Details

analyze1.2s (9.7%)

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 (25.1%)

Symmetry

(sort y z)

Results

1.6s	10735×	body	128	invalid
1.4s	8256×	body	128	valid

Compiler

Compiled 71 to 59 computations (16.9% saved)

simplify94.0ms (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

1.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	1.8b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
	2.6b	(.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
✓	0.2b	(.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))))
✓	4.6b	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))
✓	6.5b	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))

series93.0ms (0.8%)

Counts

4 → 144

Calls

4 calls:

43.0ms	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))
24.0ms	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))
18.0ms	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
7.0ms	(.f64 3 (/.f64 x (.f64 y 27)))

rewrite55.0ms (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 → 126

Calls

4 calls:

52.0ms	(.f64 3 (/.f64 x (.f64 y 27)))
52.0ms	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
52.0ms	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))
52.0ms	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))

Iterations

Useful iterations: 0 (0.0ms)

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

simplify82.0ms (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

270 → 130

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

prune119.0ms (1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	126	4	130
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	128	4	132

Error

0.0b

Counts

132 → 4

Alt Table

Status	Error	Program
▶	1.1b	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))
	3.2b	(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))))))
	3.2b	(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)
	2.3b	(-.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 2823 to 1980 computations (29.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.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)))))
✓	4.6b	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
✓	5.9b	(/.f64 x (*.f64 y z))

series110.0ms (0.9%)

Counts

4 → 0

Calls

4 calls:

41.0ms	(.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))
35.0ms	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
17.0ms	(/.f64 x (*.f64 y z))
17.0ms	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))

rewrite104.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

263×	`expm1-udef_binary64`
263×	`log1p-udef_binary64`
233×	`log-pow_binary64`
154×	`prod-diff_binary64`
147×	`add-sqr-sqrt_binary64`

Counts

4 → 97

Calls

4 calls:

102.0ms	(.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))
102.0ms	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))
102.0ms	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
102.0ms	(/.f64 x (*.f64 y z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	54
1	293	54
2	3614	54
3	4948	54
4	5075	54
0	0	0
1	0	0

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune45.0ms (0.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	98	3	101

Error

Counts

101 → 3

Alt Table

Status	Error	Program
	1.1b	(log.f64 (pow.f64 (exp.f64 1/3) (acos.f64 (.f64 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)) 1/18))))
	3.2b	(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)
▶	0.2b	(-.f64 (exp.f64 (log1p.f64 (.f64 1/3 (acos.f64 (.f64 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)) 1/18))))) 1)

Compiler

Compiled 1729 to 933 computations (46% 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 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)) 1/18))))
✓	1.0b	(.f64 1/3 (acos.f64 (.f64 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)) 1/18)))
	4.6b	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
	5.9b	(/.f64 x (*.f64 y z))

series3.1s (25.4%)

Counts

2 → 96

Calls

2 calls:

3.1s	(log1p.f64 (.f64 1/3 (acos.f64 (.f64 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)) 1/18))))
18.0ms	(.f64 1/3 (acos.f64 (.f64 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)) 1/18)))

rewrite91.0ms (0.7%)

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

2 → 29

Calls

2 calls:

90.0ms	(log1p.f64 (.f64 1/3 (acos.f64 (.f64 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)) 1/18))))
90.0ms	(.f64 1/3 (acos.f64 (.f64 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)) 1/18)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	42
1	311	42
2	3791	42
3	4913	42
0	0	0
1	0	0

simplify149.0ms (1.2%)

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

125 → 32

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	2016
1	31	2016
2	64	2016
3	144	2016
4	249	2016
5	341	2016
6	321	2016
7	320	2016

prune360.0ms (2.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	101	3	104

Error

Counts

104 → 3

Alt Table

Status	Error	Program
▶	1.1b	(log.f64 (pow.f64 (exp.f64 1/3) (acos.f64 (.f64 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)) 1/18))))
	3.2b	(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)
✓	0.2b	(-.f64 (exp.f64 (log1p.f64 (.f64 1/3 (acos.f64 (.f64 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)) 1/18))))) 1)

Compiler

Compiled 2220 to 1369 computations (38.3% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)) 1/18)
✓	1.0b	(pow.f64 (exp.f64 1/3) (acos.f64 (.f64 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)) 1/18)))
	4.6b	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
	5.9b	(/.f64 x (*.f64 y z))

series1.6s (12.7%)

Counts

2 → 84

Calls

2 calls:

1.5s	(pow.f64 (exp.f64 1/3) (acos.f64 (.f64 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)) 1/18)))
84.0ms	(.f64 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)) 1/18)

rewrite119.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

279×	`expm1-udef_binary64`
279×	`log1p-udef_binary64`
157×	`add-sqr-sqrt_binary64`
147×	`add-log-exp_binary64`
147×	`log1p-expm1-u_binary64`

Counts

2 → 37

Calls

2 calls:

117.0ms	(.f64 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)) 1/18)
117.0ms	(pow.f64 (exp.f64 1/3) (acos.f64 (.f64 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)) 1/18)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	37
1	313	37
2	3827	37
3	4995	37
4	4917	37
0	0	0
1	0	0

simplify262.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

791×	`fma-def_binary64`
473×	`sqr-pow_binary64`
434×	`unswap-sqr_binary64`
346×	`associate-/l*_binary64`
338×	`associate-*l/_binary64`

Counts

121 → 40

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	1596
1	27	1596
2	64	1548
3	154	1548
4	282	1548
5	421	1548
6	507	1548
7	823	1548
8	1564	1548
9	2091	1548
10	2369	1548
11	2701	1548
12	3280	1548
13	4845	1548
14	4774	1548

prune106.0ms (0.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	109	3	112

Error

Counts

112 → 3

Alt Table

Status	Error	Program
✓	1.1b	(log.f64 (pow.f64 (exp.f64 1/3) (acos.f64 (.f64 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)) 1/18))))
	3.2b	(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)
✓	0.2b	(-.f64 (exp.f64 (log1p.f64 (.f64 1/3 (acos.f64 (.f64 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)) 1/18))))) 1)

Compiler

Compiled 2134 to 1211 computations (43.3% saved)

regimes1.3s (10.5%)

Accuracy

Total 0.2b remaining (95.7%)

Threshold costs 0.2b (95.7%)

Counts

48 → 1

Compiler

Compiled 13400 to 10792 computations (19.5% saved)

simplify7.0ms (0.1%)

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

end157.0ms (1.3%)

Remove: (sort y z)
Compiler: Compiled 146 to 118 computations (19.2% saved)

Details

analyze1.2s (9.7%)

sample3.1s (25.1%)

simplify94.0ms (0.8%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series93.0ms (0.8%)

rewrite55.0ms (0.4%)

simplify82.0ms (0.7%)

prune119.0ms (1%)

localize9.0ms (0.1%)

series110.0ms (0.9%)

rewrite104.0ms (0.8%)

simplify7.0ms (0.1%)

prune45.0ms (0.4%)

localize13.0ms (0.1%)

series3.1s (25.4%)

rewrite91.0ms (0.7%)

simplify149.0ms (1.2%)

prune360.0ms (2.9%)

localize29.0ms (0.2%)

series1.6s (12.7%)

rewrite119.0ms (1%)

simplify262.0ms (2.1%)

prune106.0ms (0.9%)

regimes1.3s (10.5%)

simplify7.0ms (0.1%)

end157.0ms (1.3%)

Profiling