Details

analyze1.5s (10.8%)

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
1.6%	98.2%	0.2%	10
3.1%	90.4%	6.5%	11
9.2%	84.4%	6.5%	12
13%	80.6%	6.5%	13
24.8%	68.7%	6.5%	14

Compiler

Compiled 20 to 13 computations (35% saved)

sample1.7s (12.2%)

Symmetry

(sort x y)

(sort t a)

Results

1.2s	8256×	body	128	valid
427.0ms	3160×	body	128	invalid

Compiler

Compiled 59 to 38 computations (35.6% saved)

simplify65.0ms (0.5%)

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

22.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	22.0b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))

Compiler

Compiled 57 to 36 computations (36.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(-.f64 (.f64 z z) (.f64 t a))
✓	4.8b	(.f64 (.f64 x y) z)
✓	8.7b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
✓	23.2b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series260.0ms (1.8%)

Counts

4 → 136

Calls

4 calls:

202.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
39.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
10.0ms	(.f64 (.f64 x y) z)
8.0ms	(-.f64 (.f64 z z) (.f64 t a))

rewrite21.0ms (0.2%)

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:

6.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
5.0ms	(.f64 (.f64 x y) z)
3.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
2.0ms	(-.f64 (.f64 z z) (.f64 t a))

simplify122.0ms (0.9%)

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

prune160.0ms (1.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	180	10	190
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	181	10	191

Error

4.0b

Counts

191 → 10

Alt Table

Status	Error	Program
▶	20.8b	(/.f64 (.f64 x y) (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z))
	22.5b	(/.f64 (.f64 (.f64 x y) z) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
	24.0b	(/.f64 (.f64 y (.f64 z x)) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
	36.4b	(neg.f64 (*.f64 y x))
	37.6b	(*.f64 y x)
	44.2b	(.f64 y (.f64 (sqrt.f64 (/.f64 -1 (.f64 a t))) (.f64 z x)))
	26.3b	(.f64 (/.f64 (.f64 y x) (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z)) (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z)))) (/.f64 z (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z))))
	30.0b	(.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))))
	33.5b	(/.f64 (.f64 (/.f64 (.f64 y x) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z))) z) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
	29.1b	(/.f64 (.f64 (.f64 x y) z) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))))

Compiler

Compiled 5200 to 1581 computations (69.6% saved)

localize13.0ms (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)
	0.4b	(-.f64 (.f64 z z) (.f64 t a))
✓	2.7b	(/.f64 (.f64 x y) (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z))
	23.2b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series264.0ms (1.9%)

Counts

2 → 64

Calls

2 calls:

208.0ms	(/.f64 (.f64 x y) (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z))
55.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)

rewrite23.0ms (0.2%)

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:

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

simplify188.0ms (1.3%)

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

prune286.0ms (2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	294	4	298
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	297	11	308

Error

4.0b

Counts

308 → 11

Alt Table

Status	Error	Program
	25.6b	(/.f64 (.f64 x y) (/.f64 (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z))) z))
	26.3b	(.f64 (/.f64 (.f64 y x) (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z)) (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z)))) (/.f64 z (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z))))
▶	20.9b	(/.f64 (.f64 x y) (.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) (/.f64 1 z)))
	30.0b	(.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))))
	21.5b	(.f64 (/.f64 x 1) (/.f64 y (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z)))
	23.8b	(/.f64 (.f64 x y) (/.f64 (/.f64 (hypot.f64 z (sqrt.f64 (neg.f64 (.f64 a t)))) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z)))
	36.4b	(neg.f64 (*.f64 y x))
	37.6b	(*.f64 y x)
	33.5b	(/.f64 (.f64 (/.f64 (.f64 y x) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z))) z) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
	22.5b	(/.f64 (.f64 (.f64 x y) z) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
	29.1b	(/.f64 (.f64 (.f64 x y) z) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))))

Compiler

Compiled 8362 to 2298 computations (72.5% 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))) (/.f64 1 z))
	0.4b	(-.f64 (.f64 z z) (.f64 t a))
✓	2.7b	(/.f64 (.f64 x y) (.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) (/.f64 1 z)))
	23.2b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series259.0ms (1.8%)

Counts

2 → 64

Calls

2 calls:

201.0ms	(/.f64 (.f64 x y) (.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) (/.f64 1 z)))
58.0ms	(.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) (/.f64 1 z))

rewrite30.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-exp-log_binary64`
28×	`add-cbrt-cube_binary64`
25×	`add-sqr-sqrt_binary64`
17×	`prod-exp_binary64`
16×	`div-exp_binary64`

Counts

2 → 85

Calls

2 calls:

12.0ms	(/.f64 (.f64 x y) (.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) (/.f64 1 z)))
10.0ms	(.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) (/.f64 1 z))

simplify127.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

693×	`fma-def_binary64`
583×	`times-frac_binary64`
306×	`associate-/l*_binary64`
284×	`associate-r_binary64`
277×	`associate-/r*_binary64`

Counts

149 → 173

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	292	4418
1	897	3994
2	4033	3898
3	4979	3898
4	4961	3898

prune237.0ms (1.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	255	0	255
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	255	11	266

Error

4.0b

Counts

266 → 11

Alt Table

Status	Error	Program
	25.6b	(/.f64 (.f64 x y) (/.f64 (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z))) z))
	26.3b	(.f64 (/.f64 (.f64 y x) (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z)) (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z)))) (/.f64 z (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z))))
✓	20.9b	(/.f64 (.f64 x y) (.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) (/.f64 1 z)))
	30.0b	(.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))))
▶	21.5b	(.f64 (/.f64 x 1) (/.f64 y (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z)))
	23.8b	(/.f64 (.f64 x y) (/.f64 (/.f64 (hypot.f64 z (sqrt.f64 (neg.f64 (.f64 a t)))) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z)))
	36.4b	(neg.f64 (*.f64 y x))
	37.6b	(*.f64 y x)
	33.5b	(/.f64 (.f64 (/.f64 (.f64 y x) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z))) z) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
	22.5b	(/.f64 (.f64 (.f64 x y) z) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
	29.1b	(/.f64 (.f64 (.f64 x y) z) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))))

Compiler

Compiled 7349 to 2685 computations (63.5% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(-.f64 (.f64 z z) (.f64 t a))
✓	2.2b	(.f64 (/.f64 x 1) (/.f64 y (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z)))
✓	2.2b	(/.f64 y (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z))
	23.2b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series350.0ms (2.5%)

Counts

2 → 76

Calls

2 calls:

202.0ms	(.f64 (/.f64 x 1) (/.f64 y (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z)))
148.0ms	(/.f64 y (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z))

rewrite69.0ms (0.5%)

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:

23.0ms	(.f64 (/.f64 x 1) (/.f64 y (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z)))
7.0ms	(/.f64 y (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z))

simplify211.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

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

Counts

309 → 405

Iterations

Useful iterations: 1 (0.0ms)

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

prune447.0ms (3.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	487	0	487
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	487	11	498

Error

4.0b

Counts

498 → 11

Alt Table

Status	Error	Program
	25.6b	(/.f64 (.f64 x y) (/.f64 (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z))) z))
	26.3b	(.f64 (/.f64 (.f64 y x) (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z)) (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z)))) (/.f64 z (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z))))
✓	20.9b	(/.f64 (.f64 x y) (.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) (/.f64 1 z)))
	30.0b	(.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))))
✓	21.5b	(.f64 (/.f64 x 1) (/.f64 y (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z)))
	23.8b	(/.f64 (.f64 x y) (/.f64 (/.f64 (hypot.f64 z (sqrt.f64 (neg.f64 (.f64 a t)))) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z)))
	36.4b	(neg.f64 (*.f64 y x))
	37.6b	(*.f64 y x)
	33.5b	(/.f64 (.f64 (/.f64 (.f64 y x) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z))) z) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
	22.5b	(/.f64 (.f64 (.f64 x y) z) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
	29.1b	(/.f64 (.f64 (.f64 x y) z) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))))

Compiler

Compiled 15354 to 4235 computations (72.4% saved)

regimes7.4s (52.1%)

Accuracy

Total 3.1b remaining (49.1%)

Threshold costs 0b (0%)

Counts

289 → 5

Compiler

Compiled 64234 to 39631 computations (38.3% saved)

bsearch170.0ms (1.2%)

Steps

Iters	Range		Point
3	3.71773868080436e+82	5.1017219808092264e+82	5.015223024558922e+82
8	7.291242078897128e-176	6.753578880291298e-173	6.049021251734141e-173
8	-4.391692004279047e-135	-8.188439948179481e-140	-1.0802216888912775e-139
8	-3.4000274368432666e+122	-1.2266822515200078e+120	-3.347552958513927e+122

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
4×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	128
1	65	128
2	72	128
3	77	128
4	79	128
5	78	128

end182.0ms (1.3%)

Remove

(sort t a)

(sort x y)

Compiler

Compiled 819 to 412 computations (49.7% saved)

Details

analyze1.5s (10.8%)

sample1.7s (12.2%)

simplify65.0ms (0.5%)

prune2.0ms (0%)

localize11.0ms (0.1%)

series260.0ms (1.8%)

rewrite21.0ms (0.2%)

simplify122.0ms (0.9%)

prune160.0ms (1.1%)

localize13.0ms (0.1%)

series264.0ms (1.9%)

rewrite23.0ms (0.2%)

simplify188.0ms (1.3%)

prune286.0ms (2%)

localize11.0ms (0.1%)

series259.0ms (1.8%)

rewrite30.0ms (0.2%)

simplify127.0ms (0.9%)

prune237.0ms (1.7%)

localize12.0ms (0.1%)

series350.0ms (2.5%)

rewrite69.0ms (0.5%)

simplify211.0ms (1.5%)

prune447.0ms (3.2%)

regimes7.4s (52.1%)

bsearch170.0ms (1.2%)

simplify7.0ms (0%)

end182.0ms (1.3%)

Profiling