Details

analyze1.2s (11.3%)

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 (28.6%)

Symmetry

(sort y z)

Results

1.7s	10615×	body	128	invalid
1.4s	8256×	body	128	valid

Compiler

Compiled 71 to 59 computations (16.9% saved)

simplify93.0ms (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

prune5.0ms (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))))
	1.5b	(.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)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.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))))
✓	3.5b	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))
✓	5.3b	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))

series82.0ms (0.7%)

Counts

4 → 144

Calls

4 calls:

38.0ms	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))
19.0ms	(.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))
6.0ms	(.f64 3 (/.f64 x (.f64 y 27)))

rewrite50.0ms (0.5%)

Algorithm

1×	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 → 129

Calls

4 calls:

48.0ms	(.f64 3 (/.f64 x (.f64 y 27)))
48.0ms	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
48.0ms	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))
48.0ms	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	73
1	397	61
2	4841	61

simplify73.0ms (0.7%)

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

273 → 132

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

prune443.0ms (4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	128	4	132
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	130	4	134

Error

0.0b

Counts

134 → 4

Alt Table

Status	Error	Program
	1.7b	(sqrt.f64 (.f64 1/9 (pow.f64 (acos.f64 (.f64 (.f64 1/9 (/.f64 x y)) (.f64 (/.f64 1/2 z) (sqrt.f64 t)))) 2)))
	1.7b	(pow.f64 (cbrt.f64 (.f64 1/3 (acos.f64 (.f64 (.f64 1/9 (/.f64 x y)) (.f64 (/.f64 1/2 z) (sqrt.f64 t)))))) 3)
▶	0.8b	(-.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)
	1.5b	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))

Compiler

Compiled 2857 to 2002 computations (29.9% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 1/9 (/.f64 x y))
✓	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)))))
✓	7.9b	(.f64 (.f64 1/9 (/.f64 x y)) (*.f64 (/.f64 1/2 z) (sqrt.f64 t)))

series2.3s (20.7%)

Counts

4 → 132

Calls

4 calls:

2.2s	(log1p.f64 (.f64 1/3 (acos.f64 (.f64 (.f64 1/9 (/.f64 x y)) (.f64 (/.f64 1/2 z) (sqrt.f64 t))))))
42.0ms	(.f64 (.f64 1/9 (/.f64 x y)) (*.f64 (/.f64 1/2 z) (sqrt.f64 t)))
17.0ms	(.f64 1/3 (acos.f64 (.f64 (.f64 1/9 (/.f64 x y)) (.f64 (/.f64 1/2 z) (sqrt.f64 t)))))
7.0ms	(*.f64 1/9 (/.f64 x y))

rewrite73.0ms (0.7%)

Algorithm

1×	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 → 76

Calls

4 calls:

72.0ms	(*.f64 1/9 (/.f64 x y))
72.0ms	(log1p.f64 (.f64 1/3 (acos.f64 (.f64 (.f64 1/9 (/.f64 x y)) (.f64 (/.f64 1/2 z) (sqrt.f64 t))))))
72.0ms	(.f64 1/3 (acos.f64 (.f64 (.f64 1/9 (/.f64 x y)) (.f64 (/.f64 1/2 z) (sqrt.f64 t)))))
72.0ms	(.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	73
1	358	73
2	4285	73
3	5069	73

simplify95.0ms (0.9%)

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

208 → 80

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	2556
1	31	2556
2	64	2556
3	144	2556
4	249	2556
5	341	2556
6	321	2556
7	320	2556

prune74.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	80	4	84

Error

Counts

84 → 4

Alt Table

Status	Error	Program
	1.7b	(sqrt.f64 (.f64 1/9 (pow.f64 (acos.f64 (.f64 (.f64 1/9 (/.f64 x y)) (.f64 (/.f64 1/2 z) (sqrt.f64 t)))) 2)))
▶	0.6b	(-.f64 (exp.f64 (log1p.f64 (.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))))))) 1)
	1.7b	(pow.f64 (cbrt.f64 (.f64 1/3 (acos.f64 (.f64 (.f64 1/9 (/.f64 x y)) (.f64 (/.f64 1/2 z) (sqrt.f64 t)))))) 3)
✓	0.8b	(-.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)

Compiler

Compiled 1912 to 1388 computations (27.4% saved)

localize13.0ms (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)))))
✓	3.6b	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
✓	4.3b	(/.f64 x (*.f64 y z))

series1.7s (15.1%)

Counts

4 → 48

Calls

4 calls:

1.6s	(log1p.f64 (.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))))))
32.0ms	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
18.0ms	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))
17.0ms	(/.f64 x (*.f64 y z))

rewrite71.0ms (0.6%)

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`

Counts

4 → 102

Calls

4 calls:

69.0ms	(log1p.f64 (.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))))))
69.0ms	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))
69.0ms	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
69.0ms	(/.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

simplify43.0ms (0.4%)

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

prune88.0ms (0.8%)

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

Counts

108 → 4

Alt Table

Status	Error	Program
▶	1.7b	(sqrt.f64 (.f64 1/9 (pow.f64 (acos.f64 (.f64 (.f64 1/9 (/.f64 x y)) (.f64 (/.f64 1/2 z) (sqrt.f64 t)))) 2)))
✓	0.6b	(-.f64 (exp.f64 (log1p.f64 (.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))))))) 1)
	1.7b	(pow.f64 (cbrt.f64 (.f64 1/3 (acos.f64 (.f64 (.f64 1/9 (/.f64 x y)) (.f64 (/.f64 1/2 z) (sqrt.f64 t)))))) 3)
✓	0.8b	(-.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)

Compiler

Compiled 2300 to 1421 computations (38.2% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (/.f64 1/2 z) (sqrt.f64 t))
	0.3b	(*.f64 1/9 (/.f64 x y))
✓	1.0b	(sqrt.f64 (.f64 1/9 (pow.f64 (acos.f64 (.f64 (.f64 1/9 (/.f64 x y)) (.f64 (/.f64 1/2 z) (sqrt.f64 t)))) 2)))
	7.9b	(.f64 (.f64 1/9 (/.f64 x y)) (*.f64 (/.f64 1/2 z) (sqrt.f64 t)))

series32.0ms (0.3%)

Counts

2 → 60

Calls

2 calls:

19.0ms	(sqrt.f64 (.f64 1/9 (pow.f64 (acos.f64 (.f64 (.f64 1/9 (/.f64 x y)) (.f64 (/.f64 1/2 z) (sqrt.f64 t)))) 2)))
14.0ms	(*.f64 (/.f64 1/2 z) (sqrt.f64 t))

rewrite69.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

326×	`log1p-udef_binary64`
182×	`add-sqr-sqrt_binary64`
174×	`log1p-expm1-u_binary64`
174×	`expm1-log1p-u_binary64`
173×	`add-log-exp_binary64`

Counts

2 → 53

Calls

2 calls:

67.0ms	(*.f64 (/.f64 1/2 z) (sqrt.f64 t))
67.0ms	(sqrt.f64 (.f64 1/9 (pow.f64 (acos.f64 (.f64 (.f64 1/9 (/.f64 x y)) (.f64 (/.f64 1/2 z) (sqrt.f64 t)))) 2)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	37
1	383	32
2	4481	32
3	5043	32

simplify64.0ms (0.6%)

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

113 → 56

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	1104
1	37	1068
2	79	1068
3	219	1068
4	417	1068
5	604	1068
6	633	1068
7	611	1068
8	612	1068
9	612	1068
10	606	1068

prune56.0ms (0.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	102	4	106

Error

Counts

106 → 4

Alt Table

Status	Error	Program
✓	1.7b	(sqrt.f64 (.f64 1/9 (pow.f64 (acos.f64 (.f64 (.f64 1/9 (/.f64 x y)) (.f64 (/.f64 1/2 z) (sqrt.f64 t)))) 2)))
✓	0.6b	(-.f64 (exp.f64 (log1p.f64 (.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))))))) 1)
	1.7b	(pow.f64 (cbrt.f64 (.f64 1/3 (acos.f64 (.f64 (.f64 1/9 (/.f64 x y)) (.f64 (/.f64 1/2 z) (sqrt.f64 t)))))) 3)
✓	0.8b	(-.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)

Compiler

Compiled 2177 to 1521 computations (30.1% saved)

regimes1.1s (10%)

Accuracy

Total 0.4b remaining (98.3%)

Threshold costs 0.4b (98.3%)

Counts

54 → 1

Compiler

Compiled 15272 to 12352 computations (19.1% saved)

simplify3.0ms (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
3	25	27

end95.0ms (0.9%)

Remove: (sort y z)
Compiler: Compiled 172 to 140 computations (18.6% saved)

Details

analyze1.2s (11.3%)

sample3.1s (28.6%)

simplify93.0ms (0.8%)

prune5.0ms (0%)

localize13.0ms (0.1%)

series82.0ms (0.7%)

rewrite50.0ms (0.5%)

simplify73.0ms (0.7%)

prune443.0ms (4%)

localize16.0ms (0.1%)

series2.3s (20.7%)

rewrite73.0ms (0.7%)

simplify95.0ms (0.9%)

prune74.0ms (0.7%)

localize13.0ms (0.1%)

series1.7s (15.1%)

rewrite71.0ms (0.6%)

simplify43.0ms (0.4%)

prune88.0ms (0.8%)

localize12.0ms (0.1%)

series32.0ms (0.3%)

rewrite69.0ms (0.6%)

simplify64.0ms (0.6%)

prune56.0ms (0.5%)

regimes1.1s (10%)

simplify3.0ms (0%)

end95.0ms (0.9%)

Profiling