Details

analyze96.0ms (1.4%)

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)

sample1.9s (28.7%)

Results

1.8s

8256×

body

128

valid

Compiler

Compiled 93 to 79 computations (15.1% saved)

simplify50.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

818×	`unswap-sqr_binary64`
500×	`sqr-pow_binary64`
281×	`cube-prod_binary64`
277×	`*-commutative_binary64`
242×	`pow-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	24
1	38	24
2	65	24
3	114	24
4	255	24
5	739	24
6	1007	24
7	1337	24
8	2621	24
9	2723	24
10	2884	24
11	3093	24
12	3400	24
13	3828	24
14	4392	24

Stop Event

1×	node limit

Counts

1 → 2

prune6.0ms (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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.3b	(+.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)
	0.4b	(fma.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (.f64 1/6 (cos.f64 (.f64 2 (.f64 (PI.f64) u2)))) 1/2)

Status

Error

Program

▶

0.3b

(+.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)

0.4b

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

Compiler

Compiled 112 to 98 computations (12.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.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)
✓	0.3b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.4b	(.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2))

series370.0ms (5.5%)

Counts

4 → 60

Calls

4 calls:

209.0ms	(pow.f64 (*.f64 -2 (log.f64 u1)) 1/2)
126.0ms	(+.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)
32.0ms	(.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2))
3.0ms	(.f64 (.f64 2 (PI.f64)) u2)

rewrite67.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

572×	`prod-diff_binary64`
183×	`add-sqr-sqrt_binary64`
175×	`log1p-expm1-u_binary64`
175×	`expm1-log1p-u_binary64`
171×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	51
1	394	51
2	4401	51

Stop Event

1×	node limit

Counts

4 → 83

Calls

4 calls:

66.0ms	(+.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)
66.0ms	(pow.f64 (*.f64 -2 (log.f64 u1)) 1/2)
66.0ms	(.f64 (.f64 2 (PI.f64)) u2)
66.0ms	(.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2))

simplify58.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

726×	`unswap-sqr_binary64`
433×	`fma-neg_binary64`
309×	`distribute-rgt-neg-in_binary64`
298×	`distribute-lft-neg-in_binary64`
285×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	76	1098
1	193	1050
2	514	1020
3	2142	998
4	4345	998

Stop Event

1×	node limit

Counts

143 → 104

prune178.0ms (2.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	98	6	104
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	100	6	106

Error

Counts

106 → 6

Alt Table

Status	Error	Program
	0.4b	(log.f64 (exp.f64 (fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 (PI.f64) u2)))) 1/2)))
	0.4b	(+.f64 (.f64 (expm1.f64 (log1p.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
	0.5b	(/.f64 (-.f64 1/4 (.f64 (pow.f64 (cos.f64 (.f64 2 (.f64 (PI.f64) u2))) 2) (.f64 (.f64 -2 (log.f64 u1)) 1/36))) (-.f64 1/2 (.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 (PI.f64) u2)))))))
	0.6b	(fma.f64 (sqrt.f64 (.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 (PI.f64) u2)))))) (sqrt.f64 (.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 (PI.f64) u2)))))) 1/2)
	0.5b	(+.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) 3)) (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)

Compiler

Compiled 2770 to 2117 computations (23.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.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))
	0.3b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.4b	(.f64 (.f64 -2 (log.f64 u1)) 1/36)

series171.0ms (2.6%)

Counts

3 → 48

Calls

3 calls:

127.0ms	(+.f64 (.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
22.0ms	(sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36))
22.0ms	(.f64 (.f64 -2 (log.f64 u1)) 1/36)

rewrite56.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	44
1	353	35
2	4080	35

Stop Event

1×	node limit

Counts

3 → 77

Calls

3 calls:

55.0ms	(+.f64 (.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
55.0ms	(sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36))
55.0ms	(.f64 (.f64 -2 (log.f64 u1)) 1/36)

simplify49.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

726×	`unswap-sqr_binary64`
416×	`fma-neg_binary64`
312×	`distribute-rgt-neg-in_binary64`
303×	`distribute-lft-neg-in_binary64`
266×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	69	826
1	175	814
2	455	786
3	2044	774
4	4130	774

Stop Event

1×	node limit

Counts

125 → 97

prune127.0ms (1.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	110	3	113
Fresh	4	1	5
Picked	0	1	1
Done	0	0	0
Total	114	5	119

Error

Counts

119 → 5

Alt Table

Status	Error	Program
▶	0.3b	(+.f64 (.f64 (exp.f64 (.f64 (log.f64 (.f64 (log.f64 u1) -1/18)) 1/2)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
	0.4b	(+.f64 (.f64 (expm1.f64 (log1p.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
	0.4b	(/.f64 (+.f64 (.f64 (.f64 (log.f64 u1) -1/18) (pow.f64 (cos.f64 (.f64 2 (.f64 (PI.f64) u2))) 2)) -1/4) (fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 2 (*.f64 (PI.f64) u2))) -1/2))
	0.5b	(.f64 (+.f64 (.f64 (.f64 (log.f64 u1) -1/18) (pow.f64 (cos.f64 (.f64 2 (.f64 (PI.f64) u2))) 2)) -1/4) (/.f64 1 (fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 2 (.f64 (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)

Compiler

Compiled 2559 to 1879 computations (26.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(log.f64 (*.f64 (log.f64 u1) -1/18))
	0.3b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.3b	(exp.f64 (.f64 (log.f64 (.f64 (log.f64 u1) -1/18)) 1/2))
✓	0.4b	(*.f64 (log.f64 u1) -1/18)

series441.0ms (6.6%)

Counts

3 → 36

Calls

3 calls:

219.0ms	(exp.f64 (.f64 (log.f64 (.f64 (log.f64 u1) -1/18)) 1/2))
202.0ms	(log.f64 (*.f64 (log.f64 u1) -1/18))
21.0ms	(*.f64 (log.f64 u1) -1/18)

rewrite43.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

663×	`log1p-expm1-u_binary64`
663×	`expm1-log1p-u_binary64`
356×	`log-prod_binary64`
139×	`expm1-udef_binary64`
139×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	174	22
2	1861	22

Stop Event

1×	node limit

Counts

3 → 105

Calls

3 calls:

41.0ms	(log.f64 (*.f64 (log.f64 u1) -1/18))
41.0ms	(exp.f64 (.f64 (log.f64 (.f64 (log.f64 u1) -1/18)) 1/2))
41.0ms	(*.f64 (log.f64 u1) -1/18)

simplify40.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

767×	`fma-def_binary64`
482×	`fma-neg_binary64`
439×	`distribute-rgt-in_binary64`
363×	`unsub-neg_binary64`
314×	`associate--r-_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	280
1	44	280
2	65	280
3	118	280
4	223	280
5	570	280
6	1799	280
7	4038	280
8	4814	280

Stop Event

1×	node limit

Counts

141 → 115

prune135.0ms (2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	131	5	136

Error

Counts

136 → 5

Alt Table

Status	Error	Program
✓	0.3b	(+.f64 (.f64 (exp.f64 (.f64 (log.f64 (.f64 (log.f64 u1) -1/18)) 1/2)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
	0.4b	(+.f64 (.f64 (expm1.f64 (log1p.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
▶	0.4b	(/.f64 (+.f64 (.f64 (.f64 (log.f64 u1) -1/18) (pow.f64 (cos.f64 (.f64 2 (.f64 (PI.f64) u2))) 2)) -1/4) (fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 2 (*.f64 (PI.f64) u2))) -1/2))
	0.5b	(.f64 (+.f64 (.f64 (.f64 (log.f64 u1) -1/18) (pow.f64 (cos.f64 (.f64 2 (.f64 (PI.f64) u2))) 2)) -1/4) (/.f64 1 (fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 2 (.f64 (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)

Compiler

Compiled 3075 to 2374 computations (22.8% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 2 (*.f64 (PI.f64) u2))) -1/2)
✓	0.3b	(*.f64 (PI.f64) u2)
	0.4b	(*.f64 (log.f64 u1) -1/18)
✓	0.4b	(/.f64 (+.f64 (.f64 (.f64 (log.f64 u1) -1/18) (pow.f64 (cos.f64 (.f64 2 (.f64 (PI.f64) u2))) 2)) -1/4) (fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 2 (*.f64 (PI.f64) u2))) -1/2))

series467.0ms (7%)

Counts

3 → 48

Calls

3 calls:

343.0ms

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

121.0ms

(fma.f64 (sqrt.f64 (*.f64 (log.f64 u1) -1/18)) (cos.f64 (*.f64 2 (*.f64 (PI.f64) u2))) -1/2)

2.0ms

(*.f64 (PI.f64) u2)

rewrite72.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

803×	`prod-diff_binary64`
198×	`add-sqr-sqrt_binary64`
188×	`log1p-expm1-u_binary64`
188×	`expm1-log1p-u_binary64`
187×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	71
1	408	71
2	4973	71

Stop Event

1×	node limit

Counts

3 → 71

Calls

3 calls:

70.0ms

(fma.f64 (sqrt.f64 (*.f64 (log.f64 u1) -1/18)) (cos.f64 (*.f64 2 (*.f64 (PI.f64) u2))) -1/2)

70.0ms

(*.f64 (PI.f64) u2)

70.0ms

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

simplify58.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

738×	`fma-def_binary64`
308×	`cancel-sign-sub-inv_binary64`
223×	`associate-r_binary64`
165×	`times-frac_binary64`
146×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	222	2937
1	719	2891
2	2683	2734

Stop Event

1×	node limit

Counts

119 → 100

prune197.0ms (2.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	159	5	164

Error

Counts

164 → 5

Alt Table

Status	Error	Program
✓	0.3b	(+.f64 (.f64 (exp.f64 (.f64 (log.f64 (.f64 (log.f64 u1) -1/18)) 1/2)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
	0.4b	(+.f64 (.f64 (expm1.f64 (log1p.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
✓	0.4b	(/.f64 (+.f64 (.f64 (.f64 (log.f64 u1) -1/18) (pow.f64 (cos.f64 (.f64 2 (.f64 (PI.f64) u2))) 2)) -1/4) (fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 2 (*.f64 (PI.f64) u2))) -1/2))
	0.5b	(.f64 (+.f64 (.f64 (.f64 (log.f64 u1) -1/18) (pow.f64 (cos.f64 (.f64 2 (.f64 (PI.f64) u2))) 2)) -1/4) (/.f64 1 (fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 2 (.f64 (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)

Compiler

Compiled 6959 to 4876 computations (29.9% saved)

regimes1.9s (28.6%)

Accuracy

Total 0.2b remaining (90.1%)

Threshold costs 0.2b (90.1%)

Counts

152 → 1

Compiler

Compiled 38993 to 33895 computations (13.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	28
1	24	28

Stop Event

1×

saturated

end118.0ms (1.8%)

Compiler: Compiled 159 to 135 computations (15.1% saved)

Details

analyze96.0ms (1.4%)

sample1.9s (28.7%)

simplify50.0ms (0.7%)

prune6.0ms (0.1%)

localize14.0ms (0.2%)

series370.0ms (5.5%)

rewrite67.0ms (1%)

simplify58.0ms (0.9%)

prune178.0ms (2.7%)

localize11.0ms (0.2%)

series171.0ms (2.6%)

rewrite56.0ms (0.8%)

simplify49.0ms (0.7%)

prune127.0ms (1.9%)

localize13.0ms (0.2%)

series441.0ms (6.6%)

rewrite43.0ms (0.6%)

simplify40.0ms (0.6%)

prune135.0ms (2%)

localize15.0ms (0.2%)

series467.0ms (7%)

rewrite72.0ms (1.1%)

simplify58.0ms (0.9%)

prune197.0ms (2.9%)

regimes1.9s (28.6%)

simplify2.0ms (0%)

end118.0ms (1.8%)

Profiling