Details

analyze1.2s (12.2%)

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
3.1%	71.7%	25.1%	9
4.7%	69.8%	25.5%	10
7%	66.9%	26.1%	11
10.9%	61.5%	27.6%	12
11.1%	47%	41.9%	13
12.8%	44.4%	42.8%	14

Compiler

Compiled 24 to 20 computations (16.7% saved)

sample3.0s (30.8%)

Results

1.7s	10402×	body	128	invalid
1.3s	8256×	body	128	valid

Compiler

Compiled 48 to 40 computations (16.7% saved)

preprocess52.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

1584×	`associate-/l/_binary64`
504×	`associate-l_binary64`
420×	`associate-r_binary64`
375×	`associate-/l*_binary64`
285×	`associate-*l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	182
1	174	161
2	658	140
3	3018	140
4	4048	140
5	4048	140
0	4	4
1	4	4

Stop Event

1×	unsound
1×	node limit

Symmetry

(sort y z)

Compiler

Compiled 23 to 19 computations (17.4% saved)

simplify37.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

854×	`associate-/l/_binary64`
849×	`associate-l_binary64`
777×	`associate-/r/_binary64`
378×	`*-commutative_binary64`
330×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	26
1	40	23
2	123	20
3	502	20
4	2173	20
5	3870	20
6	3929	20
7	3929	20

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (0%)

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

1.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	1.2b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
	1.7b	(.f64 1/3 (acos.f64 (/.f64 (.f64 x (/.f64 (sqrt.f64 t) y)) (*.f64 z 18))))

Compiler

Compiled 116 to 91 computations (21.6% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 3 (/.f64 x (.f64 y 27)))
✓	1.0b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
✓	3.3b	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))
✓	4.1b	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))

series77.0ms (0.8%)

Counts

4 → 144

Calls

39 calls:

4.0ms	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))	t	inf
3.0ms	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))	x	inf
3.0ms	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))	x	-inf
3.0ms	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))	x	0
3.0ms	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))	y	0

rewrite42.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

191×	`add-sqr-sqrt_binary64`
180×	`log1p-expm1-u_binary64`
180×	`expm1-log1p-u_binary64`
179×	`add-cbrt-cube_binary64`
178×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	73
1	398	61

Stop Event

1×	node limit

Counts

4 → 126

simplify84.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

112×	`associate-/l*_binary64`
61×	`associate-*r/_binary64`
60×	`associate-*l/_binary64`
39×	`associate-/r/_binary64`
38×	`times-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	2028
1	32	2028
2	82	2028
3	212	2028
4	368	2028
5	503	2028
6	513	2028

Stop Event

1×

saturated

Counts

270 → 134

prune123.0ms (1.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	131	3	134
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	133	3	136

Error

0.0b

Counts

136 → 3

Alt Table

Status	Error	Program
	1.5b	(log.f64 (pow.f64 (exp.f64 1/3) (acos.f64 (.f64 (.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54)))))
	1.2b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (*.f64 (/.f64 1/18 y) (/.f64 x z)) (sqrt.f64 t))))
▶	0.5b	(-.f64 (exp.f64 (log1p.f64 (.f64 1/3 (acos.f64 (.f64 (*.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54)))))) 1)

Compiler

Compiled 2843 to 1971 computations (30.7% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (sqrt.f64 t) (/.f64 3 z))
✓	1.0b	(log1p.f64 (.f64 1/3 (acos.f64 (.f64 (*.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54)))))
✓	1.0b	(.f64 1/3 (acos.f64 (.f64 (*.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54))))
✓	5.7b	(.f64 (.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54))

series1.7s (17.3%)

Counts

4 → 144

Calls

42 calls:

165.0ms	(log1p.f64 (.f64 1/3 (acos.f64 (.f64 (*.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54)))))	x	inf
151.0ms	(log1p.f64 (.f64 1/3 (acos.f64 (.f64 (*.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54)))))	x	-inf
148.0ms	(log1p.f64 (.f64 1/3 (acos.f64 (.f64 (*.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54)))))	t	inf
135.0ms	(log1p.f64 (.f64 1/3 (acos.f64 (.f64 (*.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54)))))	y	-inf
133.0ms	(log1p.f64 (.f64 1/3 (acos.f64 (.f64 (*.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54)))))	x	0

rewrite71.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

212×	`prod-diff_binary64`
183×	`add-sqr-sqrt_binary64`
173×	`expm1-log1p-u_binary64`
172×	`log1p-expm1-u_binary64`
171×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	75
1	370	75
2	4746	75

Stop Event

1×	node limit

Counts

4 → 86

simplify126.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

233×	`associate-/l*_binary64`
156×	`times-frac_binary64`
128×	`associate-*l/_binary64`
126×	`associate-/l/_binary64`
118×	`associate-/r/_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	2700
1	41	2664
2	92	2664
3	264	2664
4	594	2664
5	1011	2664
6	1287	2664
7	1318	2664
8	1319	2664
9	1319	2664

Stop Event

1×

saturated

Counts

230 → 94

prune94.0ms (1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	93	4	97

Error

Counts

97 → 4

Alt Table

Status	Error	Program
▶	0.8b	(-.f64 (exp.f64 (log1p.f64 (.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))))))) 1)
	1.5b	(log.f64 (pow.f64 (exp.f64 1/3) (acos.f64 (.f64 (.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54)))))
	1.2b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (*.f64 (/.f64 1/18 y) (/.f64 x z)) (sqrt.f64 t))))
✓	0.5b	(-.f64 (exp.f64 (log1p.f64 (.f64 1/3 (acos.f64 (.f64 (*.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54)))))) 1)

Compiler

Compiled 2182 to 1563 computations (28.4% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))
✓	1.0b	(log1p.f64 (.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))))))
✓	3.3b	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
✓	7.5b	(/.f64 x (*.f64 y z))

series1.6s (16.7%)

Counts

4 → 48

Calls

45 calls:

147.0ms	(log1p.f64 (.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))))))	t	inf
136.0ms	(log1p.f64 (.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))))))	x	-inf
135.0ms	(log1p.f64 (.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))))))	x	inf
133.0ms	(log1p.f64 (.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))))))	t	-inf
133.0ms	(log1p.f64 (.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))))))	y	inf

rewrite71.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

278×	`expm1-udef_binary64`
278×	`log1p-udef_binary64`
203×	`prod-diff_binary64`
155×	`add-sqr-sqrt_binary64`
146×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	61
1	312	61
2	3942	61

Stop Event

1×	node limit

Counts

4 → 98

simplify45.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

107×	`associate-/l*_binary64`
60×	`associate-*r/_binary64`
57×	`associate-*l/_binary64`
47×	`associate-/l/_binary64`
44×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	1056
1	31	1056
2	66	1056
3	173	1056
4	319	1056
5	496	1056
6	519	1056

Stop Event

1×

saturated

Counts

146 → 100

prune96.0ms (1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	100	4	104

Error

Counts

104 → 4

Alt Table

Status	Error	Program
✓	0.8b	(-.f64 (exp.f64 (log1p.f64 (.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))))))) 1)
	1.5b	(log.f64 (pow.f64 (exp.f64 1/3) (acos.f64 (.f64 (.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54)))))
▶	1.2b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (*.f64 (/.f64 1/18 y) (/.f64 x z)) (sqrt.f64 t))))
✓	0.5b	(-.f64 (exp.f64 (log1p.f64 (.f64 1/3 (acos.f64 (.f64 (*.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54)))))) 1)

Compiler

Compiled 2224 to 1416 computations (36.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 1/18 y)
✓	1.0b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (*.f64 (/.f64 1/18 y) (/.f64 x z)) (sqrt.f64 t))))
✓	3.3b	(.f64 (.f64 (/.f64 1/18 y) (/.f64 x z)) (sqrt.f64 t))
✓	4.5b	(*.f64 (/.f64 1/18 y) (/.f64 x z))

series74.0ms (0.8%)

Counts

4 → 120

Calls

36 calls:

5.0ms	(*.f64 (/.f64 1/18 y) (/.f64 x z))	z	0
5.0ms	(.f64 (.f64 (/.f64 1/18 y) (/.f64 x z)) (sqrt.f64 t))	z	inf
3.0ms	(.f64 (.f64 (/.f64 1/18 y) (/.f64 x z)) (sqrt.f64 t))	x	-inf
3.0ms	(.f64 (.f64 (/.f64 1/18 y) (/.f64 x z)) (sqrt.f64 t))	x	inf
3.0ms	(.f64 (.f64 (/.f64 1/18 y) (/.f64 x z)) (sqrt.f64 t))	x	0

rewrite68.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

294×	`expm1-udef_binary64`
294×	`log1p-udef_binary64`
166×	`add-sqr-sqrt_binary64`
155×	`add-cbrt-cube_binary64`
155×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	49
1	339	49
2	4228	49

Stop Event

1×	node limit

Counts

4 → 113

simplify61.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

117×	`associate-/l*_binary64`
59×	`associate-*r/_binary64`
59×	`associate-*l/_binary64`
38×	`associate-/r/_binary64`
38×	`times-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	1860
1	27	1860
2	73	1860
3	199	1860
4	355	1860
5	496	1860
6	506	1860

Stop Event

1×

saturated

Counts

233 → 119

prune54.0ms (0.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	119	4	123

Error

Counts

123 → 4

Alt Table

Status	Error	Program
✓	0.8b	(-.f64 (exp.f64 (log1p.f64 (.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))))))) 1)
	1.5b	(log.f64 (pow.f64 (exp.f64 1/3) (acos.f64 (.f64 (.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54)))))
✓	1.2b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (*.f64 (/.f64 1/18 y) (/.f64 x z)) (sqrt.f64 t))))
✓	0.5b	(-.f64 (exp.f64 (log1p.f64 (.f64 1/3 (acos.f64 (.f64 (*.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54)))))) 1)

Compiler

Compiled 2114 to 1344 computations (36.4% saved)

regimes792.0ms (8.1%)

Accuracy

Total 0.3b remaining (98.2%)

Threshold costs 0.3b (98.2%)

Counts

61 → 1

Compiler

Compiled 16558 to 13308 computations (19.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	27
1	26	27
2	27	27

Stop Event

1×

saturated

end232.0ms (2.4%)

Stop Event

1×

fuel

Compiler

Compiled 168 to 136 computations (19% saved)

Details

analyze1.2s (12.2%)

sample3.0s (30.8%)

preprocess52.0ms (0.5%)

simplify37.0ms (0.4%)

prune4.0ms (0%)

localize14.0ms (0.1%)

series77.0ms (0.8%)

rewrite42.0ms (0.4%)

simplify84.0ms (0.9%)

prune123.0ms (1.3%)

localize14.0ms (0.1%)

series1.7s (17.3%)

rewrite71.0ms (0.7%)

simplify126.0ms (1.3%)

prune94.0ms (1%)

localize13.0ms (0.1%)

series1.6s (16.7%)

rewrite71.0ms (0.7%)

simplify45.0ms (0.5%)

prune96.0ms (1%)

localize11.0ms (0.1%)

series74.0ms (0.8%)

rewrite68.0ms (0.7%)

simplify61.0ms (0.6%)

prune54.0ms (0.5%)

regimes792.0ms (8.1%)

simplify2.0ms (0%)

end232.0ms (2.4%)

Profiling