Details

analyze1.2s (15.8%)

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
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)

sample3.1s (40.3%)

Symmetry

(sort y z)

Results

1.7s	10685×	body	128	invalid
1.3s	8256×	body	128	valid

Compiler

Compiled 71 to 59 computations (16.9% saved)

simplify36.0ms (0.5%)

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 (0.1%)

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

1.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	1.1b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
	2.2b	(.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)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.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))))
✓	4.0b	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))
✓	5.6b	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))

series90.0ms (1.2%)

Counts

4 → 144

Calls

4 calls:

41.0ms	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))
21.0ms	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
18.0ms	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))
9.0ms	(/.f64 x (*.f64 y 27))

rewrite45.0ms (0.6%)

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	70
1	398	61

Stop Event

1×	node limit

Counts

4 → 138

Calls

4 calls:

42.0ms	(/.f64 x (*.f64 y 27))
42.0ms	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
42.0ms	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))
42.0ms	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))

simplify68.0ms (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

282 → 145

prune119.0ms (1.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	141	4	145
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	143	4	147

Error

0.0b

Counts

147 → 4

Alt Table

Status	Error	Program
▶	1.2b	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))
	2.4b	(log.f64 (pow.f64 (exp.f64 1/3) (acos.f64 (.f64 (.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54)))))
	2.5b	(pow.f64 (cbrt.f64 (.f64 1/3 (acos.f64 (.f64 (*.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54))))) 3)
	1.5b	(-.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 3243 to 2280 computations (29.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))
✓	1.0b	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))
✓	4.0b	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
✓	5.4b	(/.f64 x (*.f64 y z))

series108.0ms (1.4%)

Counts

4 → 0

Calls

4 calls:

37.0ms	(.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))
33.0ms	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
23.0ms	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))
15.0ms	(/.f64 x (*.f64 y z))

rewrite61.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

263×	`expm1-udef_binary64`
263×	`log1p-udef_binary64`
233×	`log-pow_binary64`
147×	`add-sqr-sqrt_binary64`
137×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	54
1	294	54
2	3750	54

Stop Event

1×	node limit

Counts

4 → 97

Calls

4 calls:

60.0ms	(.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))
60.0ms	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))
60.0ms	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
60.0ms	(/.f64 x (*.f64 y z))

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

97 → 97

prune42.0ms (0.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	94	3	97
Fresh	3	0	3
Picked	0	1	1
Done	0	0	0
Total	97	4	101

Error

0.0b

Counts

101 → 4

Alt Table

Status	Error	Program
✓	1.2b	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))
	1.1b	(sqrt.f64 (.f64 (pow.f64 (acos.f64 (.f64 (/.f64 (/.f64 x y) z) (*.f64 (sqrt.f64 t) 1/18))) 2) 1/9))
	1.1b	(pow.f64 (cbrt.f64 (.f64 1/3 (acos.f64 (.f64 (/.f64 (/.f64 x y) z) (*.f64 (sqrt.f64 t) 1/18))))) 3)
▶	0.1b	(-.f64 (exp.f64 (log1p.f64 (.f64 1/3 (acos.f64 (.f64 (/.f64 (/.f64 x y) z) (*.f64 (sqrt.f64 t) 1/18)))))) 1)

Compiler

Compiled 1744 to 971 computations (44.3% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.9b	(log1p.f64 (.f64 1/3 (acos.f64 (.f64 (/.f64 (/.f64 x y) z) (*.f64 (sqrt.f64 t) 1/18)))))
✓	1.0b	(.f64 1/3 (acos.f64 (.f64 (/.f64 (/.f64 x y) z) (*.f64 (sqrt.f64 t) 1/18))))
✓	4.0b	(.f64 (/.f64 (/.f64 x y) z) (.f64 (sqrt.f64 t) 1/18))
✓	5.6b	(/.f64 (/.f64 x y) z)

series1.7s (22.4%)

Counts

4 → 168

Calls

4 calls:

1.6s	(log1p.f64 (.f64 1/3 (acos.f64 (.f64 (/.f64 (/.f64 x y) z) (*.f64 (sqrt.f64 t) 1/18)))))
42.0ms	(.f64 (/.f64 (/.f64 x y) z) (.f64 (sqrt.f64 t) 1/18))
18.0ms	(/.f64 (/.f64 x y) z)
18.0ms	(.f64 1/3 (acos.f64 (.f64 (/.f64 (/.f64 x y) z) (*.f64 (sqrt.f64 t) 1/18))))

rewrite66.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

286×	`log1p-udef_binary64`
212×	`prod-diff_binary64`
159×	`add-sqr-sqrt_binary64`
150×	`expm1-log1p-u_binary64`
149×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	64
1	318	64
2	4138	64

Stop Event

1×	node limit

Counts

4 → 96

Calls

4 calls:

64.0ms	(log1p.f64 (.f64 1/3 (acos.f64 (.f64 (/.f64 (/.f64 x y) z) (*.f64 (sqrt.f64 t) 1/18)))))
64.0ms	(.f64 1/3 (acos.f64 (.f64 (/.f64 (/.f64 x y) z) (*.f64 (sqrt.f64 t) 1/18))))
64.0ms	(.f64 (/.f64 (/.f64 x y) z) (.f64 (sqrt.f64 t) 1/18))
64.0ms	(/.f64 (/.f64 x y) z)

simplify89.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

110×	`associate-/l*_binary64`
61×	`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	2808
1	31	2808
2	66	2808
3	173	2808
4	324	2808
5	502	2808
6	525	2808

Stop Event

1×

saturated

Counts

264 → 104

prune82.0ms (1.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	104	4	108

Error

0.0b

Counts

108 → 4

Alt Table

Status	Error	Program
✓	1.2b	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))
▶	1.1b	(sqrt.f64 (.f64 (pow.f64 (acos.f64 (.f64 (/.f64 (/.f64 x y) z) (*.f64 (sqrt.f64 t) 1/18))) 2) 1/9))
	1.1b	(pow.f64 (cbrt.f64 (.f64 1/3 (acos.f64 (.f64 (/.f64 (/.f64 x y) z) (*.f64 (sqrt.f64 t) 1/18))))) 3)
✓	0.1b	(-.f64 (exp.f64 (log1p.f64 (.f64 1/3 (acos.f64 (.f64 (/.f64 (/.f64 x y) z) (*.f64 (sqrt.f64 t) 1/18)))))) 1)

Compiler

Compiled 2296 to 1478 computations (35.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (sqrt.f64 t) 1/18)
✓	0.9b	(sqrt.f64 (.f64 (pow.f64 (acos.f64 (.f64 (/.f64 (/.f64 x y) z) (*.f64 (sqrt.f64 t) 1/18))) 2) 1/9))
	4.0b	(.f64 (/.f64 (/.f64 x y) z) (.f64 (sqrt.f64 t) 1/18))
	5.6b	(/.f64 (/.f64 x y) z)

series24.0ms (0.3%)

Counts

2 → 48

Calls

2 calls:

19.0ms	(sqrt.f64 (.f64 (pow.f64 (acos.f64 (.f64 (/.f64 (/.f64 x y) z) (*.f64 (sqrt.f64 t) 1/18))) 2) 1/9))
5.0ms	(*.f64 (sqrt.f64 t) 1/18)

rewrite71.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

308×	`log1p-udef_binary64`
172×	`add-sqr-sqrt_binary64`
165×	`log1p-expm1-u_binary64`
165×	`expm1-log1p-u_binary64`
164×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	31
1	363	26
2	4541	26

Stop Event

1×	node limit

Counts

2 → 40

Calls

2 calls:

70.0ms	(*.f64 (sqrt.f64 t) 1/18)
70.0ms	(sqrt.f64 (.f64 (pow.f64 (acos.f64 (.f64 (/.f64 (/.f64 x y) z) (*.f64 (sqrt.f64 t) 1/18))) 2) 1/9))

simplify35.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

113×	`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	14	960
1	24	960
2	57	960
3	162	960
4	315	960
5	494	960
6	517	960

Stop Event

1×

saturated

Counts

88 → 42

prune57.0ms (0.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	0	1	1
Picked	1	0	1
Done	1	1	2
Total	114	3	117

Error

Counts

117 → 3

Alt Table

Status	Error	Program
	1.1b	(pow.f64 (cbrt.f64 (.f64 1/3 (acos.f64 (.f64 (/.f64 (/.f64 x y) z) (*.f64 (sqrt.f64 t) 1/18))))) 3)
✓	0.1b	(-.f64 (exp.f64 (log1p.f64 (.f64 1/3 (acos.f64 (.f64 (/.f64 (/.f64 x y) z) (*.f64 (sqrt.f64 t) 1/18)))))) 1)
	1.1b	(sqrt.f64 (.f64 (pow.f64 (acos.f64 (.f64 (/.f64 x (.f64 y z)) (.f64 (sqrt.f64 t) 1/18))) 2) 1/9))

Compiler

Compiled 2252 to 1372 computations (39.1% saved)

regimes488.0ms (6.4%)

Accuracy

Total 0.4b remaining (97.8%)

Threshold costs 0.4b (97.8%)

Counts

36 → 1

Compiler

Compiled 10345 to 8239 computations (20.4% 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

end80.0ms (1.1%)

Remove: (sort y z)
Compiler: Compiled 145 to 117 computations (19.3% saved)

Details

analyze1.2s (15.8%)

sample3.1s (40.3%)

simplify36.0ms (0.5%)

prune4.0ms (0.1%)

localize13.0ms (0.2%)

series90.0ms (1.2%)

rewrite45.0ms (0.6%)

simplify68.0ms (0.9%)

prune119.0ms (1.6%)

localize11.0ms (0.1%)

series108.0ms (1.4%)

rewrite61.0ms (0.8%)

simplify7.0ms (0.1%)

prune42.0ms (0.5%)

localize24.0ms (0.3%)

series1.7s (22.4%)

rewrite66.0ms (0.9%)

simplify89.0ms (1.2%)

prune82.0ms (1.1%)

localize11.0ms (0.1%)

series24.0ms (0.3%)

rewrite71.0ms (0.9%)

simplify35.0ms (0.5%)

prune57.0ms (0.8%)

regimes488.0ms (6.4%)

simplify2.0ms (0%)

end80.0ms (1.1%)

Profiling