Details

analyze718.0ms (12.8%)

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
15.6%	84.2%	0.2%	8
28.1%	71.7%	0.2%	9
37.4%	62.4%	0.2%	10
41.7%	58.1%	0.2%	11
53%	46.8%	0.2%	12
64.1%	35.6%	0.3%	13
66.7%	32.8%	0.5%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample2.0s (34.8%)

Symmetry

(sort y t)

Results

1.6s	8256×	body	128	valid
184.0ms	390×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify109.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

961×	`fma-neg_binary64`
750×	`fma-def_binary64`
246×	`distribute-rgt-in_binary64`
204×	`unsub-neg_binary64`
135×	`cancel-sign-sub-inv_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	35	13
3	88	13
4	231	13
5	568	13
6	1029	13
7	1474	13
8	1787	13
9	1744	13
10	1744	13
11	1905	13
12	1905	13
13	1862	13

prune3.0ms (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

6.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	6.1b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

Compiler

Compiled 39 to 24 computations (38.5% saved)

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 y z) (-.f64 t z))
✓	6.1b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

series186.0ms (3.3%)

Counts

2 → 84

Calls

2 calls:

173.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))
13.0ms	(*.f64 (-.f64 y z) (-.f64 t z))

rewrite70.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

745×	`prod-diff_binary64`
200×	`expm1-udef_binary64`
200×	`log1p-udef_binary64`
109×	`add-sqr-sqrt_binary64`
104×	`log1p-expm1-u_binary64`

Counts

2 → 77

Calls

2 calls:

68.0ms	(*.f64 (-.f64 y z) (-.f64 t z))
68.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	205	23
2	2991	23
3	5071	23
0	0	0
1	0	0

simplify91.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

487×	`times-frac_binary64`
395×	`associate-/l*_binary64`
351×	`associate-/r*_binary64`
233×	`associate-+r+_binary64`
183×	`+-commutative_binary64`

Counts

161 → 145

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	257	3781
1	945	3540
2	4609	3537
3	4982	3537

prune130.0ms (2.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	134	11	145
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	135	11	146

Error

0.0b

Counts

146 → 11

Alt Table

Status	Error	Program
	7.1b	(/.f64 x (+.f64 (.f64 t y) (.f64 z (-.f64 z (+.f64 t y)))))
	30.8b	(*.f64 (/.f64 (sqrt.f64 x) (-.f64 y z)) (/.f64 (sqrt.f64 x) (-.f64 t z)))
	6.2b	(.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 t z))))
	6.5b	(pow.f64 (/.f64 (*.f64 (-.f64 y z) (-.f64 t z)) x) -1)
	18.5b	(.f64 (/.f64 (cbrt.f64 (.f64 x x)) (-.f64 t z)) (/.f64 (cbrt.f64 x) (-.f64 y z)))
	18.9b	(.f64 (/.f64 (cbrt.f64 (.f64 x x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))
	23.3b	(/.f64 x (cbrt.f64 (pow.f64 (*.f64 (-.f64 y z) (-.f64 t z)) 3)))
▶	2.4b	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
	2.4b	(*.f64 (/.f64 x (-.f64 y z)) (/.f64 1 (-.f64 t z)))
	33.7b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (/.f64 1 (*.f64 (-.f64 y z) (-.f64 t z)))))
	17.9b	(/.f64 x (/.f64 (.f64 (-.f64 (.f64 t t) (*.f64 z z)) (-.f64 y z)) (+.f64 z t)))

Compiler

Compiled 4472 to 1915 computations (57.2% saved)

localize17.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (-.f64 t z))
✓	0.0b	(/.f64 1 (-.f64 y z))
✓	2.3b	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))

series147.0ms (2.6%)

Counts

3 → 96

Calls

3 calls:

120.0ms	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
16.0ms	(/.f64 x (-.f64 t z))
10.0ms	(/.f64 1 (-.f64 y z))

rewrite80.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

745×	`prod-diff_binary64`
228×	`log1p-udef_binary64`
127×	`add-sqr-sqrt_binary64`
120×	`log1p-expm1-u_binary64`
120×	`expm1-log1p-u_binary64`

Counts

3 → 111

Calls

3 calls:

78.0ms	(/.f64 x (-.f64 t z))
78.0ms	(/.f64 1 (-.f64 y z))
78.0ms	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	27
1	247	27
2	3464	27
3	5287	27
0	0	0
1	0	0

simplify101.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

503×	`times-frac_binary64`
420×	`associate-/l*_binary64`
360×	`associate-/r*_binary64`
267×	`associate-+r+_binary64`
217×	`+-commutative_binary64`

Counts

207 → 192

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	298	4326
1	1040	4159
2	4906	4159
3	5029	4159

prune179.0ms (3.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	185	7	192
Fresh	8	2	10
Picked	1	0	1
Done	0	0	0
Total	194	9	203

Error

Counts

203 → 9

Alt Table

Status	Error	Program
	23.3b	(/.f64 x (cbrt.f64 (pow.f64 (*.f64 (-.f64 y z) (-.f64 t z)) 3)))
	2.9b	(*.f64 (/.f64 1 (-.f64 y z)) (pow.f64 (cbrt.f64 (/.f64 x (-.f64 t z))) 3))
▶	2.3b	(/.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))
	19.8b	(pow.f64 (sqrt.f64 (/.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))) 2)
	2.4b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
	6.1b	(/.f64 x (/.f64 (-.f64 y z) (/.f64 1 (-.f64 t z))))
	25.1b	(*.f64 (/.f64 1 (-.f64 y z)) (pow.f64 (sqrt.f64 (/.f64 x (-.f64 t z))) 2))
	2.4b	(*.f64 (/.f64 x (-.f64 y z)) (/.f64 1 (-.f64 t z)))
	6.1b	(/.f64 x (*.f64 (-.f64 t z) (-.f64 y z)))

Compiler

Compiled 5216 to 2327 computations (55.4% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(/.f64 x (-.f64 t z))
✓	2.2b	(/.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))

series124.0ms (2.2%)

Counts

1 → 48

Calls

1 calls:

124.0ms

(/.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))

rewrite63.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

754×	`prod-diff_binary64`
208×	`log1p-udef_binary64`
113×	`add-sqr-sqrt_binary64`
108×	`log1p-expm1-u_binary64`
108×	`expm1-log1p-u_binary64`

Counts

1 → 42

Calls

1 calls:

62.0ms

(/.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	211	13
2	3187	13
3	5034	13
0	0	0
1	0	0

simplify84.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

487×	`times-frac_binary64`
395×	`associate-/l*_binary64`
351×	`associate-/r*_binary64`
233×	`associate-+r+_binary64`
191×	`unswap-sqr_binary64`

Counts

90 → 94

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	253	3228
1	927	3073
2	4558	3070
3	5280	3070

prune171.0ms (3.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	144	9	153

Error

Counts

153 → 9

Alt Table

Status	Error	Program
	25.1b	(/.f64 (pow.f64 (sqrt.f64 (/.f64 x (-.f64 t z))) 2) (-.f64 y z))
▶	2.4b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
	23.3b	(/.f64 x (cbrt.f64 (pow.f64 (*.f64 (-.f64 y z) (-.f64 t z)) 3)))
	2.9b	(*.f64 (/.f64 1 (-.f64 y z)) (pow.f64 (cbrt.f64 (/.f64 x (-.f64 t z))) 3))
✓	2.3b	(/.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))
	19.8b	(pow.f64 (sqrt.f64 (/.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))) 2)
	6.1b	(/.f64 x (/.f64 (-.f64 y z) (/.f64 1 (-.f64 t z))))
	2.4b	(*.f64 (/.f64 x (-.f64 y z)) (/.f64 1 (-.f64 t z)))
	6.1b	(/.f64 x (*.f64 (-.f64 t z) (-.f64 y z)))

Compiler

Compiled 4431 to 1930 computations (56.4% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (-.f64 y z))
✓	2.3b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))

series141.0ms (2.5%)

Counts

2 → 72

Calls

2 calls:

119.0ms	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
22.0ms	(/.f64 x (-.f64 y z))

rewrite67.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

754×	`prod-diff_binary64`
208×	`log1p-udef_binary64`
113×	`add-sqr-sqrt_binary64`
108×	`log1p-expm1-u_binary64`
108×	`expm1-log1p-u_binary64`

Counts

2 → 77

Calls

2 calls:

65.0ms	(/.f64 x (-.f64 y z))
65.0ms	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	211	20
2	3187	20
3	5034	20
0	0	0
1	0	0

simplify91.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

497×	`times-frac_binary64`
416×	`associate-/l*_binary64`
355×	`associate-/r*_binary64`
251×	`associate-+r+_binary64`
200×	`+-commutative_binary64`

Counts

149 → 144

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	275	3834
1	989	3679
2	4760	3676
3	5024	3676

prune126.0ms (2.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	144	9	153

Error

Counts

153 → 9

Alt Table

Status	Error	Program
	25.1b	(/.f64 (pow.f64 (sqrt.f64 (/.f64 x (-.f64 t z))) 2) (-.f64 y z))
✓	2.4b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
	23.3b	(/.f64 x (cbrt.f64 (pow.f64 (*.f64 (-.f64 y z) (-.f64 t z)) 3)))
	2.9b	(*.f64 (/.f64 1 (-.f64 y z)) (pow.f64 (cbrt.f64 (/.f64 x (-.f64 t z))) 3))
✓	2.3b	(/.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))
	19.8b	(pow.f64 (sqrt.f64 (/.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))) 2)
	6.1b	(/.f64 x (/.f64 (-.f64 y z) (/.f64 1 (-.f64 t z))))
	2.4b	(*.f64 (/.f64 x (-.f64 y z)) (/.f64 1 (-.f64 t z)))
	6.1b	(/.f64 x (*.f64 (-.f64 t z) (-.f64 y z)))

Compiler

Compiled 4309 to 1847 computations (57.1% saved)

regimes675.0ms (12%)

Accuracy

Total 1.9b remaining (99%)

Threshold costs 0b (0%)

Counts

67 → 2

Compiler

Compiled 6864 to 4395 computations (36% saved)

bsearch11.0ms (0.2%)

Steps

Iters	Range		Point
4	-2.4448908191986088e-50	-1.3303697736333628e-50	-2.0212189911353896e-50

Compiler

Compiled 5 to 4 computations (20% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	32
1	18	32
2	24	32
3	26	32
4	27	32
5	27	32

end245.0ms (4.4%)

Compiler: Compiled 239 to 142 computations (40.6% saved)

Details

analyze718.0ms (12.8%)

sample2.0s (34.8%)

simplify109.0ms (1.9%)

prune3.0ms (0.1%)

localize11.0ms (0.2%)

series186.0ms (3.3%)

rewrite70.0ms (1.2%)

simplify91.0ms (1.6%)

prune130.0ms (2.3%)

localize17.0ms (0.3%)

series147.0ms (2.6%)

rewrite80.0ms (1.4%)

simplify101.0ms (1.8%)

prune179.0ms (3.2%)

localize6.0ms (0.1%)

series124.0ms (2.2%)

rewrite63.0ms (1.1%)

simplify84.0ms (1.5%)

prune171.0ms (3.1%)

localize6.0ms (0.1%)

series141.0ms (2.5%)

rewrite67.0ms (1.2%)

simplify91.0ms (1.6%)

prune126.0ms (2.2%)

regimes675.0ms (12%)

bsearch11.0ms (0.2%)

simplify3.0ms (0.1%)

end245.0ms (4.4%)

Profiling