Details

analyze96.0ms (3.1%)

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
25%	74.9%	0.1%	5
25%	50%	25.1%	6
25%	31.2%	43.8%	7
31.2%	25%	43.8%	8
39%	17.2%	43.8%	9
42.9%	13.3%	43.8%	10
47.2%	9%	43.8%	11
49.4%	6.8%	43.8%	12
51.6%	4.6%	43.8%	13
52.7%	3.5%	43.8%	14

Compiler

Compiled 18 to 8 computations (55.6% saved)

sample888.0ms (28.5%)

Symmetry

(sort x y)

Results

798.0ms	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 53 to 23 computations (56.6% saved)

simplify58.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

958×	`rules-42_binary64`
808×	`fma-neg_binary64`
790×	`rules-41_binary64`
790×	`rules-43_binary64`
701×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	57	16
2	224	15
3	1128	15
4	3504	15
5	16	15

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

25.9b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	25.9b	(fma.f64 x x (fma.f64 y (+.f64 y y) (*.f64 y y)))
	25.9b	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))

Compiler

Compiled 88 to 36 computations (59.1% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y (+.f64 y y) (*.f64 y y))

series4.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

4.0ms

(fma.f64 y (+.f64 y y) (*.f64 y y))

rewrite112.0ms (3.6%)

Algorithm

2×	batch-egg-rewrite

Rules

527×	`log1p-expm1-u_binary64`
527×	`expm1-log1p-u_binary64`
476×	`fma-neg_binary64`
355×	`fma-def_binary64`
250×	`prod-diff_binary64`

Counts

1 → 38

Calls

1 calls:

111.0ms

(fma.f64 y (+.f64 y y) (*.f64 y y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	11
1	122	10
2	1529	8
3	4954	8
4	4939	8
5	4917	8
0	0	0
1	0	0

simplify13.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

54×	`fma-neg_binary64`
43×	`rules-40_binary64`
43×	`rules-41_binary64`
43×	`rules-42_binary64`
43×	`rules-43_binary64`

Counts

50 → 40

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	84
1	34	84
2	83	84
3	202	84
4	246	84

prune43.0ms (1.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	34	6	40
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	35	7	42

Error

25.8b

Counts

42 → 7

Alt Table

Status	Error	Program
	27.0b	(fma.f64 x x (exp.f64 (log.f64 (*.f64 y (fma.f64 y 2 y)))))
▶	25.9b	(fma.f64 x x (.f64 y (+.f64 y (/.f64 (.f64 y (+.f64 y y)) y))))
	26.1b	(fma.f64 x x (pow.f64 (cbrt.f64 (*.f64 y (fma.f64 y 2 y))) 3))
	38.2b	(fma.f64 x x (pow.f64 (pow.f64 (*.f64 y (fma.f64 y 2 y)) 3) 1/3))
✓	25.9b	(fma.f64 x x (fma.f64 y (+.f64 y y) (*.f64 y y)))
	26.1b	(fma.f64 x x (.f64 (cbrt.f64 (.f64 y (fma.f64 y 2 y))) (pow.f64 (cbrt.f64 (*.f64 y (fma.f64 y 2 y))) 2)))
	25.9b	(fma.f64 x x (pow.f64 (hypot.f64 y (hypot.f64 y y)) 2))

Compiler

Compiled 781 to 398 computations (49% saved)

localize10.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 y (+.f64 y (/.f64 (.f64 y (+.f64 y y)) y)))
✓	20.3b	(/.f64 (*.f64 y (+.f64 y y)) y)

series4.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

2.0ms	(.f64 y (+.f64 y (/.f64 (.f64 y (+.f64 y y)) y)))
2.0ms	(/.f64 (*.f64 y (+.f64 y y)) y)

rewrite73.0ms (2.3%)

Algorithm

2×	batch-egg-rewrite

Rules

998×	`prod-diff_binary64`
859×	`expm1-log1p-u_binary64`
136×	`egg-rr`
83×	`rules-40_binary64`
83×	`rules-42_binary64`

Counts

2 → 136

Calls

2 calls:

70.0ms	(.f64 y (+.f64 y (/.f64 (.f64 y (+.f64 y y)) y)))
70.0ms	(/.f64 (*.f64 y (+.f64 y y)) y)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	23
1	178	20
2	2473	20
3	5906	20
0	0	0
1	0	0

simplify18.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

65×	`fma-neg_binary64`
52×	`rules-11_binary64`
49×	`rules-40_binary64`
49×	`rules-41_binary64`
49×	`rules-42_binary64`

Counts

160 → 139

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	132
1	40	132
2	101	132
3	247	132
4	294	132

prune152.0ms (4.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	134	5	139
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	137	9	146

Error

21.4b

Counts

146 → 9

Alt Table

Status	Error	Program
	38.8b	(fma.f64 x x (.f64 y (+.f64 y (log.f64 (exp.f64 (/.f64 (.f64 y (+.f64 y y)) y))))))
	27.0b	(fma.f64 x x (exp.f64 (log.f64 (*.f64 y (fma.f64 y 2 y)))))
	26.1b	(fma.f64 x x (pow.f64 (cbrt.f64 (*.f64 y (fma.f64 y 2 y))) 3))
	38.2b	(fma.f64 x x (pow.f64 (pow.f64 (*.f64 y (fma.f64 y 2 y)) 3) 1/3))
▶	25.9b	(fma.f64 x x (fabs.f64 (*.f64 y (+.f64 (+.f64 y y) y))))
	26.1b	(fma.f64 x x (+.f64 (fma.f64 (cbrt.f64 (fma.f64 y (/.f64 (+.f64 y y) y) y)) (.f64 y (pow.f64 (cbrt.f64 (fma.f64 y (/.f64 (+.f64 y y) y) y)) 2)) (neg.f64 (.f64 0 y))) (fma.f64 0 y (*.f64 0 y))))
✓	25.9b	(fma.f64 x x (fma.f64 y (+.f64 y y) (*.f64 y y)))
	30.3b	(fma.f64 x x (.f64 y (+.f64 y (exp.f64 (log.f64 (/.f64 (.f64 y (+.f64 y y)) y))))))
	33.0b	(fma.f64 x x (.f64 y (+.f64 y (pow.f64 (pow.f64 (/.f64 (.f64 y (+.f64 y y)) y) 3) 1/3))))

Compiler

Compiled 3633 to 1174 computations (67.7% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 y (+.f64 (+.f64 y y) y))

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(*.f64 y (+.f64 (+.f64 y y) y))

rewrite54.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

628×	`log1p-expm1-u_binary64`
628×	`expm1-log1p-u_binary64`
561×	`prod-diff_binary64`
72×	`egg-rr`
61×	`rules-40_binary64`

Counts

1 → 72

Calls

1 calls:

52.0ms

(*.f64 y (+.f64 (+.f64 y y) y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	10
1	128	10
2	1774	10
3	5114	10
0	0	0
1	0	0

simplify17.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

54×	`fma-neg_binary64`
43×	`rules-40_binary64`
43×	`rules-41_binary64`
43×	`rules-42_binary64`
43×	`rules-43_binary64`

Counts

84 → 74

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	84
1	34	84
2	83	84
3	202	84
4	246	84

prune87.0ms (2.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	74	9	83

Error

21.4b

Counts

83 → 9

Alt Table

Status	Error	Program
	38.8b	(fma.f64 x x (.f64 y (+.f64 y (log.f64 (exp.f64 (/.f64 (.f64 y (+.f64 y y)) y))))))
	27.0b	(fma.f64 x x (exp.f64 (log.f64 (*.f64 y (fma.f64 y 2 y)))))
▶	26.1b	(fma.f64 x x (pow.f64 (cbrt.f64 (*.f64 y (fma.f64 y 2 y))) 3))
	38.2b	(fma.f64 x x (pow.f64 (pow.f64 (*.f64 y (fma.f64 y 2 y)) 3) 1/3))
✓	25.9b	(fma.f64 x x (fabs.f64 (*.f64 y (+.f64 (+.f64 y y) y))))
	26.1b	(fma.f64 x x (fabs.f64 (+.f64 (fma.f64 (cbrt.f64 (+.f64 y (+.f64 y y))) (.f64 y (pow.f64 (cbrt.f64 (+.f64 y (+.f64 y y))) 2)) (neg.f64 (.f64 0 y))) (fma.f64 0 y (*.f64 0 y)))))
✓	25.9b	(fma.f64 x x (fma.f64 y (+.f64 y y) (*.f64 y y)))
	30.3b	(fma.f64 x x (.f64 y (+.f64 y (exp.f64 (log.f64 (/.f64 (.f64 y (+.f64 y y)) y))))))
	33.0b	(fma.f64 x x (.f64 y (+.f64 y (pow.f64 (pow.f64 (/.f64 (.f64 y (+.f64 y y)) y) 3) 1/3))))

Compiler

Compiled 2089 to 801 computations (61.7% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 y (fma.f64 y 2 y))
✓	0.4b	(pow.f64 (cbrt.f64 (*.f64 y (fma.f64 y 2 y))) 3)
✓	21.0b	(cbrt.f64 (*.f64 y (fma.f64 y 2 y)))

series123.0ms (3.9%)

Counts

3 → 36

Calls

3 calls:

83.0ms	(pow.f64 (cbrt.f64 (*.f64 y (fma.f64 y 2 y))) 3)
37.0ms	(cbrt.f64 (*.f64 y (fma.f64 y 2 y)))
3.0ms	(*.f64 y (fma.f64 y 2 y))

rewrite95.0ms (3.1%)

Algorithm

2×	batch-egg-rewrite

Rules

616×	`log1p-expm1-u_binary64`
616×	`expm1-log1p-u_binary64`
510×	`fma-neg_binary64`
447×	`egg-rr`
166×	`prod-diff_binary64`

Counts

3 → 447

Calls

3 calls:

87.0ms	(*.f64 y (fma.f64 y 2 y))
87.0ms	(pow.f64 (cbrt.f64 (*.f64 y (fma.f64 y 2 y))) 3)
87.0ms	(cbrt.f64 (*.f64 y (fma.f64 y 2 y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	26
1	167	23
2	1853	23
3	5092	23
0	0	0
1	0	0

simplify99.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

616×	`rules-40_binary64`
616×	`rules-42_binary64`
598×	`rules-41_binary64`
598×	`rules-43_binary64`
453×	`exp-prod_binary64`

Counts

483 → 268

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	35	680
1	224	616
2	620	464
3	2365	308
4	4040	296
5	4900	296
6	5083	296

prune318.0ms (10.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	263	5	268
Fresh	5	1	6
Picked	0	1	1
Done	0	2	2
Total	268	9	277

Error

21.4b

Counts

277 → 9

Alt Table

Status	Error	Program
	41.9b	(fma.f64 x x (pow.f64 (/.f64 (.f64 y (.f64 y 3)) (+.f64 (pow.f64 (.f64 y (.f64 y 3)) 2/3) (+.f64 0 (.f64 (cbrt.f64 (.f64 y (*.f64 y 3))) 0)))) 3))
	38.8b	(fma.f64 x x (.f64 y (+.f64 y (log.f64 (exp.f64 (/.f64 (.f64 y (+.f64 y y)) y))))))
	27.2b	(fma.f64 x x (.f64 (pow.f64 (pow.f64 (.f64 y (.f64 y 3)) 1/6) 3) (pow.f64 (pow.f64 (.f64 y (*.f64 y 3)) 1/6) 3)))
	27.3b	(fma.f64 x x (pow.f64 (.f64 (cbrt.f64 (cbrt.f64 (.f64 y (.f64 y 3)))) (pow.f64 (pow.f64 (.f64 y (*.f64 y 3)) 2/3) 1/3)) 3))
✓	26.1b	(fma.f64 x x (pow.f64 (cbrt.f64 (*.f64 y (fma.f64 y 2 y))) 3))
✓	25.9b	(fma.f64 x x (fabs.f64 (*.f64 y (+.f64 (+.f64 y y) y))))
	27.1b	(fma.f64 x x (pow.f64 (exp.f64 (.f64 (log.f64 (.f64 y (*.f64 y 3))) 1/3)) 3))
✓	25.9b	(fma.f64 x x (fma.f64 y (+.f64 y y) (*.f64 y y)))
	35.8b	(fma.f64 x x (pow.f64 (exp.f64 (.f64 1/3 (+.f64 (log.f64 3) (.f64 2 (log.f64 y))))) 3))

Compiler

Compiled 6289 to 4365 computations (30.6% saved)

regimes614.0ms (19.7%)

Accuracy

Total 10.6b remaining (99.9%)

Threshold costs 0b (0%)

Counts

72 → 2

Compiler

Compiled 5884 to 3695 computations (37.2% saved)

bsearch15.0ms (0.5%)

Steps

Iters	Range		Point
5	-9.46811994636118e-281	-2.6718720450384123e-281	-2.710148075684743e-281

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	48
1	22	48
2	21	48

end195.0ms (6.3%)

Remove: (sort x y)
Compiler: Compiled 310 to 189 computations (39% saved)

Details

analyze96.0ms (3.1%)

sample888.0ms (28.5%)

simplify58.0ms (1.9%)

prune4.0ms (0.1%)

localize6.0ms (0.2%)

series4.0ms (0.1%)

rewrite112.0ms (3.6%)

simplify13.0ms (0.4%)

prune43.0ms (1.4%)

localize10.0ms (0.3%)

series4.0ms (0.1%)

rewrite73.0ms (2.3%)

simplify18.0ms (0.6%)

prune152.0ms (4.9%)

localize6.0ms (0.2%)

series3.0ms (0.1%)

rewrite54.0ms (1.7%)

simplify17.0ms (0.5%)

prune87.0ms (2.8%)

localize8.0ms (0.2%)

series123.0ms (3.9%)

rewrite95.0ms (3.1%)

simplify99.0ms (3.2%)

prune318.0ms (10.2%)

regimes614.0ms (19.7%)

bsearch15.0ms (0.5%)

simplify2.0ms (0.1%)

end195.0ms (6.3%)

Profiling