Details

analyze2.8s (19.2%)

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
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)

sample62.0ms (0.4%)

Algorithm

1×

intervals

Results

17.0ms	256×	body	128	valid
4.0ms	30×	body	128	invalid
4.0ms	74×	body	128	nan

Compiler

Compiled 44 to 30 computations (31.8% saved)

simplify66.0ms (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

23.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	23.4b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))

Compiler

Compiled 57 to 36 computations (36.8% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.8b	(-.f64 (.f64 z z) (.f64 t a))
✓	5.0b	(.f64 (.f64 x y) z)
✓	8.3b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
✓	24.2b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series445.0ms (3%)

Counts

4 → 136

Calls

4 calls:

331.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
76.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
19.0ms	(.f64 (.f64 x y) z)
18.0ms	(-.f64 (.f64 z z) (.f64 t a))

rewrite47.0ms (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))))
8.0ms	(.f64 (.f64 x y) z)
8.0ms	(-.f64 (.f64 z z) (.f64 t a))
6.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

simplify213.0ms (1.5%)

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

prune261.0ms (1.8%)

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

5.5b

Counts

191 → 10

Alt Table

Status	Error	Program
	35.2b	(neg.f64 (*.f64 y x))
▶	21.8b	(.f64 (/.f64 (.f64 x y) 1) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
	36.7b	(*.f64 y x)
	48.0b	(.f64 y (.f64 (sqrt.f64 (/.f64 -1 (.f64 a t))) (.f64 z x)))
	23.3b	(.f64 (/.f64 (.f64 y x) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 a t))))) (/.f64 z (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 a t))))))
	23.4b	(/.f64 (.f64 (.f64 y x) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
	22.6b	(.f64 (/.f64 (.f64 x y) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (/.f64 z (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
	30.4b	(/.f64 (.f64 (.f64 x y) z) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))))
	59.1b	(exp.f64 (-.f64 (+.f64 (+.f64 (log.f64 x) (log.f64 y)) (log.f64 z)) (log.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
	34.3b	(expm1.f64 (log1p.f64 (/.f64 (.f64 y (.f64 z x)) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))))

Compiler

Compiled 5102 to 1577 computations (69.1% saved)

localize16.0ms (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))))
	0.8b	(-.f64 (.f64 z z) (.f64 t a))
✓	2.9b	(.f64 (/.f64 (.f64 x y) 1) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
	24.2b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series472.0ms (3.2%)

Counts

2 → 64

Calls

2 calls:

335.0ms	(.f64 (/.f64 (.f64 x y) 1) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
137.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))

rewrite49.0ms (0.3%)

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:

24.0ms	(.f64 (/.f64 (.f64 x y) 1) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
10.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))

simplify193.0ms (1.3%)

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

prune390.0ms (2.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	289	3	292
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	292	10	302

Error

5.5b

Counts

302 → 10

Alt Table

Status	Error	Program
	22.6b	(.f64 (/.f64 (.f64 x y) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (/.f64 z (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
	23.2b	(.f64 (/.f64 x 1) (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 a t))))))
	35.2b	(neg.f64 (*.f64 y x))
	36.7b	(*.f64 y x)
	23.3b	(.f64 (/.f64 (.f64 y x) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 a t))))) (/.f64 z (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 a t))))))
	23.4b	(/.f64 (.f64 (.f64 y x) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
	30.4b	(/.f64 (.f64 (.f64 x y) z) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))))
	28.4b	(.f64 (/.f64 (.f64 x y) 1) (/.f64 z (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z)))))
	34.3b	(expm1.f64 (log1p.f64 (/.f64 (.f64 y (.f64 z x)) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))))
▶	21.9b	(.f64 (/.f64 (.f64 x y) 1) (.f64 z (/.f64 1 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))))

Compiler

Compiled 8822 to 3022 computations (65.7% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 z (/.f64 1 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
	0.8b	(-.f64 (.f64 z z) (.f64 t a))
✓	2.9b	(.f64 (/.f64 (.f64 x y) 1) (.f64 z (/.f64 1 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))))
	24.2b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series528.0ms (3.6%)

Counts

2 → 64

Calls

2 calls:

401.0ms	(.f64 (/.f64 (.f64 x y) 1) (.f64 z (/.f64 1 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))))
126.0ms	(.f64 z (/.f64 1 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))

rewrite52.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

106×	`add-exp-log_binary64`
59×	`prod-exp_binary64`
43×	`add-cbrt-cube_binary64`
32×	`div-exp_binary64`
30×	`add-sqr-sqrt_binary64`

Counts

2 → 110

Calls

2 calls:

20.0ms	(.f64 (/.f64 (.f64 x y) 1) (.f64 z (/.f64 1 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))))
11.0ms	(.f64 z (/.f64 1 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))

simplify218.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

857×	`fma-def_binary64`
430×	`times-frac_binary64`
419×	`associate-r_binary64`
361×	`associate-l_binary64`
253×	`associate-/r*_binary64`

Counts

174 → 194

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	316	5117
1	894	4541
2	4291	4530
3	5132	4530

prune412.0ms (2.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	275	1	276
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	275	11	286

Error

5.5b

Counts

286 → 11

Alt Table

Status	Error	Program
▶	22.6b	(.f64 (/.f64 (.f64 x y) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (/.f64 z (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
	23.2b	(.f64 (/.f64 x 1) (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 a t))))))
	30.4b	(/.f64 (.f64 (.f64 x y) z) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))))
	35.2b	(.f64 (/.f64 (.f64 x y) 1) (*.f64 z (/.f64 1 (neg.f64 z))))
	35.2b	(neg.f64 (*.f64 y x))
	36.7b	(*.f64 y x)
	23.3b	(.f64 (/.f64 (.f64 y x) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 a t))))) (/.f64 z (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 a t))))))
	23.4b	(/.f64 (.f64 (.f64 y x) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
	28.4b	(.f64 (/.f64 (.f64 x y) 1) (/.f64 z (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z)))))
	34.3b	(expm1.f64 (log1p.f64 (/.f64 (.f64 y (.f64 z x)) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))))
✓	21.9b	(.f64 (/.f64 (.f64 x y) 1) (.f64 z (/.f64 1 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))))

Compiler

Compiled 8624 to 3597 computations (58.3% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.8b	(-.f64 (.f64 z z) (.f64 t a))
✓	0.9b	(/.f64 (.f64 x y) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
✓	5.0b	(.f64 (/.f64 (.f64 x y) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (/.f64 z (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
	24.2b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series2.4s (16.1%)

Counts

2 → 104

Calls

2 calls:

2.0s

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

345.0ms

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

rewrite68.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`sqrt-prod_binary64`
48×	`times-frac_binary64`
42×	`add-sqr-sqrt_binary64`
33×	`associate-r_binary64`
31×	`*-un-lft-identity_binary64`

Counts

2 → 115

Calls

2 calls:

30.0ms

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

15.0ms

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

simplify286.0ms (2%)

Algorithm

1×	egg-herbie

Rules

618×	`times-frac_binary64`
438×	`fma-def_binary64`
387×	`associate-/l*_binary64`
317×	`associate-/r*_binary64`
298×	`associate-*l/_binary64`

Counts

219 → 240

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	453	9378
1	1387	8379
2	4922	8379
3	5121	8379

prune480.0ms (3.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	404	0	404
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	404	11	415

Error

5.5b

Counts

415 → 11

Alt Table

Status	Error	Program
✓	22.6b	(.f64 (/.f64 (.f64 x y) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (/.f64 z (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
	23.2b	(.f64 (/.f64 x 1) (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 a t))))))
	30.4b	(/.f64 (.f64 (.f64 x y) z) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))))
	35.2b	(.f64 (/.f64 (.f64 x y) 1) (*.f64 z (/.f64 1 (neg.f64 z))))
	35.2b	(neg.f64 (*.f64 y x))
	36.7b	(*.f64 y x)
	23.3b	(.f64 (/.f64 (.f64 y x) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 a t))))) (/.f64 z (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 a t))))))
	23.4b	(/.f64 (.f64 (.f64 y x) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
	28.4b	(.f64 (/.f64 (.f64 x y) 1) (/.f64 z (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z)))))
	34.3b	(expm1.f64 (log1p.f64 (/.f64 (.f64 y (.f64 z x)) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))))
✓	21.9b	(.f64 (/.f64 (.f64 x y) 1) (.f64 z (/.f64 1 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))))

Compiler

Compiled 15909 to 3905 computations (75.5% saved)

regimes2.9s (20.1%)

Accuracy

Total 4.5b remaining (57.3%)

Threshold costs 0b (0%)

Counts

92 → 4

Compiler

Compiled 18461 to 11841 computations (35.9% saved)

bsearch150.0ms (1%)

Steps

Iters	Range	Point
8	7.387664042623558e-42	1.5806664502483216e-37	1.1312353151972541e-37
7	-9.220843068975659e-234	-1.2735980277574724e-235	-9.098723144956853e-234
3	-6.289658185029303e+109	-1.544151485154195e+106	-2.2076112030402606e+109

Iters

Range

Point

7.387664042623558e-42

1.5806664502483216e-37

1.1312353151972541e-37

-9.220843068975659e-234

-1.2735980277574724e-235

-9.098723144956853e-234

-6.289658185029303e+109

-1.544151485154195e+106

-2.2076112030402606e+109

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`*-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	33	69
1	53	69
2	70	69
3	80	69
4	84	69
5	83	69

end35.0ms (0.2%)

Remove

(sort t a)

(sort x y)

Compiler

Compiled 255 to 135 computations (47.1% saved)

sample2.0s (13.7%)

Algorithm

1×

intervals

Results

775.0ms	8000×	body	128	valid
209.0ms	2210×	body	128	nan
75.0ms	809×	body	128	invalid

Compiler

Compiled 295 to 186 computations (36.9% saved)

Details

analyze2.8s (19.2%)

sample62.0ms (0.4%)

simplify66.0ms (0.5%)

prune2.0ms (0%)

localize14.0ms (0.1%)

series445.0ms (3%)

rewrite47.0ms (0.3%)

simplify213.0ms (1.5%)

prune261.0ms (1.8%)

localize16.0ms (0.1%)

series472.0ms (3.2%)

rewrite49.0ms (0.3%)

simplify193.0ms (1.3%)

prune390.0ms (2.7%)

localize27.0ms (0.2%)

series528.0ms (3.6%)

rewrite52.0ms (0.4%)

simplify218.0ms (1.5%)

prune412.0ms (2.8%)

localize26.0ms (0.2%)

series2.4s (16.1%)

rewrite68.0ms (0.5%)

simplify286.0ms (2%)

prune480.0ms (3.3%)

regimes2.9s (20.1%)

bsearch150.0ms (1%)

simplify7.0ms (0.1%)

end35.0ms (0.2%)

sample2.0s (13.7%)

Profiling