Details

analyze1.2s (9.9%)

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)

sample3.4s (27%)

Symmetry

(sort y z)

Results

2.0s	10513×	body	128	invalid
1.3s	8256×	body	128	valid

Compiler

Compiled 71 to 59 computations (16.9% saved)

simplify97.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

2067×	`associate-/l*_binary64`
1151×	`associate-/l/_binary64`
961×	`associate-/r/_binary64`
904×	`*-commutative_binary64`
879×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	26
1	40	23
2	121	20
3	446	20
4	1750	20
5	3005	20
6	3002	20
7	3002	20
8	3753	20
9	4074	20
10	4215	20
11	4225	20
12	4229	20
13	4230	20
14	5398	20

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
▶	1.5b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
	2.0b	(.f64 1/3 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18)))))

Compiler

Compiled 116 to 91 computations (21.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(/.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))))
✓	2.3b	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))
✓	6.3b	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))

series91.0ms (0.7%)

Counts

4 → 144

Calls

4 calls:

44.0ms	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))
19.0ms	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))
17.0ms	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
11.0ms	(/.f64 x (*.f64 y 27))

rewrite54.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

4 → 141

Calls

4 calls:

50.0ms	(/.f64 x (*.f64 y 27))
50.0ms	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
50.0ms	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))
50.0ms	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	70
1	397	61
2	4841	61
0	0	0
1	0	0

simplify76.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

121×	`associate-/l*_binary64`
64×	`associate-*r/_binary64`
61×	`associate-*l/_binary64`
39×	`associate-/r/_binary64`
38×	`times-frac_binary64`

Counts

285 → 144

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	2028
1	32	2028
2	79	2028
3	172	2028
4	269	2028
5	329	2028
6	324	2028
7	324	2028

prune142.0ms (1.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	142	2	144
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	142	4	146

Error

0.0b

Counts

146 → 4

Alt Table

Status	Error	Program
✓	1.5b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
	2.5b	(log.f64 (pow.f64 (exp.f64 1/3) (acos.f64 (.f64 (.f64 1/9 (/.f64 x y)) (*.f64 (/.f64 1/2 z) (sqrt.f64 t))))))
▶	1.5b	(-.f64 (exp.f64 (log1p.f64 (.f64 1/3 (acos.f64 (.f64 (.f64 1/9 (/.f64 x y)) (.f64 (/.f64 1/2 z) (sqrt.f64 t))))))) 1)
	2.0b	(.f64 1/3 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18)))))

Compiler

Compiled 3211 to 2272 computations (29.2% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (/.f64 1/2 z) (sqrt.f64 t))
✓	1.0b	(log1p.f64 (.f64 1/3 (acos.f64 (.f64 (.f64 1/9 (/.f64 x y)) (.f64 (/.f64 1/2 z) (sqrt.f64 t))))))
✓	1.0b	(.f64 1/3 (acos.f64 (.f64 (.f64 1/9 (/.f64 x y)) (.f64 (/.f64 1/2 z) (sqrt.f64 t)))))
✓	7.2b	(.f64 (.f64 1/9 (/.f64 x y)) (*.f64 (/.f64 1/2 z) (sqrt.f64 t)))

series2.0s (15.6%)

Counts

4 → 144

Calls

4 calls:

1.9s	(log1p.f64 (.f64 1/3 (acos.f64 (.f64 (.f64 1/9 (/.f64 x y)) (.f64 (/.f64 1/2 z) (sqrt.f64 t))))))
43.0ms	(.f64 (.f64 1/9 (/.f64 x y)) (*.f64 (/.f64 1/2 z) (sqrt.f64 t)))
19.0ms	(.f64 1/3 (acos.f64 (.f64 (.f64 1/9 (/.f64 x y)) (.f64 (/.f64 1/2 z) (sqrt.f64 t)))))
13.0ms	(*.f64 (/.f64 1/2 z) (sqrt.f64 t))

rewrite75.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

314×	`log1p-udef_binary64`
203×	`prod-diff_binary64`
174×	`add-sqr-sqrt_binary64`
166×	`expm1-log1p-u_binary64`
165×	`log1p-expm1-u_binary64`

Counts

4 → 79

Calls

4 calls:

73.0ms	(*.f64 (/.f64 1/2 z) (sqrt.f64 t))
73.0ms	(log1p.f64 (.f64 1/3 (acos.f64 (.f64 (.f64 1/9 (/.f64 x y)) (.f64 (/.f64 1/2 z) (sqrt.f64 t))))))
73.0ms	(.f64 1/3 (acos.f64 (.f64 (.f64 1/9 (/.f64 x y)) (.f64 (/.f64 1/2 z) (sqrt.f64 t)))))
73.0ms	(.f64 (.f64 1/9 (/.f64 x y)) (*.f64 (/.f64 1/2 z) (sqrt.f64 t)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	75
1	358	75
2	4285	75
3	5069	75
0	0	0
1	0	0

simplify154.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

243×	`associate-/l*_binary64`
156×	`times-frac_binary64`
138×	`associate-*l/_binary64`
132×	`associate-/l/_binary64`
119×	`associate-/r/_binary64`

Counts

223 → 85

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	2700
1	41	2664
2	85	2664
3	225	2664
4	423	2664
5	610	2664
6	639	2664
7	617	2664
8	618	2664
9	618	2664
10	612	2664

prune81.0ms (0.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	0	2	2
Picked	0	1	1
Done	1	0	1
Total	84	5	89

Error

Counts

89 → 5

Alt Table

Status	Error	Program
	1.8b	(-.f64 (exp.f64 (log.f64 (+.f64 1 (.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))))) 1)
▶	0.3b	(-.f64 (exp.f64 (log1p.f64 (.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))))))) 1)
	2.5b	(log.f64 (pow.f64 (exp.f64 1/3) (acos.f64 (.f64 (.f64 1/9 (/.f64 x y)) (*.f64 (/.f64 1/2 z) (sqrt.f64 t))))))
✓	1.5b	(-.f64 (exp.f64 (log1p.f64 (.f64 1/3 (acos.f64 (.f64 (.f64 1/9 (/.f64 x y)) (.f64 (/.f64 1/2 z) (sqrt.f64 t))))))) 1)
	2.0b	(.f64 1/3 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18)))))

Compiler

Compiled 2048 to 1480 computations (27.7% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(log1p.f64 (.f64 1/3 (acos.f64 (.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)))))
✓	2.3b	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
✓	5.3b	(/.f64 x (*.f64 y z))

series1.9s (15.3%)

Counts

4 → 48

Calls

4 calls:

1.9s	(log1p.f64 (.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))))))
35.0ms	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
18.0ms	(/.f64 x (*.f64 y z))
18.0ms	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))

rewrite72.0ms (0.6%)

Algorithm

2×	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`

Counts

4 → 102

Calls

4 calls:

70.0ms	(log1p.f64 (.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))))))
70.0ms	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))
70.0ms	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
70.0ms	(/.f64 x (*.f64 y z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	61
1	311	61
2	3792	61
3	4914	61
0	0	0
1	0	0

simplify42.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

116×	`associate-/l*_binary64`
65×	`associate-*r/_binary64`
57×	`associate-*l/_binary64`
47×	`associate-/l/_binary64`
44×	`associate-/r/_binary64`

Counts

150 → 104

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	1056
1	31	1056
2	64	1056
3	144	1056
4	249	1056
5	341	1056
6	321	1056
7	320	1056

prune101.0ms (0.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	104	5	109

Error

Counts

109 → 5

Alt Table

Status	Error	Program
▶	1.8b	(-.f64 (exp.f64 (log.f64 (+.f64 1 (.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))))) 1)
✓	0.3b	(-.f64 (exp.f64 (log1p.f64 (.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))))))) 1)
	2.5b	(log.f64 (pow.f64 (exp.f64 1/3) (acos.f64 (.f64 (.f64 1/9 (/.f64 x y)) (*.f64 (/.f64 1/2 z) (sqrt.f64 t))))))
✓	1.5b	(-.f64 (exp.f64 (log1p.f64 (.f64 1/3 (acos.f64 (.f64 (.f64 1/9 (/.f64 x y)) (.f64 (/.f64 1/2 z) (sqrt.f64 t))))))) 1)
	2.0b	(.f64 1/3 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18)))))

Compiler

Compiled 2334 to 1447 computations (38% saved)

localize17.0ms (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	(log.f64 (+.f64 1 (.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))))
	2.3b	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
	5.3b	(/.f64 x (*.f64 y z))

series2.1s (17%)

Counts

1 → 0

Calls

1 calls:

2.1s	(log.f64 (+.f64 1 (.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))))

rewrite85.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

307×	`log1p-udef_binary64`
302×	`prod-diff_binary64`
173×	`add-sqr-sqrt_binary64`
162×	`log1p-expm1-u_binary64`
162×	`expm1-log1p-u_binary64`

Counts

1 → 21

Calls

1 calls:

84.0ms

(log.f64 (+.f64 1 (*.f64 1/3 (acos.f64 (*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	22
1	350	22
2	4293	22
3	5328	22
0	0	0
1	0	0

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune73.0ms (0.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	106	5	111

Error

Counts

111 → 5

Alt Table

Status	Error	Program
✓	1.8b	(-.f64 (exp.f64 (log.f64 (+.f64 1 (.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))))) 1)
✓	0.3b	(-.f64 (exp.f64 (log1p.f64 (.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))))))) 1)
	2.5b	(log.f64 (pow.f64 (exp.f64 1/3) (acos.f64 (.f64 (.f64 1/9 (/.f64 x y)) (*.f64 (/.f64 1/2 z) (sqrt.f64 t))))))
✓	1.5b	(-.f64 (exp.f64 (log1p.f64 (.f64 1/3 (acos.f64 (.f64 (.f64 1/9 (/.f64 x y)) (.f64 (/.f64 1/2 z) (sqrt.f64 t))))))) 1)
	2.0b	(.f64 1/3 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18)))))

Compiler

Compiled 2569 to 1638 computations (36.2% saved)

regimes575.0ms (4.6%)

Accuracy

Total 0.3b remaining (98.3%)

Threshold costs 0.3b (98.3%)

Counts

38 → 1

Compiler

Compiled 10961 to 8877 computations (19% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-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	27	27
2	28	27
3	26	27

end118.0ms (0.9%)

Remove: (sort y z)
Compiler: Compiled 189 to 153 computations (19% saved)

Details

analyze1.2s (9.9%)

sample3.4s (27%)

simplify97.0ms (0.8%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series91.0ms (0.7%)

rewrite54.0ms (0.4%)

simplify76.0ms (0.6%)

prune142.0ms (1.1%)

localize15.0ms (0.1%)

series2.0s (15.6%)

rewrite75.0ms (0.6%)

simplify154.0ms (1.2%)

prune81.0ms (0.6%)

localize15.0ms (0.1%)

series1.9s (15.3%)

rewrite72.0ms (0.6%)

simplify42.0ms (0.3%)

prune101.0ms (0.8%)

localize17.0ms (0.1%)

series2.1s (17%)

rewrite85.0ms (0.7%)

simplify7.0ms (0.1%)

prune73.0ms (0.6%)

regimes575.0ms (4.6%)

simplify4.0ms (0%)

end118.0ms (0.9%)

Profiling