Details

analyze111.0ms (4.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
50%	50%	0.1%	5
50%	50%	0.1%	6
62.4%	34.3%	3.2%	7
62.4%	32.8%	4.8%	8
68.7%	21.1%	10.2%	9
68.7%	19.1%	12.2%	10
71.8%	11.5%	16.7%	11
71.8%	10.2%	18%	12
73.4%	6%	20.6%	13
73.4%	5.3%	21.3%	14

Compiler

Compiled 8 to 5 computations (37.5% saved)

sample762.0ms (32.9%)

Symmetry

(sort x y)

Results

688.0ms	8256×	body	128	valid
31.0ms	397×	body	128	invalid

Compiler

Compiled 23 to 14 computations (39.1% saved)

simplify20.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

276×	`fma-neg_binary64`
177×	`rules-43_binary64`
174×	`rules-42_binary64`
173×	`rules-41_binary64`
170×	`rules-40_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	30	7
2	91	7
3	254	7
4	647	7
5	6	7

prune1.0ms (0.1%)

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

39.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	39.9b	(/.f64 x (*.f64 y y))

Compiler

Compiled 21 to 12 computations (42.9% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	7.6b	(/.f64 x (*.f64 y y))

series27.0ms (1.2%)

Counts

1 → 24

Calls

1 calls:

27.0ms

(/.f64 x (*.f64 y y))

rewrite78.0ms (3.4%)

Algorithm

2×	batch-egg-rewrite

Rules

467×	`log1p-expm1-u_binary64`
467×	`expm1-log1p-u_binary64`
360×	`fma-neg_binary64`
232×	`prod-diff_binary64`
230×	`log-prod_binary64`

Counts

1 → 37

Calls

1 calls:

77.0ms

(/.f64 x (*.f64 y y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	116	7
2	1402	7
3	4945	7
4	5097	7
0	0	0
1	0	0

simplify21.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

197×	`fma-neg_binary64`
148×	`rules-41_binary64`
147×	`rules-43_binary64`
144×	`rules-42_binary64`
143×	`rules-40_binary64`

Counts

61 → 39

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	168
1	33	168
2	83	168
3	219	168
4	538	168
5	10	168

prune43.0ms (1.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	27	12	39
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	27	13	40

Error

37.8b

Counts

40 → 13

Alt Table

Status	Error	Program
	40.2b	(.f64 (cbrt.f64 (/.f64 x (.f64 y y))) (pow.f64 (cbrt.f64 (/.f64 x (*.f64 y y))) 2))
✓	39.9b	(/.f64 x (*.f64 y y))
	53.1b	(exp.f64 (log.f64 (/.f64 x (*.f64 y y))))
	53.8b	(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 x (.f64 y y)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 x (.f64 y y))))))
	48.2b	(cbrt.f64 (pow.f64 (/.f64 x (*.f64 y y)) 3))
	52.3b	(fabs.f64 (/.f64 x (*.f64 y y)))
	55.7b	(pow.f64 (/.f64 (pow.f64 x 3) (pow.f64 (*.f64 y y) 3)) 1/3)
	55.7b	(pow.f64 (/.f64 (sqrt.f64 x) y) 2)
	40.2b	(pow.f64 (cbrt.f64 (/.f64 x (*.f64 y y))) 3)
	53.7b	(pow.f64 (pow.f64 (/.f64 x (*.f64 y y)) 3) 1/3)
	57.3b	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (.f64 y y)))
	40.2b	(.f64 (pow.f64 (cbrt.f64 x) 2) (/.f64 (cbrt.f64 x) (.f64 y y)))
▶	40.0b	(.f64 x (/.f64 1 (.f64 y y)))

Compiler

Compiled 652 to 300 computations (54% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.7b	(/.f64 1 (*.f64 y y))
✓	7.5b	(.f64 x (/.f64 1 (.f64 y y)))

series29.0ms (1.2%)

Counts

2 → 36

Calls

2 calls:

27.0ms	(.f64 x (/.f64 1 (.f64 y y)))
2.0ms	(/.f64 1 (*.f64 y y))

rewrite67.0ms (2.9%)

Algorithm

2×	batch-egg-rewrite

Rules

604×	`log1p-expm1-u_binary64`
604×	`expm1-log1p-u_binary64`
505×	`fma-neg_binary64`
194×	`prod-diff_binary64`
155×	`egg-rr`

Counts

2 → 155

Calls

2 calls:

65.0ms	(/.f64 1 (*.f64 y y))
65.0ms	(.f64 x (/.f64 1 (.f64 y y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	159	11
2	1843	11
3	5145	11
0	0	0
1	0	0

simplify29.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

218×	`fma-neg_binary64`
175×	`rules-41_binary64`
174×	`rules-43_binary64`
171×	`rules-42_binary64`
170×	`rules-40_binary64`

Counts

191 → 157

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	252
1	43	252
2	95	252
3	257	252
4	628	252
5	10	252

prune210.0ms (9.1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	147	10	157
Fresh	4	7	11
Picked	1	0	1
Done	1	0	1
Total	153	17	170

Error

33.8b

Counts

170 → 17

Alt Table

Status	Error	Program
	41.4b	(*.f64 x (exp.f64 (log.f64 (pow.f64 y -2))))
	40.4b	(fma.f64 (cbrt.f64 x) (*.f64 (pow.f64 y -2) (pow.f64 (cbrt.f64 x) 2)) 0)
	47.7b	(*.f64 x (pow.f64 (pow.f64 (pow.f64 y -2) 3) 1/3))
	40.2b	(pow.f64 (cbrt.f64 (/.f64 x (*.f64 y y))) 3)
	37.1b	(/.f64 (/.f64 1 y) (/.f64 y x))
	40.2b	(.f64 (cbrt.f64 (/.f64 x (.f64 y y))) (pow.f64 (cbrt.f64 (/.f64 x (*.f64 y y))) 2))
	37.1b	(fma.f64 (/.f64 1 y) (*.f64 x (/.f64 1 y)) 0)
	57.3b	(fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (pow.f64 y -2)) 0)
	57.4b	(/.f64 (pow.f64 (/.f64 x (.f64 y y)) 3) (+.f64 (pow.f64 (/.f64 x (.f64 y y)) 2) (+.f64 0 (.f64 (/.f64 x (.f64 y y)) 0))))
	53.1b	(exp.f64 (log.f64 (/.f64 x (*.f64 y y))))
	52.3b	(fabs.f64 (/.f64 x (*.f64 y y)))
	55.7b	(pow.f64 (/.f64 (pow.f64 x 3) (pow.f64 (*.f64 y y) 3)) 1/3)
	55.7b	(pow.f64 (/.f64 (sqrt.f64 x) y) 2)
	53.7b	(pow.f64 (pow.f64 (/.f64 x (*.f64 y y)) 3) 1/3)
	45.4b	(*.f64 x (-.f64 (exp.f64 (log1p.f64 (pow.f64 y -2))) 1))
▶	37.0b	(/.f64 (/.f64 x y) y)
	40.2b	(/.f64 (pow.f64 y -2) (/.f64 1 x))

Compiler

Compiled 2534 to 1527 computations (39.7% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 x y) y)

series28.0ms (1.2%)

Counts

1 → 24

Calls

1 calls:

27.0ms

(/.f64 (/.f64 x y) y)

rewrite85.0ms (3.7%)

Algorithm

2×	batch-egg-rewrite

Rules

474×	`log1p-expm1-u_binary64`
474×	`expm1-log1p-u_binary64`
379×	`fma-neg_binary64`
249×	`prod-diff_binary64`
239×	`log-prod_binary64`

Counts

1 → 43

Calls

1 calls:

84.0ms

(/.f64 (/.f64 x y) y)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	113	7
2	1423	7
3	4959	7
4	5171	7
0	0	0
1	0	0

simplify24.0ms (1%)

Algorithm

1×	egg-herbie

Rules

197×	`fma-neg_binary64`
148×	`rules-41_binary64`
147×	`rules-43_binary64`
144×	`rules-42_binary64`
143×	`rules-40_binary64`

Counts

67 → 45

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	168
1	33	168
2	83	168
3	219	168
4	538	168
5	10	168

prune63.0ms (2.7%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	39	6	45
Fresh	5	11	16
Picked	0	1	1
Done	0	0	0
Total	44	18	62

Error

33.7b

Counts

62 → 18

Alt Table

Status	Error	Program
	41.4b	(*.f64 x (exp.f64 (log.f64 (pow.f64 y -2))))
	40.4b	(fma.f64 (cbrt.f64 x) (*.f64 (pow.f64 y -2) (pow.f64 (cbrt.f64 x) 2)) 0)
	37.4b	(pow.f64 (cbrt.f64 (/.f64 (/.f64 x y) y)) 3)
	52.3b	(fabs.f64 (/.f64 x (*.f64 y y)))
	37.4b	(*.f64 (cbrt.f64 (/.f64 (/.f64 x y) y)) (pow.f64 (cbrt.f64 (/.f64 (/.f64 x y) y)) 2))
	55.7b	(pow.f64 (/.f64 (pow.f64 x 3) (pow.f64 (*.f64 y y) 3)) 1/3)
	47.2b	(.f64 (cbrt.f64 (.f64 x x)) (/.f64 (cbrt.f64 x) (*.f64 y y)))
▶	37.1b	(/.f64 (/.f64 1 y) (/.f64 y x))
	52.5b	(exp.f64 (log.f64 (/.f64 (/.f64 x y) y)))
	51.3b	(fabs.f64 (/.f64 (/.f64 x y) y))
	49.5b	(*.f64 (sqrt.f64 (/.f64 x y)) (/.f64 (sqrt.f64 (/.f64 x y)) y))
	55.7b	(pow.f64 (/.f64 (sqrt.f64 x) y) 2)
	47.7b	(*.f64 x (pow.f64 (pow.f64 (pow.f64 y -2) 3) 1/3))
	53.7b	(pow.f64 (pow.f64 (/.f64 x (*.f64 y y)) 3) 1/3)
	45.4b	(*.f64 x (-.f64 (exp.f64 (log1p.f64 (pow.f64 y -2))) 1))
✓	37.0b	(/.f64 (/.f64 x y) y)
	57.4b	(/.f64 (pow.f64 (/.f64 x (.f64 y y)) 3) (+.f64 (pow.f64 (/.f64 x (.f64 y y)) 2) (+.f64 0 (.f64 (/.f64 x (.f64 y y)) 0))))
	40.2b	(/.f64 (pow.f64 y -2) (/.f64 1 x))

Compiler

Compiled 843 to 406 computations (51.8% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (/.f64 1 y) (/.f64 y x))

series24.0ms (1.1%)

Counts

1 → 24

Calls

1 calls:

24.0ms

(/.f64 (/.f64 1 y) (/.f64 y x))

rewrite61.0ms (2.6%)

Algorithm

2×	batch-egg-rewrite

Rules

620×	`log1p-expm1-u_binary64`
620×	`expm1-log1p-u_binary64`
491×	`fma-neg_binary64`
186×	`prod-diff_binary64`
117×	`expm1-udef_binary64`

Counts

1 → 39

Calls

1 calls:

60.0ms

(/.f64 (/.f64 1 y) (/.f64 y x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	155	7
2	1863	7
3	5228	7
0	0	0
1	0	0

simplify22.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

197×	`fma-neg_binary64`
148×	`rules-41_binary64`
147×	`rules-43_binary64`
144×	`rules-42_binary64`
143×	`rules-40_binary64`

Counts

63 → 41

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	168
1	33	168
2	83	168
3	219	168
4	538	168
5	10	168

prune59.0ms (2.6%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	37	4	41
Fresh	1	15	16
Picked	1	0	1
Done	0	1	1
Total	39	20	59

Error

33.6b

Counts

59 → 20

Alt Table

Status	Error	Program
	53.9b	(pow.f64 (pow.f64 (*.f64 x (pow.f64 y -2)) 3) 1/3)
	51.3b	(fabs.f64 (/.f64 (/.f64 x y) y))
	41.4b	(*.f64 x (exp.f64 (log.f64 (pow.f64 y -2))))
	40.4b	(fma.f64 (cbrt.f64 x) (*.f64 (pow.f64 y -2) (pow.f64 (cbrt.f64 x) 2)) 0)
	37.4b	(pow.f64 (cbrt.f64 (/.f64 (/.f64 x y) y)) 3)
	52.3b	(fabs.f64 (/.f64 x (*.f64 y y)))
	37.4b	(*.f64 (cbrt.f64 (/.f64 (/.f64 x y) y)) (pow.f64 (cbrt.f64 (/.f64 (/.f64 x y) y)) 2))
	54.7b	(log.f64 (pow.f64 (exp.f64 x) (pow.f64 y -2)))
	52.5b	(exp.f64 (log.f64 (/.f64 (/.f64 x y) y)))
	52.6b	(fabs.f64 (*.f64 x (pow.f64 y -2)))
	57.4b	(/.f64 (pow.f64 (/.f64 x (.f64 y y)) 3) (+.f64 (pow.f64 (/.f64 x (.f64 y y)) 2) (+.f64 0 (.f64 (/.f64 x (.f64 y y)) 0))))
	37.2b	(pow.f64 (*.f64 y (/.f64 y x)) -1)
	40.2b	(/.f64 (pow.f64 y -2) (/.f64 1 x))
	49.5b	(*.f64 (sqrt.f64 (/.f64 x y)) (/.f64 (sqrt.f64 (/.f64 x y)) y))
	47.2b	(.f64 (cbrt.f64 (.f64 x x)) (/.f64 (cbrt.f64 x) (*.f64 y y)))
	55.7b	(pow.f64 (/.f64 (sqrt.f64 x) y) 2)
	47.7b	(*.f64 x (pow.f64 (pow.f64 (pow.f64 y -2) 3) 1/3))
	53.7b	(pow.f64 (pow.f64 (/.f64 x (*.f64 y y)) 3) 1/3)
	45.4b	(*.f64 x (-.f64 (exp.f64 (log1p.f64 (pow.f64 y -2))) 1))
✓	37.0b	(/.f64 (/.f64 x y) y)

Compiler

Compiled 593 to 399 computations (32.7% saved)

regimes342.0ms (14.8%)

Accuracy

Total 1.3b remaining (98.8%)

Threshold costs 0b (0%)

Counts

79 → 2

Compiler

Compiled 4362 to 2961 computations (32.1% saved)

bsearch6.0ms (0.2%)

Steps

Iters	Range		Point
1	-8.034658410996253e+265	-7.358449623048331e+265	-7.865606214009272e+265

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	15	25

end191.0ms (8.2%)

Remove: (sort x y)
Compiler: Compiled 298 to 199 computations (33.2% saved)

Details

analyze111.0ms (4.8%)

sample762.0ms (32.9%)

simplify20.0ms (0.8%)

prune1.0ms (0.1%)

localize3.0ms (0.1%)

series27.0ms (1.2%)

rewrite78.0ms (3.4%)

simplify21.0ms (0.9%)

prune43.0ms (1.9%)

localize4.0ms (0.2%)

series29.0ms (1.2%)

rewrite67.0ms (2.9%)

simplify29.0ms (1.2%)

prune210.0ms (9.1%)

localize3.0ms (0.1%)

series28.0ms (1.2%)

rewrite85.0ms (3.7%)

simplify24.0ms (1%)

prune63.0ms (2.7%)

localize4.0ms (0.2%)

series24.0ms (1.1%)

rewrite61.0ms (2.6%)

simplify22.0ms (0.9%)

prune59.0ms (2.6%)

regimes342.0ms (14.8%)

bsearch6.0ms (0.2%)

simplify2.0ms (0.1%)

end191.0ms (8.2%)

Profiling