Details

analyze1.5s (15.7%)

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 (17.3%)

Symmetry

(sort x y)

(sort t a)

Results

1.1s	8256×	body	128	valid
428.0ms	3238×	body	128	invalid

Compiler

Compiled 59 to 38 computations (35.6% saved)

simplify58.0ms (0.6%)

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

25.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	25.7b	(/.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
✓	0.4b	(-.f64 (.f64 z z) (.f64 t a))
✓	4.5b	(.f64 (.f64 x y) z)
✓	10.2b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
✓	24.1b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series256.0ms (2.6%)

Counts

4 → 136

Calls

4 calls:

194.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
41.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
13.0ms	(.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:

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))

simplify124.0ms (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

prune162.0ms (1.7%)

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

3.4b

Counts

191 → 10

Alt Table

Status	Error	Program
▶	23.2b	(.f64 (/.f64 (.f64 x y) 1) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
	26.5b	(/.f64 (.f64 y (.f64 z x)) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
	26.1b	(/.f64 (.f64 x (.f64 y z)) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
	25.8b	(/.f64 (.f64 (.f64 x y) z) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))))
	36.0b	(*.f64 y x)
	30.8b	(/.f64 (.f64 (.f64 x y) z) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))))
	27.0b	(.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))))
	24.2b	(/.f64 (.f64 x y) (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z) z))
	37.0b	(neg.f64 (*.f64 y x))
	47.4b	(.f64 y (.f64 (sqrt.f64 (/.f64 -1 (.f64 a t))) (.f64 z x)))

Compiler

Compiled 5102 to 1563 computations (69.4% saved)

localize10.0ms (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))))
	0.4b	(-.f64 (.f64 z z) (.f64 t a))
✓	2.0b	(.f64 (/.f64 (.f64 x y) 1) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
	24.1b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series286.0ms (2.9%)

Counts

2 → 64

Calls

2 calls:

197.0ms	(.f64 (/.f64 (.f64 x y) 1) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
88.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))

rewrite29.0ms (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:

12.0ms	(.f64 (/.f64 (.f64 x y) 1) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
4.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))

simplify112.0ms (1.2%)

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

prune236.0ms (2.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	290	2	292
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	291	11	302

Error

3.4b

Counts

302 → 11

Alt Table

Status	Error	Program
✓	23.2b	(.f64 (/.f64 (.f64 x y) 1) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
	26.5b	(/.f64 (.f64 y (.f64 z x)) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
	25.8b	(/.f64 (.f64 (.f64 x y) z) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))))
	36.0b	(*.f64 y x)
	30.8b	(/.f64 (.f64 (.f64 x y) z) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))))
	27.0b	(.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))))
	24.2b	(/.f64 (.f64 x y) (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z) z))
▶	23.1b	(.f64 (/.f64 x 1) (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 a t))))))
	37.0b	(neg.f64 (*.f64 y x))
	23.2b	(.f64 (/.f64 (.f64 x y) 1) (.f64 z (/.f64 1 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))))
	47.4b	(.f64 y (.f64 (sqrt.f64 (/.f64 -1 (.f64 a t))) (.f64 z x)))

Compiler

Compiled 8843 to 3024 computations (65.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(-.f64 (.f64 z z) (.f64 a t))
✓	0.8b	(.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (*.f64 a t)))))
✓	1.3b	(.f64 (/.f64 x 1) (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 a t))))))
✓	24.1b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 a t)))

series386.0ms (4%)

Counts

4 → 132

Calls

4 calls:

194.0ms	(.f64 (/.f64 x 1) (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 a t))))))
144.0ms	(.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (*.f64 a t)))))
39.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 a t)))
8.0ms	(-.f64 (.f64 z z) (.f64 a t))

rewrite39.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-exp-log_binary64`
35×	`add-sqr-sqrt_binary64`
30×	`add-cbrt-cube_binary64`
29×	`times-frac_binary64`
26×	`*-un-lft-identity_binary64`

Counts

4 → 123

Calls

4 calls:

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

simplify123.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

599×	`times-frac_binary64`
488×	`associate-r_binary64`
407×	`associate-l_binary64`
381×	`associate-/l*_binary64`
317×	`associate-/r*_binary64`

Counts

255 → 235

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	399	6478
1	1155	5992
2	5210	5992

prune190.0ms (2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	233	2	235
Fresh	3	6	9
Picked	1	0	1
Done	0	1	1
Total	237	9	246

Error

3.4b

Counts

246 → 9

Alt Table

Status	Error	Program
	30.8b	(/.f64 (.f64 (.f64 x y) z) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))))
	27.0b	(.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))))
	24.2b	(/.f64 (.f64 x y) (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z) z))
	24.4b	(.f64 (/.f64 x 1) (.f64 (/.f64 y (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 a t))))) (/.f64 z (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 a t)))))))
✓	23.2b	(.f64 (/.f64 (.f64 x y) 1) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
	37.0b	(neg.f64 (*.f64 y x))
▶	24.1b	(.f64 (/.f64 x 1) (/.f64 (.f64 y z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 a t)))))
	36.0b	(*.f64 y x)
	47.4b	(.f64 y (.f64 (sqrt.f64 (/.f64 -1 (.f64 a t))) (.f64 z x)))

Compiler

Compiled 7190 to 2815 computations (60.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(-.f64 (.f64 z z) (.f64 a t))
✓	1.3b	(.f64 (/.f64 x 1) (/.f64 (.f64 y z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 a t)))))
✓	8.7b	(/.f64 (.f64 y z) (sqrt.f64 (-.f64 (.f64 z z) (*.f64 a t))))
	24.1b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 a t)))

series340.0ms (3.5%)

Counts

2 → 76

Calls

2 calls:

194.0ms	(.f64 (/.f64 x 1) (/.f64 (.f64 y z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 a t)))))
145.0ms	(/.f64 (.f64 y z) (sqrt.f64 (-.f64 (.f64 z z) (*.f64 a t))))

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-exp-log_binary64`
28×	`add-cbrt-cube_binary64`
23×	`times-frac_binary64`
23×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`

Counts

2 → 88

Calls

2 calls:

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

simplify110.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

581×	`times-frac_binary64`
466×	`fma-def_binary64`
394×	`associate-r_binary64`
343×	`associate-/l*_binary64`
313×	`associate-l_binary64`

Counts

164 → 174

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	328	5179
1	978	4730
2	4598	4730
3	4967	4730

prune172.0ms (1.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	239	1	240
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	239	10	249

Error

3.4b

Counts

249 → 10

Alt Table

Status	Error	Program
✓	23.2b	(.f64 (/.f64 (.f64 x y) 1) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
	37.3b	(.f64 (/.f64 x 1) (/.f64 (.f64 y z) (-.f64 z (.f64 1/2 (/.f64 (.f64 a t) z)))))
	30.8b	(/.f64 (.f64 (.f64 x y) z) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))))
	27.0b	(.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))))
	24.2b	(/.f64 (.f64 x y) (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z) z))
	24.4b	(.f64 (/.f64 x 1) (.f64 (/.f64 y (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 a t))))) (/.f64 z (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 a t)))))))
	37.0b	(neg.f64 (*.f64 y x))
✓	24.1b	(.f64 (/.f64 x 1) (/.f64 (.f64 y z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 a t)))))
	36.0b	(*.f64 y x)
	47.4b	(.f64 y (.f64 (sqrt.f64 (/.f64 -1 (.f64 a t))) (.f64 z x)))

Compiler

Compiled 7231 to 2652 computations (63.3% saved)

regimes3.6s (37.1%)

Accuracy

Total 3.0b remaining (48.6%)

Threshold costs 0b (0%)

Counts

134 → 3

Compiler

Compiled 27624 to 17140 computations (38% saved)

bsearch46.0ms (0.5%)

Steps

Iters	Range		Point
7	6.421573462103422e+81	2.0098915098832295e+83	1.6097388499861037e+83
3	-1.291730125085383e+157	-4.4913171539602196e+153	-1.195058800664299e+154

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	24	43
1	41	43
2	58	43
3	69	43
4	75	43
5	76	43
6	75	43

end139.0ms (1.4%)

Remove

(sort t a)

(sort x y)

Compiler

Compiled 409 to 245 computations (40.1% saved)

Details

analyze1.5s (15.7%)

sample1.7s (17.3%)

simplify58.0ms (0.6%)

prune2.0ms (0%)

localize10.0ms (0.1%)

series256.0ms (2.6%)

rewrite21.0ms (0.2%)

simplify124.0ms (1.3%)

prune162.0ms (1.7%)

localize10.0ms (0.1%)

series286.0ms (2.9%)

rewrite29.0ms (0.3%)

simplify112.0ms (1.2%)

prune236.0ms (2.4%)

localize10.0ms (0.1%)

series386.0ms (4%)

rewrite39.0ms (0.4%)

simplify123.0ms (1.3%)

prune190.0ms (2%)

localize10.0ms (0.1%)

series340.0ms (3.5%)

rewrite25.0ms (0.3%)

simplify110.0ms (1.1%)

prune172.0ms (1.8%)

regimes3.6s (37.1%)

bsearch46.0ms (0.5%)

simplify4.0ms (0%)

end139.0ms (1.4%)

Profiling