Details

analyze88.0ms (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)

sample1.9s (33.1%)

Results

1.8s

8256×

body

128

valid

Compiler

Compiled 93 to 79 computations (15.1% saved)

simplify54.0ms (0.9%)

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

prune4.0ms (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

0.4b

Counts

3 → 2

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)
	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

▶

0.4b

(+.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)

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))

series199.0ms (3.4%)

Counts

4 → 60

Calls

4 calls:

142.0ms	(+.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)
31.0ms	(.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2))
23.0ms	(pow.f64 (*.f64 -2 (log.f64 u1)) 1/2)
3.0ms	(.f64 (.f64 2 (PI.f64)) u2)

rewrite74.0ms (1.3%)

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:

72.0ms	(+.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)
72.0ms	(pow.f64 (*.f64 -2 (log.f64 u1)) 1/2)
72.0ms	(.f64 (.f64 2 (PI.f64)) u2)
72.0ms	(.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2))

simplify53.0ms (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

prune123.0ms (2.1%)

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
	0.5b	(+.f64 (.f64 (.f64 (/.f64 1 6) (.f64 (sqrt.f64 (cbrt.f64 (.f64 4 (pow.f64 (log.f64 u1) 2)))) (sqrt.f64 (cbrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
	0.3b	(+.f64 (.f64 (.f64 1/6 (.f64 (sqrt.f64 (log.f64 (/.f64 1 u1))) (sqrt.f64 2))) (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	(fma.f64 (cbrt.f64 (.f64 (pow.f64 (cos.f64 (.f64 2 (.f64 (PI.f64) u2))) 2) (.f64 (.f64 -2 (log.f64 u1)) 1/36))) (cbrt.f64 (.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 (PI.f64) u2)))))) 1/2)
	0.3b	(+.f64 (.f64 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 1/6 (sqrt.f64 2))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
	0.7b	(+.f64 (.f64 (.f64 (/.f64 1 6) (.f64 (cbrt.f64 (.f64 -2 (log.f64 u1))) (cbrt.f64 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)

Compiler

Compiled 2776 to 2125 computations (23.5% 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)
✓	0.3b	(.f64 (.f64 -2 (log.f64 u1)) 1/36)

series246.0ms (4.2%)

Counts

3 → 48

Calls

3 calls:

201.0ms	(+.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))
22.0ms	(.f64 (.f64 -2 (log.f64 u1)) 1/36)

rewrite60.0ms (1%)

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:

58.0ms	(+.f64 (.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
58.0ms	(sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36))
58.0ms	(.f64 (.f64 -2 (log.f64 u1)) 1/36)

simplify51.0ms (0.9%)

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

prune128.0ms (2.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	110	3	113
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	113	6	119

Error

Counts

119 → 6

Alt Table

Status	Error	Program
	0.5b	(+.f64 (.f64 (.f64 (/.f64 1 6) (.f64 (sqrt.f64 (cbrt.f64 (.f64 4 (pow.f64 (log.f64 u1) 2)))) (sqrt.f64 (cbrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
	0.3b	(+.f64 (.f64 (.f64 1/6 (.f64 (sqrt.f64 (log.f64 (/.f64 1 u1))) (sqrt.f64 2))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
	0.6b	(fma.f64 (cbrt.f64 (.f64 (.f64 (log.f64 u1) -1/18) (pow.f64 (cos.f64 (.f64 2 (.f64 (PI.f64) u2))) 2))) (cbrt.f64 (.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 2 (.f64 (PI.f64) u2))))) 1/2)
▶	0.3b	(fma.f64 (cos.f64 (.f64 2 (.f64 (PI.f64) u2))) (*.f64 (sqrt.f64 1/18) (sqrt.f64 (neg.f64 (log.f64 u1)))) 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)
	0.3b	(+.f64 (.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (.f64 (log.f64 u1) -1/18) 3))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2))) 1/2)

Compiler

Compiled 2589 to 1911 computations (26.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (cos.f64 (.f64 2 (.f64 (PI.f64) u2))) (*.f64 (sqrt.f64 1/18) (sqrt.f64 (neg.f64 (log.f64 u1)))) 1/2)
✓	0.1b	(sqrt.f64 (neg.f64 (log.f64 u1)))
✓	0.3b	(*.f64 (PI.f64) u2)
✓	0.3b	(*.f64 (sqrt.f64 1/18) (sqrt.f64 (neg.f64 (log.f64 u1))))

series194.0ms (3.3%)

Counts

4 → 40

Calls

4 calls:

146.0ms	(fma.f64 (cos.f64 (.f64 2 (.f64 (PI.f64) u2))) (*.f64 (sqrt.f64 1/18) (sqrt.f64 (neg.f64 (log.f64 u1)))) 1/2)
24.0ms	(*.f64 (sqrt.f64 1/18) (sqrt.f64 (neg.f64 (log.f64 u1))))
21.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
2.0ms	(*.f64 (PI.f64) u2)

rewrite56.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

575×	`prod-diff_binary64`
262×	`log1p-udef_binary64`
158×	`add-sqr-sqrt_binary64`
149×	`log1p-expm1-u_binary64`
149×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	45
1	329	39
2	3790	39

Stop Event

1×	node limit

Counts

4 → 79

Calls

4 calls:

55.0ms	(fma.f64 (cos.f64 (.f64 2 (.f64 (PI.f64) u2))) (*.f64 (sqrt.f64 1/18) (sqrt.f64 (neg.f64 (log.f64 u1)))) 1/2)
55.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
55.0ms	(*.f64 (PI.f64) u2)
55.0ms	(*.f64 (sqrt.f64 1/18) (sqrt.f64 (neg.f64 (log.f64 u1))))

simplify41.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

601×	`fma-neg_binary64`
511×	`distribute-rgt-neg-in_binary64`
500×	`associate-r_binary64`
493×	`distribute-lft-neg-in_binary64`
483×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	78	966
1	209	950
2	607	924
3	2929	922

Stop Event

1×	node limit

Counts

119 → 99

prune70.0ms (1.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	99	6	105

Error

Counts

105 → 6

Alt Table

Status	Error	Program
	0.5b	(+.f64 (.f64 (.f64 (/.f64 1 6) (.f64 (sqrt.f64 (cbrt.f64 (.f64 4 (pow.f64 (log.f64 u1) 2)))) (sqrt.f64 (cbrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
▶	0.3b	(+.f64 (.f64 (.f64 1/6 (.f64 (sqrt.f64 (log.f64 (/.f64 1 u1))) (sqrt.f64 2))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
	0.6b	(fma.f64 (cbrt.f64 (.f64 (.f64 (log.f64 u1) -1/18) (pow.f64 (cos.f64 (.f64 2 (.f64 (PI.f64) u2))) 2))) (cbrt.f64 (.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 2 (.f64 (PI.f64) u2))))) 1/2)
✓	0.3b	(fma.f64 (cos.f64 (.f64 2 (.f64 (PI.f64) u2))) (*.f64 (sqrt.f64 1/18) (sqrt.f64 (neg.f64 (log.f64 u1)))) 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)
	0.3b	(+.f64 (.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (.f64 (log.f64 u1) -1/18) 3))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2))) 1/2)

Compiler

Compiled 2144 to 1491 computations (30.5% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (log.f64 (/.f64 1 u1)))
	0.3b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.4b	(.f64 1/6 (.f64 (sqrt.f64 (log.f64 (/.f64 1 u1))) (sqrt.f64 2)))
✓	0.5b	(*.f64 (sqrt.f64 (log.f64 (/.f64 1 u1))) (sqrt.f64 2))

series68.0ms (1.2%)

Counts

3 → 24

Calls

3 calls:

25.0ms	(.f64 1/6 (.f64 (sqrt.f64 (log.f64 (/.f64 1 u1))) (sqrt.f64 2)))
23.0ms	(*.f64 (sqrt.f64 (log.f64 (/.f64 1 u1))) (sqrt.f64 2))
20.0ms	(sqrt.f64 (log.f64 (/.f64 1 u1)))

rewrite39.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

824×	`log1p-expm1-u_binary64`
824×	`expm1-log1p-u_binary64`
99×	`add-sqr-sqrt_binary64`
94×	`add-log-exp_binary64`
93×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	30
1	222	30
2	2382	30

Stop Event

1×	node limit

Counts

3 → 52

Calls

3 calls:

38.0ms	(sqrt.f64 (log.f64 (/.f64 1 u1)))
38.0ms	(.f64 1/6 (.f64 (sqrt.f64 (log.f64 (/.f64 1 u1))) (sqrt.f64 2)))
38.0ms	(*.f64 (sqrt.f64 (log.f64 (/.f64 1 u1))) (sqrt.f64 2))

simplify26.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

102×	`fma-neg_binary64`
48×	`fma-def_binary64`
33×	`cancel-sign-sub-inv_binary64`
20×	`sub-neg_binary64`
14×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	344
1	30	344
2	50	344
3	67	344
4	92	344
5	146	344
6	253	344
7	383	344
8	452	344
9	493	344
10	498	344

Stop Event

1×

saturated

Counts

76 → 62

prune91.0ms (1.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	78	6	84

Error

Counts

84 → 6

Alt Table

Status	Error	Program
	0.5b	(+.f64 (.f64 (.f64 (/.f64 1 6) (.f64 (sqrt.f64 (cbrt.f64 (.f64 4 (pow.f64 (log.f64 u1) 2)))) (sqrt.f64 (cbrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
✓	0.3b	(+.f64 (.f64 (.f64 1/6 (.f64 (sqrt.f64 (log.f64 (/.f64 1 u1))) (sqrt.f64 2))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
	0.6b	(fma.f64 (cbrt.f64 (.f64 (.f64 (log.f64 u1) -1/18) (pow.f64 (cos.f64 (.f64 2 (.f64 (PI.f64) u2))) 2))) (cbrt.f64 (.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 2 (.f64 (PI.f64) u2))))) 1/2)
✓	0.3b	(fma.f64 (cos.f64 (.f64 2 (.f64 (PI.f64) u2))) (*.f64 (sqrt.f64 1/18) (sqrt.f64 (neg.f64 (log.f64 u1)))) 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)
	0.3b	(+.f64 (.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (.f64 (log.f64 u1) -1/18) 3))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2))) 1/2)

Compiler

Compiled 1767 to 1343 computations (24% saved)

regimes2.1s (35.3%)

Accuracy

Total 0.2b remaining (87.1%)

Threshold costs 0.2b (87.1%)

Counts

154 → 1

Compiler

Compiled 38308 to 33652 computations (12.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	24
1	22	24

Stop Event

1×

saturated

end124.0ms (2.1%)

Compiler: Compiled 170 to 147 computations (13.5% saved)

Iter	Nodes	Cost
0	18	344
1	30	344
2	50	344
3	67	344
4	92	344
5	146	344
6	253	344
7	383	344
8	452	344
9	493	344
10	498	344

Iter	Nodes	Cost
0	18	344
1	30	344
2	50	344
3	67	344
4	92	344
5	146	344
6	253	344
7	383	344
8	452	344
9	493	344
10	498	344

Details

analyze88.0ms (1.5%)

sample1.9s (33.1%)

simplify54.0ms (0.9%)

prune4.0ms (0.1%)

localize14.0ms (0.2%)

series199.0ms (3.4%)

rewrite74.0ms (1.3%)

simplify53.0ms (0.9%)

prune123.0ms (2.1%)

localize11.0ms (0.2%)

series246.0ms (4.2%)

rewrite60.0ms (1%)

simplify51.0ms (0.9%)

prune128.0ms (2.2%)

localize12.0ms (0.2%)

series194.0ms (3.3%)

rewrite56.0ms (1%)

simplify41.0ms (0.7%)

prune70.0ms (1.2%)

localize13.0ms (0.2%)

series68.0ms (1.2%)

rewrite39.0ms (0.7%)

simplify26.0ms (0.5%)

prune91.0ms (1.6%)

regimes2.1s (35.3%)

simplify2.0ms (0%)

end124.0ms (2.1%)

Profiling

Iter	Nodes	Cost
0	18	344
1	30	344
2	50	344
3	67	344
4	92	344
5	146	344
6	253	344
7	383	344
8	452	344
9	493	344
10	498	344