Details

analyze101.0ms (1.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	6.2%	93.8%	0
0%	6.2%	93.8%	1
3.1%	3.1%	93.8%	2
3.1%	3.1%	93.8%	3
4.7%	1.6%	93.8%	4
4.7%	1.6%	93.8%	5
5.5%	0.8%	93.8%	6
5.5%	0.8%	93.8%	7
5.8%	0.4%	93.8%	8
5.8%	0.4%	93.8%	9
6%	0.2%	93.8%	10
6%	0.2%	93.8%	11
6.1%	0.1%	93.8%	12
6.1%	0.1%	93.8%	13
6.2%	0%	93.8%	14

Compiler

Compiled 36 to 30 computations (16.7% saved)

sample2.2s (33.6%)

Alt Table

Status	Error	Program
▶	0.4b	(+.f64 (.f64 (.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)

Results

1.9s

8256×

body

128

valid

Compiler

Compiled 135 to 117 computations (13.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(+.f64 (.f64 (.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
✓	0.1b	(pow.f64 (*.f64 -2 (log.f64 u1)) 1/2)
✓	0.2b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.4b	(.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2))

series463.0ms (7.1%)

Counts

4 → 60

Calls

4 calls:

272.0ms	(pow.f64 (*.f64 -2 (log.f64 u1)) 1/2)
158.0ms	(+.f64 (.f64 (.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
29.0ms	(.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2))
3.0ms	(.f64 (.f64 2 (PI.f64)) u2)

rewrite71.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

572×	`prod-diff_binary64`
184×	`add-sqr-sqrt_binary64`
175×	`log1p-expm1-u_binary64`
175×	`expm1-log1p-u_binary64`
172×	`add-log-exp_binary64`

Counts

4 → 83

Calls

4 calls:

68.0ms	(+.f64 (.f64 (.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
68.0ms	(pow.f64 (*.f64 -2 (log.f64 u1)) 1/2)
68.0ms	(.f64 (.f64 2 (PI.f64)) u2)
68.0ms	(.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	51
1	392	51
2	4174	51
3	5015	51
0	0	0
1	0	0

prune146.0ms (2.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	138	5	143
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	139	5	144

Error

Counts

144 → 5

Alt Table

Status	Error	Program
	0.5b	(+.f64 (.f64 (exp.f64 (log.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
▶	0.2b	(+.f64 (.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
	0.6b	(cbrt.f64 (pow.f64 (fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2) 3))
	0.6b	(pow.f64 (sqrt.f64 (fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)) 2)
	0.5b	(/.f64 (-.f64 1/4 (.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36) (pow.f64 (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 2))) (-.f64 1/2 (.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)))))

Compiler

Compiled 3416 to 2697 computations (21% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(+.f64 (.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
✓	0.1b	(sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36))
✓	0.2b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.4b	(.f64 (.f64 -2 (log.f64 u1)) 1/36)

series201.0ms (3.1%)

Counts

4 → 60

Calls

4 calls:

154.0ms	(+.f64 (.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
23.0ms	(sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36))
21.0ms	(.f64 (.f64 -2 (log.f64 u1)) 1/36)
3.0ms	(.f64 (.f64 2 (PI.f64)) u2)

rewrite68.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

520×	`prod-diff_binary64`
298×	`log1p-udef_binary64`
167×	`add-sqr-sqrt_binary64`
159×	`add-log-exp_binary64`
159×	`log1p-expm1-u_binary64`

Counts

4 → 92

Calls

4 calls:

66.0ms	(+.f64 (.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
66.0ms	(sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36))
66.0ms	(.f64 (.f64 2 (PI.f64)) u2)
66.0ms	(.f64 (.f64 -2 (log.f64 u1)) 1/36)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	52
1	351	43
2	3912	43
3	5213	43
0	0	0
1	0	0

prune142.0ms (2.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	148	4	152
Fresh	4	0	4
Picked	0	1	1
Done	0	0	0
Total	152	5	157

Error

Counts

157 → 5

Alt Table

Status	Error	Program
	0.4b	(/.f64 (+.f64 (.f64 (.f64 (log.f64 u1) -1/18) (pow.f64 (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 2)) -1/4) (fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) -1/2))
✓	0.2b	(+.f64 (.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
▶	0.4b	(+.f64 (.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
	0.4b	(+.f64 (.f64 (sqrt.f64 (exp.f64 (log.f64 (.f64 (log.f64 u1) -1/18)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2))) 1/2)
	0.5b	(cbrt.f64 (pow.f64 (fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2) 3))

Compiler

Compiled 3117 to 2366 computations (24.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(+.f64 (.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
✓	0.1b	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
✓	0.2b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.4b	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6)

series206.0ms (3.1%)

Counts

4 → 56

Calls

4 calls:

153.0ms	(+.f64 (.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
25.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
25.0ms	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6)
3.0ms	(.f64 (.f64 2 (PI.f64)) u2)

rewrite73.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

572×	`prod-diff_binary64`
299×	`log1p-udef_binary64`
169×	`add-sqr-sqrt_binary64`
159×	`add-log-exp_binary64`
159×	`log1p-expm1-u_binary64`

Counts

4 → 88

Calls

4 calls:

70.0ms	(+.f64 (.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
70.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
70.0ms	(.f64 (.f64 2 (PI.f64)) u2)
70.0ms	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	51
1	350	51
2	3915	51
3	5334	51
0	0	0
1	0	0

prune129.0ms (2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	144	5	149

Error

Counts

149 → 5

Alt Table

Status	Error	Program
▶	0.4b	(/.f64 (+.f64 (.f64 (.f64 (log.f64 u1) -1/18) (pow.f64 (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 2)) -1/4) (fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) -1/2))
✓	0.2b	(+.f64 (.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
✓	0.4b	(+.f64 (.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
	0.4b	(+.f64 (.f64 (sqrt.f64 (exp.f64 (log.f64 (.f64 (log.f64 u1) -1/18)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2))) 1/2)
	0.5b	(cbrt.f64 (pow.f64 (fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2) 3))

Compiler

Compiled 3244 to 2525 computations (22.2% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) -1/2)
✓	0.2b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.4b	(/.f64 (+.f64 (.f64 (.f64 (log.f64 u1) -1/18) (pow.f64 (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 2)) -1/4) (fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) -1/2))
✓	0.4b	(*.f64 (log.f64 u1) -1/18)

series629.0ms (9.6%)

Counts

4 → 72

Calls

4 calls:

458.0ms	(/.f64 (+.f64 (.f64 (.f64 (log.f64 u1) -1/18) (pow.f64 (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 2)) -1/4) (fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) -1/2))
148.0ms	(fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) -1/2)
20.0ms	(*.f64 (log.f64 u1) -1/18)
3.0ms	(.f64 (.f64 2 (PI.f64)) u2)

rewrite82.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

590×	`prod-diff_binary64`
194×	`add-sqr-sqrt_binary64`
184×	`log1p-expm1-u_binary64`
184×	`expm1-log1p-u_binary64`
183×	`add-log-exp_binary64`

Counts

4 → 85

Calls

4 calls:

79.0ms	(fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) -1/2)
79.0ms	(.f64 (.f64 2 (PI.f64)) u2)
79.0ms	(/.f64 (+.f64 (.f64 (.f64 (log.f64 u1) -1/18) (pow.f64 (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 2)) -1/4) (fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) -1/2))
79.0ms	(*.f64 (log.f64 u1) -1/18)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	80
1	401	80
2	4614	80
3	5523	80
0	0	0
1	0	0

prune238.0ms (3.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	210	0	210
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	210	5	215

Error

Counts

215 → 5

Alt Table

Status	Error	Program
✓	0.4b	(/.f64 (+.f64 (.f64 (.f64 (log.f64 u1) -1/18) (pow.f64 (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 2)) -1/4) (fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) -1/2))
✓	0.2b	(+.f64 (.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
✓	0.4b	(+.f64 (.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
	0.4b	(+.f64 (.f64 (sqrt.f64 (exp.f64 (log.f64 (.f64 (log.f64 u1) -1/18)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2))) 1/2)
	0.5b	(cbrt.f64 (pow.f64 (fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2) 3))

Compiler

Compiled 7872 to 5854 computations (25.6% saved)

regimes1.6s (25%)

Accuracy

Total 0.2b remaining (89.3%)

Threshold costs 0.2b (89.3%)

Counts

132 → 1

Compiler

Compiled 32095 to 27958 computations (12.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	21
1	21	21
2	20	21

end107.0ms (1.6%)

Compiler: Compiled 133 to 115 computations (13.5% saved)

Details

analyze101.0ms (1.5%)

sample2.2s (33.6%)

localize14.0ms (0.2%)

series463.0ms (7.1%)

rewrite71.0ms (1.1%)

prune146.0ms (2.2%)

localize11.0ms (0.2%)

series201.0ms (3.1%)

rewrite68.0ms (1%)

prune142.0ms (2.2%)

localize11.0ms (0.2%)

series206.0ms (3.1%)

rewrite73.0ms (1.1%)

prune129.0ms (2%)

localize17.0ms (0.3%)

series629.0ms (9.6%)

rewrite82.0ms (1.3%)

prune238.0ms (3.6%)

regimes1.6s (25%)

simplify2.0ms (0%)

end107.0ms (1.6%)

Profiling