Details

analyze1.4s (16%)

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)

sample127.0ms (1.4%)

Algorithm

1×

intervals

Symmetry

(sort x y)

(sort t a)

Results

16.0ms	256×	body	128	valid
5.0ms	64×	body	128	nan
2.0ms	29×	body	128	invalid

Compiler

Compiled 44 to 30 computations (31.8% saved)

simplify60.0ms (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

23.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	23.6b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))

Compiler

Compiled 57 to 36 computations (36.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(-.f64 (.f64 z z) (.f64 t a))
✓	4.3b	(.f64 (.f64 x y) z)
✓	9.2b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
✓	22.4b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series259.0ms (2.9%)

Counts

4 → 136

Calls

4 calls:

201.0ms	(/.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)
9.0ms	(-.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:

7.0ms	(/.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)))
3.0ms	(-.f64 (.f64 z z) (.f64 t a))

simplify142.0ms (1.6%)

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

prune163.0ms (1.9%)

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

3.5b

Counts

191 → 10

Alt Table

Status	Error	Program
	36.3b	(*.f64 y x)
	23.7b	(/.f64 1 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) (.f64 (.f64 x y) z)))
	21.1b	(.f64 (/.f64 (.f64 x y) 1) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
	26.7b	(/.f64 (.f64 (.f64 x y) z) (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z)) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))))
	27.0b	(/.f64 (.f64 x (.f64 y z)) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
	22.8b	(.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))))
	40.8b	(/.f64 (cbrt.f64 (.f64 (.f64 (.f64 (.f64 x y) z) (.f64 (.f64 x y) z)) (.f64 (.f64 x y) z))) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
▶	21.1b	(/.f64 (.f64 x y) (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z))
	27.0b	(/.f64 (.f64 y (.f64 z x)) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
	36.3b	(neg.f64 (*.f64 y x))

Compiler

Compiled 5114 to 1567 computations (69.4% 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)
	1.0b	(-.f64 (.f64 z z) (.f64 t a))
✓	2.4b	(/.f64 (.f64 x y) (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z))
	22.4b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series253.0ms (2.9%)

Counts

2 → 64

Calls

2 calls:

199.0ms	(/.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)

rewrite26.0ms (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:

10.0ms	(/.f64 (.f64 x y) (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z))
6.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)

simplify211.0ms (2.4%)

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

prune236.0ms (2.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	293	5	298
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	299	9	308

Error

3.5b

Counts

308 → 9

Alt Table

Status	Error	Program
▶	21.1b	(.f64 (/.f64 (.f64 x y) 1) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
	24.8b	(.f64 (/.f64 x (/.f64 (sqrt.f64 (hypot.f64 z (sqrt.f64 (neg.f64 (.f64 a t))))) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 y (/.f64 (sqrt.f64 (hypot.f64 z (sqrt.f64 (neg.f64 (.f64 a t))))) (cbrt.f64 z))))
	27.0b	(/.f64 (.f64 x (.f64 y z)) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
	22.7b	(/.f64 (.f64 x y) (.f64 (/.f64 (sqrt.f64 (hypot.f64 z (sqrt.f64 (neg.f64 (.f64 a t))))) (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (sqrt.f64 (hypot.f64 z (sqrt.f64 (neg.f64 (*.f64 a t))))) (cbrt.f64 z))))
	21.6b	(.f64 (/.f64 x 1) (/.f64 y (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z)))
	42.4b	(.f64 (/.f64 x (/.f64 1 (sqrt.f64 z))) (/.f64 y (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) (sqrt.f64 z))))
	36.3b	(neg.f64 (*.f64 y x))
	22.1b	(/.f64 (.f64 x y) (/.f64 (hypot.f64 z (sqrt.f64 (neg.f64 (.f64 a t)))) z))
	36.3b	(*.f64 y x)

Compiler

Compiled 8186 to 2232 computations (72.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
	1.0b	(-.f64 (.f64 z z) (.f64 t a))
✓	2.4b	(.f64 (/.f64 (.f64 x y) 1) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
	22.4b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series297.0ms (3.4%)

Counts

2 → 64

Calls

2 calls:

207.0ms	(.f64 (/.f64 (.f64 x y) 1) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
90.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))

rewrite31.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`times-frac_binary64`
40×	`add-sqr-sqrt_binary64`
37×	`add-exp-log_binary64`
32×	`*-un-lft-identity_binary64`
32×	`add-cube-cbrt_binary64`

Counts

2 → 107

Calls

2 calls:

13.0ms	(.f64 (/.f64 (.f64 x y) 1) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
6.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))

simplify137.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

831×	`fma-def_binary64`
453×	`times-frac_binary64`
382×	`associate-r_binary64`
345×	`associate-l_binary64`
303×	`associate-/l*_binary64`

Counts

171 → 210

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	327	5306
1	929	4920
2	4726	4909
3	5506	4909

prune227.0ms (2.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	291	1	292
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	292	9	301

Error

3.5b

Counts

301 → 9

Alt Table

Status	Error	Program
✓	21.1b	(.f64 (/.f64 (.f64 x y) 1) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
	27.0b	(/.f64 (.f64 x (.f64 y z)) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
	22.7b	(/.f64 (.f64 x y) (.f64 (/.f64 (sqrt.f64 (hypot.f64 z (sqrt.f64 (neg.f64 (.f64 a t))))) (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (sqrt.f64 (hypot.f64 z (sqrt.f64 (neg.f64 (*.f64 a t))))) (cbrt.f64 z))))
▶	21.6b	(.f64 (/.f64 x 1) (/.f64 y (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z)))
	42.4b	(.f64 (/.f64 x (/.f64 1 (sqrt.f64 z))) (/.f64 y (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) (sqrt.f64 z))))
	27.0b	(/.f64 (.f64 y (.f64 z x)) (sqrt.f64 (-.f64 (.f64 z z) (.f64 a t))))
	36.3b	(neg.f64 (*.f64 y x))
	22.1b	(/.f64 (.f64 x y) (/.f64 (hypot.f64 z (sqrt.f64 (neg.f64 (.f64 a t)))) z))
	36.3b	(*.f64 y x)

Compiler

Compiled 8747 to 2972 computations (66% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.0b	(-.f64 (.f64 z z) (.f64 t a))
✓	1.3b	(/.f64 y (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z))
✓	2.2b	(.f64 (/.f64 x 1) (/.f64 y (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z)))
	22.4b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series351.0ms (4%)

Counts

2 → 76

Calls

2 calls:

204.0ms	(.f64 (/.f64 x 1) (/.f64 y (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z)))
147.0ms	(/.f64 y (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z))

rewrite88.0ms (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:

25.0ms	(.f64 (/.f64 x 1) (/.f64 y (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z)))
8.0ms	(/.f64 y (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z))

simplify215.0ms (2.4%)

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

prune364.0ms (4.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	487	1	488
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	488	9	497

Error

3.5b

Counts

497 → 9

Alt Table

Status	Error	Program
✓	21.1b	(.f64 (/.f64 (.f64 x y) 1) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
	27.0b	(/.f64 (.f64 x (.f64 y z)) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
	22.7b	(/.f64 (.f64 x y) (.f64 (/.f64 (sqrt.f64 (hypot.f64 z (sqrt.f64 (neg.f64 (.f64 a t))))) (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (sqrt.f64 (hypot.f64 z (sqrt.f64 (neg.f64 (*.f64 a t))))) (cbrt.f64 z))))
✓	21.6b	(.f64 (/.f64 x 1) (/.f64 y (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z)))
	42.3b	(.f64 (.f64 x (sqrt.f64 z)) (/.f64 y (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) (sqrt.f64 z))))
	27.0b	(/.f64 (.f64 y (.f64 z x)) (sqrt.f64 (-.f64 (.f64 z z) (.f64 a t))))
	36.3b	(neg.f64 (*.f64 y x))
	22.1b	(/.f64 (.f64 x y) (/.f64 (hypot.f64 z (sqrt.f64 (neg.f64 (.f64 a t)))) z))
	36.3b	(*.f64 y x)

Compiler

Compiled 15260 to 4203 computations (72.5% saved)

regimes2.8s (32.1%)

Accuracy

Total 3.1b remaining (48.9%)

Threshold costs 0b (0%)

Counts

136 → 3

Compiler

Compiled 28515 to 17192 computations (39.7% saved)

bsearch30.0ms (0.3%)

Steps

Iters	Range		Point
3	3.775608759310589e+144	8.202005132647082e+152	4.1905476995839096e+145
4	-9.474325126268806e+71	-4.371150731781445e+70	-7.914973368704496e+71

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`*-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	21	43
1	36	43
2	52	43
3	63	43
4	69	43
5	70	43
6	70	43

end22.0ms (0.3%)

Remove

(sort t a)

(sort x y)

Compiler

Compiled 170 to 95 computations (44.1% saved)

sample1.3s (14.3%)

Algorithm

1×

intervals

Results

504.0ms	8000×	body	128	valid
117.0ms	2168×	body	128	nan
58.0ms	894×	body	128	invalid

Compiler

Compiled 232 to 145 computations (37.5% saved)

Details

analyze1.4s (16%)

sample127.0ms (1.4%)

simplify60.0ms (0.7%)

prune2.0ms (0%)

localize9.0ms (0.1%)

series259.0ms (2.9%)

rewrite21.0ms (0.2%)

simplify142.0ms (1.6%)

prune163.0ms (1.9%)

localize11.0ms (0.1%)

series253.0ms (2.9%)

rewrite26.0ms (0.3%)

simplify211.0ms (2.4%)

prune236.0ms (2.7%)

localize11.0ms (0.1%)

series297.0ms (3.4%)

rewrite31.0ms (0.4%)

simplify137.0ms (1.6%)

prune227.0ms (2.6%)

localize10.0ms (0.1%)

series351.0ms (4%)

rewrite88.0ms (1%)

simplify215.0ms (2.4%)

prune364.0ms (4.1%)

regimes2.8s (32.1%)

bsearch30.0ms (0.3%)

simplify4.0ms (0%)

end22.0ms (0.3%)

sample1.3s (14.3%)

Profiling