Details

analyze1.2s (8.6%)

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
24.9%	74.8%	0.2%	6
24.9%	74.8%	0.2%	7
24.9%	74.8%	0.2%	8
37.4%	62.3%	0.2%	9
40.5%	59.2%	0.2%	10
48.3%	45.2%	6.5%	11
48.3%	45.2%	6.5%	12
48.3%	45.2%	6.5%	13
58.5%	35.1%	6.5%	14

Compiler

Compiled 20 to 13 computations (35% saved)

sample2.1s (15.4%)

Symmetry

(sort x y)

(sort t a)

Results

1.6s	8256×	body	128	valid
363.0ms	1936×	body	128	invalid

Compiler

Compiled 59 to 38 computations (35.6% saved)

simplify93.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1034×	`fma-def_binary64`
336×	`fma-neg_binary64`
138×	`distribute-rgt-in_binary64`
130×	`cancel-sign-sub-inv_binary64`
128×	`associate-/r/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	26	21
2	52	21
3	87	21
4	128	21
5	161	21
6	203	21
7	247	21
8	464	21
9	822	21
10	1234	21
11	1169	21
12	1237	21
13	1311	21
14	1375	21
15	1375	21
16	1282	21

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

23.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	23.7b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))

Compiler

Compiled 57 to 36 computations (36.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(-.f64 (.f64 z z) (.f64 t a))
✓	6.6b	(.f64 (.f64 x y) z)
✓	7.0b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
✓	24.9b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series329.0ms (2.4%)

Counts

4 → 136

Calls

4 calls:

249.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
46.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
19.0ms	(.f64 (.f64 x y) z)
14.0ms	(-.f64 (.f64 z z) (.f64 t a))

rewrite40.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-cbrt-cube_binary64`
18×	`add-exp-log_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`

Counts

4 → 86

Calls

4 calls:

15.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
7.0ms	(.f64 (.f64 x y) z)
5.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
5.0ms	(-.f64 (.f64 z z) (.f64 t a))

simplify172.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

731×	`fma-def_binary64`
379×	`times-frac_binary64`
318×	`associate-r_binary64`
293×	`associate-l_binary64`
277×	`associate-/l*_binary64`

Counts

222 → 190

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	283	4463
1	842	4196
2	3899	4138
3	4961	4138
4	4976	4138

prune237.0ms (1.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	181	9	190
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	182	9	191

Error

2.5b

Counts

191 → 9

Alt Table

Status	Error	Program
	23.7b	(/.f64 (.f64 x (.f64 y z)) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
▶	22.1b	(/.f64 (.f64 x y) (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z))
	24.9b	(.f64 (/.f64 (.f64 y x) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z))) (/.f64 z (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z))))
	31.4b	(/.f64 (.f64 (.f64 x y) z) (cbrt.f64 (.f64 (.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
	24.0b	(/.f64 (.f64 (/.f64 (.f64 y x) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 a t))))) z) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
	37.7b	(neg.f64 (*.f64 y x))
	33.1b	(*.f64 y x)
	44.1b	(.f64 y (.f64 (sqrt.f64 (/.f64 -1 (.f64 a t))) (.f64 z x)))
	29.8b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 y (.f64 z x)) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z))) (cbrt.f64 (/.f64 (.f64 y (.f64 z x)) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z)))) (cbrt.f64 (/.f64 (.f64 y (.f64 z x)) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))))

Compiler

Compiled 5140 to 1549 computations (69.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)
	0.2b	(-.f64 (.f64 z z) (.f64 t a))
✓	3.1b	(/.f64 (.f64 x y) (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z))
	24.9b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series305.0ms (2.3%)

Counts

2 → 64

Calls

2 calls:

224.0ms	(/.f64 (.f64 x y) (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z))
80.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)

rewrite42.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`times-frac_binary64`
43×	`*-un-lft-identity_binary64`
43×	`add-sqr-sqrt_binary64`
43×	`add-cube-cbrt_binary64`
30×	`sqrt-prod_binary64`

Counts

2 → 109

Calls

2 calls:

12.0ms	(/.f64 (.f64 x y) (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z))
10.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)

simplify264.0ms (2%)

Algorithm

1×	egg-herbie

Rules

655×	`fma-def_binary64`
344×	`times-frac_binary64`
252×	`associate-r_binary64`
244×	`associate-/l*_binary64`
206×	`associate-l_binary64`

Counts

173 → 216

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	317	5418
1	910	5126
2	3755	4978
3	4826	4978
4	4980	4978
5	5000	4978
6	4954	4978

prune393.0ms (2.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	292	6	298
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	296	11	307

Error

2.5b

Counts

307 → 11

Alt Table

Status	Error	Program
▶	20.5b	(.f64 (/.f64 x 1) (/.f64 y (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z)))
	21.3b	(.f64 (/.f64 x (.f64 (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)) (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)))) (/.f64 y (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z))))
	23.7b	(/.f64 (.f64 x (.f64 y z)) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
✓	22.1b	(/.f64 (.f64 x y) (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z))
	22.4b	(.f64 (/.f64 x (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 a t))))) (/.f64 y (/.f64 (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (*.f64 a t)))) z)))
	44.1b	(.f64 y (.f64 (sqrt.f64 (/.f64 -1 (.f64 a t))) (.f64 z x)))
	22.1b	(.f64 (.f64 x y) (/.f64 1 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)))
	26.6b	(.f64 (/.f64 x (.f64 (cbrt.f64 (hypot.f64 z (sqrt.f64 (neg.f64 (.f64 a t))))) (cbrt.f64 (hypot.f64 z (sqrt.f64 (neg.f64 (.f64 a t))))))) (/.f64 y (/.f64 (cbrt.f64 (hypot.f64 z (sqrt.f64 (neg.f64 (*.f64 a t))))) z)))
	24.4b	(/.f64 (.f64 x y) (.f64 (/.f64 1 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (hypot.f64 z (sqrt.f64 (neg.f64 (.f64 a t)))) (cbrt.f64 z))))
	37.7b	(neg.f64 (*.f64 y x))
	33.1b	(*.f64 y x)

Compiler

Compiled 8289 to 2268 computations (72.6% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(-.f64 (.f64 z z) (.f64 t a))
✓	1.0b	(/.f64 y (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z))
✓	1.2b	(.f64 (/.f64 x 1) (/.f64 y (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z)))
	24.9b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series668.0ms (4.9%)

Counts

2 → 76

Calls

2 calls:

383.0ms	(.f64 (/.f64 x 1) (/.f64 y (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z)))
284.0ms	(/.f64 y (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z))

rewrite149.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

290×	`times-frac_binary64`
189×	`add-sqr-sqrt_binary64`
150×	`*-un-lft-identity_binary64`
146×	`add-cube-cbrt_binary64`
71×	`associate-r_binary64`

Counts

2 → 233

Calls

2 calls:

58.0ms	(.f64 (/.f64 x 1) (/.f64 y (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z)))
16.0ms	(/.f64 y (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z))

simplify220.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

471×	`associate-/l*_binary64`
414×	`times-frac_binary64`
390×	`fma-def_binary64`
370×	`associate-l_binary64`
326×	`associate-*l/_binary64`

Counts

309 → 406

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	482	10162
1	1355	9722
2	4915	9722
3	5197	9722

prune613.0ms (4.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	486	2	488
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	488	11	499

Error

2.5b

Counts

499 → 11

Alt Table

Status	Error	Program
✓	20.5b	(.f64 (/.f64 x 1) (/.f64 y (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z)))
	21.3b	(.f64 (/.f64 x (.f64 (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)) (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)))) (/.f64 y (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z))))
	22.6b	(.f64 (/.f64 x 1) (.f64 (/.f64 y (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) z))
	44.1b	(.f64 y (.f64 (sqrt.f64 (/.f64 -1 (.f64 a t))) (.f64 z x)))
	22.1b	(.f64 (.f64 x y) (/.f64 1 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)))
	26.6b	(.f64 (/.f64 x (.f64 (cbrt.f64 (hypot.f64 z (sqrt.f64 (neg.f64 (.f64 a t))))) (cbrt.f64 (hypot.f64 z (sqrt.f64 (neg.f64 (.f64 a t))))))) (/.f64 y (/.f64 (cbrt.f64 (hypot.f64 z (sqrt.f64 (neg.f64 (*.f64 a t))))) z)))
	24.4b	(/.f64 (.f64 x y) (.f64 (/.f64 1 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (hypot.f64 z (sqrt.f64 (neg.f64 (.f64 a t)))) (cbrt.f64 z))))
	37.7b	(neg.f64 (*.f64 y x))
✓	22.1b	(/.f64 (.f64 x y) (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z))
	33.1b	(*.f64 y x)
▶	20.6b	(.f64 (/.f64 x 1) (.f64 y (.f64 (/.f64 1 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 a t)))) z)))

Compiler

Compiled 15541 to 4353 computations (72% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(-.f64 (.f64 z z) (.f64 a t))
✓	1.0b	(.f64 y (.f64 (/.f64 1 (sqrt.f64 (-.f64 (.f64 z z) (.f64 a t)))) z))
✓	1.2b	(.f64 (/.f64 x 1) (.f64 y (.f64 (/.f64 1 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 a t)))) z)))
✓	24.9b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 a t)))

series576.0ms (4.3%)

Counts

4 → 132

Calls

4 calls:

265.0ms	(.f64 (/.f64 x 1) (.f64 y (.f64 (/.f64 1 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 a t)))) z)))
230.0ms	(.f64 y (.f64 (/.f64 1 (sqrt.f64 (-.f64 (.f64 z z) (.f64 a t)))) z))
72.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 a t)))
9.0ms	(-.f64 (.f64 z z) (.f64 a t))

rewrite45.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

91×	`add-exp-log_binary64`
54×	`prod-exp_binary64`
45×	`add-cbrt-cube_binary64`
23×	`cbrt-unprod_binary64`
20×	`div-exp_binary64`

Counts

4 → 114

Calls

4 calls:

13.0ms	(.f64 (/.f64 x 1) (.f64 y (.f64 (/.f64 1 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 a t)))) z)))
10.0ms	(.f64 y (.f64 (/.f64 1 (sqrt.f64 (-.f64 (.f64 z z) (.f64 a t)))) z))
5.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 a t)))
3.0ms	(-.f64 (.f64 z z) (.f64 a t))

simplify183.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

573×	`fma-def_binary64`
571×	`times-frac_binary64`
502×	`associate-r_binary64`
374×	`associate-l_binary64`
307×	`associate-/r*_binary64`

Counts

246 → 227

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	384	6397
1	1114	5785
2	4806	5785
3	5264	5785

prune439.0ms (3.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	226	1	227
Fresh	1	7	8
Picked	0	1	1
Done	1	1	2
Total	228	10	238

Error

2.5b

Counts

238 → 10

Alt Table

Status	Error	Program
	22.6b	(.f64 (/.f64 x 1) (.f64 (/.f64 y (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) z))
	44.1b	(.f64 y (.f64 (sqrt.f64 (/.f64 -1 (.f64 a t))) (.f64 z x)))
	22.1b	(.f64 (.f64 x y) (/.f64 1 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)))
	26.6b	(.f64 (/.f64 x (.f64 (cbrt.f64 (hypot.f64 z (sqrt.f64 (neg.f64 (.f64 a t))))) (cbrt.f64 (hypot.f64 z (sqrt.f64 (neg.f64 (.f64 a t))))))) (/.f64 y (/.f64 (cbrt.f64 (hypot.f64 z (sqrt.f64 (neg.f64 (*.f64 a t))))) z)))
	21.0b	(.f64 (/.f64 x 1) (.f64 (.f64 (cbrt.f64 (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 a t)))))) (cbrt.f64 (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 a t))))))) (cbrt.f64 (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 a t))))))))
	24.4b	(/.f64 (.f64 x y) (.f64 (/.f64 1 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (hypot.f64 z (sqrt.f64 (neg.f64 (.f64 a t)))) (cbrt.f64 z))))
	37.7b	(neg.f64 (*.f64 y x))
✓	22.1b	(/.f64 (.f64 x y) (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z))
	33.1b	(*.f64 y x)
✓	20.6b	(.f64 (/.f64 x 1) (.f64 y (.f64 (/.f64 1 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 a t)))) z)))

Compiler

Compiled 7019 to 3168 computations (54.9% saved)

regimes5.0s (37.3%)

Accuracy

Total 3.2b remaining (48.8%)

Threshold costs 0b (0%)

Counts

184 → 3

Compiler

Compiled 39771 to 23963 computations (39.7% saved)

bsearch45.0ms (0.3%)

Steps

Iters	Range		Point
4	5.283963595986049e+78	2.0520267029654177e+79	1.870606781150024e+79
7	-7.466101799350215e+163	-6.677078067734696e+161	-6.796797640097235e+161

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
7×	`+-commutative_binary64`
7×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	43
1	38	43
2	54	43
3	65	43
4	71	43
5	72	43
6	72	43

end361.0ms (2.7%)

Remove: (sort t a)
Compiler: Compiled 504 to 290 computations (42.5% saved)

Details

analyze1.2s (8.6%)

sample2.1s (15.4%)

simplify93.0ms (0.7%)

prune2.0ms (0%)

localize10.0ms (0.1%)

series329.0ms (2.4%)

rewrite40.0ms (0.3%)

simplify172.0ms (1.3%)

prune237.0ms (1.8%)

localize11.0ms (0.1%)

series305.0ms (2.3%)

rewrite42.0ms (0.3%)

simplify264.0ms (2%)

prune393.0ms (2.9%)

localize22.0ms (0.2%)

series668.0ms (4.9%)

rewrite149.0ms (1.1%)

simplify220.0ms (1.6%)

prune613.0ms (4.5%)

localize16.0ms (0.1%)

series576.0ms (4.3%)

rewrite45.0ms (0.3%)

simplify183.0ms (1.4%)

prune439.0ms (3.3%)

regimes5.0s (37.3%)

bsearch45.0ms (0.3%)

simplify4.0ms (0%)

end361.0ms (2.7%)

Profiling