Details

analyze960.0ms (22%)

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
12.5%	87.3%	0.2%	8
18.7%	81.1%	0.2%	9
22.6%	77.2%	0.2%	10
25%	74.9%	0.2%	11
39.4%	60.4%	0.2%	12
46.5%	53.2%	0.3%	13
48%	51.4%	0.6%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.2s (26.4%)

Results

1.0s	8256×	body	128	valid
105.0ms	741×	body	128	invalid

Compiler

Compiled 32 to 22 computations (31.3% saved)

preprocess48.0ms (1.1%)

Algorithm

2×	egg-herbie

Rules

783×	`div-sub_binary64`
390×	`distribute-rgt-in_binary64`
289×	`distribute-lft-in_binary64`
270×	`associate-/l*_binary64`
208×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	91
1	111	91
2	291	91
3	606	91
4	1171	91
5	2594	91
6	4621	91
0	4	4

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify48.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1016×	`fma-neg_binary64`
470×	`fma-def_binary64`
265×	`associate-/l*_binary64`
257×	`cancel-sign-sub-inv_binary64`
254×	`div-sub_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	24	13
2	57	13
3	114	13
4	218	13
5	414	13
6	805	13
7	1396	13
8	2763	13
9	4227	13
10	4909	13

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	6.7b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 t z)))
▶	4.7b	(*.f64 2 (/.f64 (/.f64 x z) (-.f64 y t)))

Compiler

Compiled 80 to 53 computations (33.8% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 2 (/.f64 (/.f64 x z) (-.f64 y t)))
✓	4.5b	(/.f64 (/.f64 x z) (-.f64 y t))

series66.0ms (1.5%)

Counts

2 → 96

Calls

24 calls:

8.0ms	(/.f64 (/.f64 x z) (-.f64 y t))	x	-inf
5.0ms	(*.f64 2 (/.f64 (/.f64 x z) (-.f64 y t)))	z	0
5.0ms	(*.f64 2 (/.f64 (/.f64 x z) (-.f64 y t)))	x	-inf
5.0ms	(*.f64 2 (/.f64 (/.f64 x z) (-.f64 y t)))	x	inf
4.0ms	(/.f64 (/.f64 x z) (-.f64 y t))	x	inf

rewrite52.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

395×	`prod-diff_binary64`
213×	`expm1-udef_binary64`
213×	`log1p-udef_binary64`
188×	`fma-def_binary64`
117×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	225	23
2	3270	23

Stop Event

1×	node limit

Counts

2 → 66

simplify45.0ms (1%)

Algorithm

1×	egg-herbie

Rules

812×	`times-frac_binary64`
508×	`associate-/l*_binary64`
457×	`fma-def_binary64`
358×	`associate-/r*_binary64`
265×	`associate-*l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	77	2208
1	270	2010
2	1116	1839

Stop Event

1×	node limit

Counts

162 → 103

prune105.0ms (2.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	96	7	103
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	97	8	105

Error

0.0b

Counts

105 → 8

Alt Table

Status	Error	Program
▶	4.8b	(/.f64 2 (*.f64 (-.f64 y t) (/.f64 z x)))
	5.1b	(.f64 2 (.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (-.f64 y t)) (/.f64 (cbrt.f64 x) z)))
	6.7b	(pow.f64 (cbrt.f64 (.f64 (/.f64 x (.f64 z (-.f64 y t))) 2)) 3)
✓	4.7b	(*.f64 2 (/.f64 (/.f64 x z) (-.f64 y t)))
	5.8b	(.f64 2 (.f64 (/.f64 x 1) (/.f64 (/.f64 1 z) (-.f64 y t))))
	29.4b	(.f64 2 (.f64 (sqrt.f64 (/.f64 x z)) (*.f64 (sqrt.f64 (/.f64 x z)) (/.f64 1 (-.f64 y t)))))
	29.1b	(.f64 (/.f64 x z) (-.f64 (/.f64 -2 t) (.f64 2 (/.f64 y (*.f64 t t)))))
	5.9b	(/.f64 (.f64 x 2) (.f64 z (-.f64 y t)))

Compiler

Compiled 1926 to 904 computations (53.1% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.7b	(/.f64 2 (*.f64 (-.f64 y t) (/.f64 z x)))
✓	4.1b	(*.f64 (-.f64 y t) (/.f64 z x))

series70.0ms (1.6%)

Counts

2 → 96

Calls

24 calls:

18.0ms	(/.f64 2 (*.f64 (-.f64 y t) (/.f64 z x)))	z	-inf
7.0ms	(/.f64 2 (*.f64 (-.f64 y t) (/.f64 z x)))	y	0
5.0ms	(/.f64 2 (*.f64 (-.f64 y t) (/.f64 z x)))	x	-inf
5.0ms	(/.f64 2 (*.f64 (-.f64 y t) (/.f64 z x)))	x	inf
3.0ms	(/.f64 2 (*.f64 (-.f64 y t) (/.f64 z x)))	x	0

rewrite51.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

386×	`prod-diff_binary64`
212×	`expm1-udef_binary64`
212×	`log1p-udef_binary64`
190×	`fma-def_binary64`
117×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	226	23
2	3217	23

Stop Event

1×	node limit

Counts

2 → 71

simplify50.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

806×	`times-frac_binary64`
511×	`associate-/l*_binary64`
351×	`fma-def_binary64`
344×	`associate-/r*_binary64`
236×	`associate-*l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	74	1658
1	258	1586
2	1014	1508

Stop Event

1×	node limit

Counts

167 → 98

prune84.0ms (1.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	96	2	98
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	98	8	106

Error

0.0b

Counts

106 → 8

Alt Table

Status	Error	Program
	5.8b	(*.f64 (/.f64 (/.f64 2 (-.f64 y t)) z) x)
	29.4b	(.f64 2 (.f64 (sqrt.f64 (/.f64 x z)) (*.f64 (sqrt.f64 (/.f64 x z)) (/.f64 1 (-.f64 y t)))))
	6.7b	(pow.f64 (cbrt.f64 (.f64 (/.f64 x (.f64 z (-.f64 y t))) 2)) 3)
✓	4.7b	(*.f64 2 (/.f64 (/.f64 x z) (-.f64 y t)))
	5.8b	(.f64 2 (.f64 (/.f64 x 1) (/.f64 (/.f64 1 z) (-.f64 y t))))
✓	4.8b	(/.f64 2 (*.f64 (-.f64 y t) (/.f64 z x)))
▶	4.8b	(*.f64 (/.f64 2 (-.f64 y t)) (/.f64 x z))
	5.9b	(/.f64 (.f64 x 2) (.f64 z (-.f64 y t)))

Compiler

Compiled 1698 to 787 computations (53.7% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 2 (-.f64 y t))
✓	4.6b	(*.f64 (/.f64 2 (-.f64 y t)) (/.f64 x z))

series43.0ms (1%)

Counts

2 → 72

Calls

18 calls:

5.0ms	(*.f64 (/.f64 2 (-.f64 y t)) (/.f64 x z))	x	-inf
5.0ms	(*.f64 (/.f64 2 (-.f64 y t)) (/.f64 x z))	x	inf
4.0ms	(*.f64 (/.f64 2 (-.f64 y t)) (/.f64 x z))	t	inf
3.0ms	(*.f64 (/.f64 2 (-.f64 y t)) (/.f64 x z))	z	0
3.0ms	(*.f64 (/.f64 2 (-.f64 y t)) (/.f64 x z))	x	0

rewrite54.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

386×	`prod-diff_binary64`
216×	`expm1-udef_binary64`
216×	`log1p-udef_binary64`
191×	`fma-def_binary64`
119×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	229	20
2	3310	20

Stop Event

1×	node limit

Counts

2 → 78

simplify42.0ms (1%)

Algorithm

1×	egg-herbie

Rules

884×	`times-frac_binary64`
566×	`fma-def_binary64`
561×	`associate-/l*_binary64`
383×	`associate-/r*_binary64`
275×	`associate-*l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	98	1731
1	334	1626
2	1284	1479

Stop Event

1×	node limit

Counts

150 → 111

prune94.0ms (2.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	111	8	119

Error

0.0b

Counts

119 → 8

Alt Table

Status	Error	Program
	5.8b	(*.f64 (/.f64 (/.f64 2 (-.f64 y t)) z) x)
	29.4b	(.f64 2 (.f64 (sqrt.f64 (/.f64 x z)) (*.f64 (sqrt.f64 (/.f64 x z)) (/.f64 1 (-.f64 y t)))))
	6.7b	(pow.f64 (cbrt.f64 (.f64 (/.f64 x (.f64 z (-.f64 y t))) 2)) 3)
✓	4.7b	(*.f64 2 (/.f64 (/.f64 x z) (-.f64 y t)))
▶	5.8b	(.f64 2 (.f64 (/.f64 x 1) (/.f64 (/.f64 1 z) (-.f64 y t))))
✓	4.8b	(/.f64 2 (*.f64 (-.f64 y t) (/.f64 z x)))
✓	4.8b	(*.f64 (/.f64 2 (-.f64 y t)) (/.f64 x z))
	5.9b	(/.f64 (.f64 x 2) (.f64 z (-.f64 y t)))

Compiler

Compiled 1832 to 942 computations (48.6% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (.f64 (/.f64 x 1) (/.f64 (/.f64 1 z) (-.f64 y t))))
✓	0.2b	(/.f64 (/.f64 1 z) (-.f64 y t))
✓	5.7b	(*.f64 (/.f64 x 1) (/.f64 (/.f64 1 z) (-.f64 y t)))

series85.0ms (1.9%)

Counts

3 → 132

Calls

33 calls:

7.0ms	(*.f64 (/.f64 x 1) (/.f64 (/.f64 1 z) (-.f64 y t)))	x	0
6.0ms	(*.f64 (/.f64 x 1) (/.f64 (/.f64 1 z) (-.f64 y t)))	z	-inf
5.0ms	(.f64 2 (.f64 (/.f64 x 1) (/.f64 (/.f64 1 z) (-.f64 y t))))	x	0
5.0ms	(.f64 2 (.f64 (/.f64 x 1) (/.f64 (/.f64 1 z) (-.f64 y t))))	x	-inf
5.0ms	(*.f64 (/.f64 x 1) (/.f64 (/.f64 1 z) (-.f64 y t)))	x	-inf

rewrite60.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

383×	`prod-diff_binary64`
233×	`expm1-udef_binary64`
233×	`log1p-udef_binary64`
133×	`add-sqr-sqrt_binary64`
126×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	39
1	291	33
2	3720	33

Stop Event

1×	node limit

Counts

3 → 99

simplify71.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

876×	`times-frac_binary64`
578×	`associate-/l*_binary64`
537×	`fma-def_binary64`
410×	`associate-/r*_binary64`
99×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	103	3000
1	343	2784
2	1339	2583

Stop Event

1×	node limit

Counts

231 → 151

prune126.0ms (2.9%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	149	2	151
Fresh	2	2	4
Picked	0	1	1
Done	0	3	3
Total	151	8	159

Error

Counts

159 → 8

Alt Table

Status	Error	Program
✓	4.8b	(*.f64 (/.f64 2 (-.f64 y t)) (/.f64 x z))
	6.1b	(.f64 2 (/.f64 (/.f64 1 (.f64 z (-.f64 y t))) (/.f64 1 x)))
	5.9b	(/.f64 (.f64 x 2) (.f64 z (-.f64 y t)))
	35.6b	(.f64 2 (.f64 (/.f64 x 1) (pow.f64 (/.f64 1 (sqrt.f64 (*.f64 z (-.f64 y t)))) 2)))
✓	5.8b	(.f64 2 (.f64 (/.f64 x 1) (/.f64 (/.f64 1 z) (-.f64 y t))))
✓	4.8b	(/.f64 2 (*.f64 (-.f64 y t) (/.f64 z x)))
	29.4b	(.f64 2 (.f64 (sqrt.f64 (/.f64 x z)) (*.f64 (sqrt.f64 (/.f64 x z)) (/.f64 1 (-.f64 y t)))))
✓	4.7b	(*.f64 2 (/.f64 (/.f64 x z) (-.f64 y t)))

Compiler

Compiled 2742 to 1438 computations (47.6% saved)

regimes912.0ms (20.9%)

Accuracy

Total 1.4b remaining (98.9%)

Threshold costs 0b (0%)

Counts

88 → 3

Compiler

Compiled 9765 to 7082 computations (27.5% saved)

bsearch2.0ms (0.1%)

Algorithm

2×	left-value

Calls

2 calls:

0.0ms	(-.f64 (.f64 y z) (.f64 t z))
0.0ms	(-.f64 (.f64 y z) (.f64 t z))

Steps

Iters	Point		Range
1.8358957548390894e+154	∈ [	1.8358957548390894e+154	,	5.681114305123988e+157	]
#hash((type . real) (value . -inf))	∈ [	#hash((type . real) (value . -inf))	,	-2.017558153009471e+301	]

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	69
1	37	69
2	50	69
3	56	69
4	60	69
5	61	69

Stop Event

1×

saturated

end103.0ms (2.4%)

Stop Event

1×

fuel

Compiler

Compiled 229 to 143 computations (37.6% saved)

Details

analyze960.0ms (22%)

sample1.2s (26.4%)

preprocess48.0ms (1.1%)

simplify48.0ms (1.1%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series66.0ms (1.5%)

rewrite52.0ms (1.2%)

simplify45.0ms (1%)

prune105.0ms (2.4%)

localize9.0ms (0.2%)

series70.0ms (1.6%)

rewrite51.0ms (1.2%)

simplify50.0ms (1.2%)

prune84.0ms (1.9%)

localize8.0ms (0.2%)

series43.0ms (1%)

rewrite54.0ms (1.2%)

simplify42.0ms (1%)

prune94.0ms (2.2%)

localize8.0ms (0.2%)

series85.0ms (1.9%)

rewrite60.0ms (1.4%)

simplify71.0ms (1.6%)

prune126.0ms (2.9%)

regimes912.0ms (20.9%)

bsearch2.0ms (0.1%)

simplify4.0ms (0.1%)

end103.0ms (2.4%)

Profiling