	(cbrt.f64 (-.f64 t z))
✓	7.4b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z))) (/.f64 (cbrt.f64 (-.f64 t z)) (-.f64 a t))) (+.f64 x y))

series141.0ms (1.5%)

Counts

4 → 144

Calls

4 calls:

47.0ms	(fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z))) (/.f64 (cbrt.f64 (-.f64 t z)) (-.f64 a t))) (+.f64 x y))
38.0ms	(*.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z)))
32.0ms	(cbrt.f64 (-.f64 t z))
24.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z))) (/.f64 (cbrt.f64 (-.f64 t z)) (-.f64 a t)))

rewrite52.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`add-sqr-sqrt_binary64`
74×	`*-un-lft-identity_binary64`
59×	`cbrt-prod_binary64`
54×	`associate-r_binary64`
42×	`times-frac_binary64`

Counts

4 → 172

Calls

4 calls:

21.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z))) (/.f64 (cbrt.f64 (-.f64 t z)) (-.f64 a t)))
8.0ms	(*.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z)))
2.0ms	(cbrt.f64 (-.f64 t z))
0.0ms	(fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z))) (/.f64 (cbrt.f64 (-.f64 t z)) (-.f64 a t))) (+.f64 x y))

simplify163.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

511×	`associate-l_binary64`
447×	`associate-r_binary64`
248×	`associate-/l*_binary64`
189×	`associate--r+_binary64`
173×	`times-frac_binary64`

Counts

316 → 345

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	538	8828
1	1471	8460
2	5003	8460

prune433.0ms (4.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	445	0	445
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	445	10	455

Error

0.0b

Counts

455 → 10

Alt Table

Status	Error	Program
	31.2b	(-.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))
	40.3b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
	34.6b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))) (sqrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))))
	29.0b	(+.f64 (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t)) (-.f64 x (/.f64 (*.f64 y a) t)))
	25.3b	(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))
✓	10.7b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z))) (/.f64 (cbrt.f64 (-.f64 t z)) (-.f64 a t))) (+.f64 x y))
▶	14.0b	(-.f64 (+.f64 y (+.f64 (/.f64 (.f64 y t) (-.f64 a t)) x)) (/.f64 (.f64 y z) (-.f64 a t)))
	46.2b	(cbrt.f64 (.f64 (.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y)) (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))) (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))))
	30.9b	(-.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))))
	25.8b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))

Compiler

Compiled 16268 to 5095 computations (68.7% 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)))
✓	2.1b	(+.f64 y (+.f64 (/.f64 (*.f64 y t) (-.f64 a t)) x))
✓	6.2b	(/.f64 (*.f64 y z) (-.f64 a t))
✓	8.6b	(/.f64 (*.f64 y t) (-.f64 a t))

series124.0ms (1.4%)

Counts

4 → 111

Calls

4 calls:

55.0ms	(-.f64 (+.f64 y (+.f64 (/.f64 (.f64 y t) (-.f64 a t)) x)) (/.f64 (.f64 y z) (-.f64 a t)))
27.0ms	(/.f64 (*.f64 y z) (-.f64 a t))
23.0ms	(+.f64 y (+.f64 (/.f64 (*.f64 y t) (-.f64 a t)) x))
19.0ms	(/.f64 (*.f64 y t) (-.f64 a t))

rewrite58.0ms (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)))
11.0ms	(+.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))

simplify188.0ms (2.1%)

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

prune268.0ms (2.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	287	2	289
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	290	9	299

Error

0.0b

Counts

299 → 9

Alt Table

Status	Error	Program
	31.2b	(-.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))
	40.3b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
	25.3b	(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))
✓	10.7b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z))) (/.f64 (cbrt.f64 (-.f64 t z)) (-.f64 a t))) (+.f64 x y))
	34.6b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))) (sqrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))))
▶	23.8b	(-.f64 (-.f64 x (/.f64 (.f64 a y) t)) (/.f64 (.f64 y z) (-.f64 a t)))
	23.9b	(-.f64 (+.f64 y (+.f64 (/.f64 (.f64 y t) (-.f64 a t)) x)) (cbrt.f64 (.f64 (.f64 (/.f64 (.f64 y z) (-.f64 a t)) (/.f64 (.f64 y z) (-.f64 a t))) (/.f64 (.f64 y z) (-.f64 a t)))))
	30.9b	(-.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))))
	25.8b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))

Compiler

Compiled 10534 to 2056 computations (80.5% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (-.f64 x (/.f64 (.f64 a y) t)) (/.f64 (.f64 y z) (-.f64 a t)))
✓	4.9b	(/.f64 (*.f64 a y) t)
	6.2b	(/.f64 (*.f64 y z) (-.f64 a t))

series49.0ms (0.5%)

Counts

2 → 80

Calls

2 calls:

36.0ms	(-.f64 (-.f64 x (/.f64 (.f64 a y) t)) (/.f64 (.f64 y z) (-.f64 a t)))
13.0ms	(/.f64 (*.f64 a y) t)

rewrite39.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`*-un-lft-identity_binary64`
81×	`add-sqr-sqrt_binary64`
76×	`prod-diff_binary64`
45×	`times-frac_binary64`
43×	`add-cube-cbrt_binary64`

Counts

2 → 143

Calls

2 calls:

14.0ms	(-.f64 (-.f64 x (/.f64 (.f64 a y) t)) (/.f64 (.f64 y z) (-.f64 a t)))
6.0ms	(/.f64 (*.f64 a y) t)

simplify194.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

606×	`fma-neg_binary64`
245×	`exp-prod_binary64`
210×	`distribute-neg-frac_binary64`
192×	`associate-l_binary64`
192×	`sub-neg_binary64`

Counts

223 → 221

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	347	6772
1	881	5427
2	3262	4767
3	4436	4767
4	4989	4767
5	4813	4767

prune212.0ms (2.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	279	2	281
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	280	10	290

Error

0.0b

Counts

290 → 10

Alt Table

Status	Error	Program
	31.2b	(-.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))
	40.3b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
	23.9b	(-.f64 (+.f64 y (+.f64 (/.f64 (.f64 y t) (-.f64 a t)) x)) (cbrt.f64 (.f64 (.f64 (/.f64 (.f64 y z) (-.f64 a t)) (/.f64 (.f64 y z) (-.f64 a t))) (/.f64 (.f64 y z) (-.f64 a t)))))
	48.9b	(+.f64 (fma.f64 (+.f64 (sqrt.f64 (/.f64 (.f64 y a) t)) (sqrt.f64 x)) (-.f64 (sqrt.f64 x) (sqrt.f64 (/.f64 (.f64 y a) t))) (neg.f64 (.f64 (/.f64 z (cbrt.f64 (-.f64 a t))) (/.f64 y (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t))))))) 0)
	25.3b	(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))
✓	10.7b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z))) (/.f64 (cbrt.f64 (-.f64 t z)) (-.f64 a t))) (+.f64 x y))
	34.6b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))) (sqrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))))
	22.9b	(-.f64 x (*.f64 y (+.f64 (/.f64 z (-.f64 a t)) (/.f64 a t))))
✓	23.8b	(-.f64 (-.f64 x (/.f64 (.f64 a y) t)) (/.f64 (.f64 y z) (-.f64 a t)))
	25.8b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))

Compiler

Compiled 9368 to 1667 computations (82.2% saved)

regimes2.9s (31.5%)

Accuracy

Total 4.7b remaining (98.6%)

Threshold costs 0b (0%)

Counts

192 → 5

Compiler

Compiled 27372 to 15372 computations (43.8% saved)

bsearch9.0ms (0.1%)

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

simplify30.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

94×	`distribute-rgt-neg-in_binary64`
85×	`cancel-sign-sub-inv_binary64`
65×	`distribute-lft-neg-in_binary64`
56×	`neg-sub0_binary64`
56×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	228
1	87	228
2	114	228
3	146	228
4	165	228
5	180	228
6	189	228
7	195	228
8	209	228
9	224	228
10	255	228
11	303	228
12	362	228
13	416	228
14	461	228
15	492	228
16	516	228
17	527	228
18	529	228
19	525	228

end150.0ms (1.6%)

Compiler: Compiled 590 to 243 computations (58.8% saved)

Iter	Nodes	Cost
0	57	228
1	87	228
2	114	228
3	146	228
4	165	228
5	180	228
6	189	228
7	195	228
8	209	228
9	224	228
10	255	228
11	303	228
12	362	228
13	416	228
14	461	228
15	492	228
16	516	228
17	527	228
18	529	228
19	525	228

Iter	Nodes	Cost
0	57	228
1	87	228
2	114	228
3	146	228
4	165	228
5	180	228
6	189	228
7	195	228
8	209	228
9	224	228
10	255	228
11	303	228
12	362	228
13	416	228
14	461	228
15	492	228
16	516	228
17	527	228
18	529	228
19	525	228

Details

analyze1.6s (18.2%)

sample1.9s (21.2%)

simplify134.0ms (1.5%)

prune4.0ms (0%)

localize8.0ms (0.1%)

series66.0ms (0.7%)

rewrite13.0ms (0.1%)

simplify121.0ms (1.3%)

prune155.0ms (1.7%)

localize12.0ms (0.1%)

series141.0ms (1.5%)

rewrite52.0ms (0.6%)

simplify163.0ms (1.8%)

prune433.0ms (4.8%)

localize11.0ms (0.1%)

series124.0ms (1.4%)

rewrite58.0ms (0.6%)

simplify188.0ms (2.1%)

prune268.0ms (2.9%)

localize10.0ms (0.1%)

series49.0ms (0.5%)

rewrite39.0ms (0.4%)

simplify194.0ms (2.1%)

prune212.0ms (2.3%)

regimes2.9s (31.5%)

bsearch9.0ms (0.1%)

simplify30.0ms (0.3%)

end150.0ms (1.6%)

Profiling

Iter	Nodes	Cost
0	57	228
1	87	228
2	114	228
3	146	228
4	165	228
5	180	228
6	189	228
7	195	228
8	209	228
9	224	228
10	255	228
11	303	228
12	362	228
13	416	228
14	461	228
15	492	228
16	516	228
17	527	228
18	529	228
19	525	228