Details

analyze90.0ms (1.6%)

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)

sample2.0s (34.1%)

Results

1.9s

8256×

body

128

valid

Compiler

Compiled 93 to 79 computations (15.1% saved)

simplify50.0ms (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	(fma.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (.f64 1/6 (cos.f64 (.f64 2 (.f64 (PI.f64) u2)))) 1/2)
▶	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)

Status

Error

Program

0.4b

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

▶

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)

Compiler

Compiled 112 to 98 computations (12.5% saved)

localize15.0ms (0.3%)

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))

series400.0ms (7%)

Counts

4 → 60

Calls

4 calls:

229.0ms	(pow.f64 (*.f64 -2 (log.f64 u1)) 1/2)
139.0ms	(+.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)

rewrite65.0ms (1.1%)

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:

63.0ms	(+.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)
63.0ms	(pow.f64 (*.f64 -2 (log.f64 u1)) 1/2)
63.0ms	(.f64 (.f64 2 (PI.f64)) u2)
63.0ms	(.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2))

simplify58.0ms (1%)

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

prune186.0ms (3.3%)

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

Compiler

Compiled 2806 to 2143 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)

series183.0ms (3.2%)

Counts

3 → 48

Calls

3 calls:

138.0ms	(+.f64 (.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
24.0ms	(sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36))
22.0ms	(.f64 (.f64 -2 (log.f64 u1)) 1/36)

rewrite61.0ms (1.1%)

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:

59.0ms	(+.f64 (.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
59.0ms	(sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36))
59.0ms	(.f64 (.f64 -2 (log.f64 u1)) 1/36)

simplify49.0ms (0.8%)

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

prune129.0ms (2.3%)

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	(fma.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (.f64 u2 (PI.f64)))))) 1/2)
	0.5b	(-.f64 (/.f64 (.f64 (.f64 (log.f64 u1) -1/18) (pow.f64 (cos.f64 (.f64 2 (.f64 (PI.f64) u2))) 2)) (fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 2 (.f64 (PI.f64) u2))) -1/2)) (/.f64 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 (cbrt.f64 (pow.f64 (.f64 (log.f64 u1) -1/18) 3/2)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2))) 1/2)
	0.3b	(+.f64 (.f64 (sqrt.f64 (expm1.f64 (log1p.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)

Compiler

Compiled 2553 to 1873 computations (26.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series310.0ms (5.4%)

Counts

4 → 68

Calls

4 calls:

143.0ms	(.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (.f64 u2 (PI.f64))))))
143.0ms	(fma.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (.f64 u2 (PI.f64)))))) 1/2)
22.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
2.0ms	(*.f64 u2 (PI.f64))

rewrite58.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

575×	`prod-diff_binary64`
168×	`add-sqr-sqrt_binary64`
158×	`log1p-expm1-u_binary64`
158×	`expm1-log1p-u_binary64`
157×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	64
1	349	54
2	4073	54

Stop Event

1×	node limit

Counts

4 → 78

Calls

4 calls:

56.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
56.0ms	(*.f64 u2 (PI.f64))
56.0ms	(.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (.f64 u2 (PI.f64))))))
56.0ms	(fma.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (.f64 u2 (PI.f64)))))) 1/2)

simplify57.0ms (1%)

Algorithm

1×	egg-herbie

Rules

682×	`distribute-rgt-neg-in_binary64`
617×	`associate-r_binary64`
604×	`associate-l_binary64`
256×	`fma-def_binary64`
252×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	74	1728
1	213	1684
2	712	1596
3	3852	1596

Stop Event

1×	node limit

Counts

146 → 106

prune84.0ms (1.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	106	5	111

Error

Counts

111 → 5

Alt Table

Status	Error	Program
✓	0.3b	(fma.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (.f64 u2 (PI.f64)))))) 1/2)
	0.5b	(-.f64 (/.f64 (.f64 (.f64 (log.f64 u1) -1/18) (pow.f64 (cos.f64 (.f64 2 (.f64 (PI.f64) u2))) 2)) (fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 2 (.f64 (PI.f64) u2))) -1/2)) (/.f64 1/4 (fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 2 (.f64 (PI.f64) u2))) -1/2)))
▶	0.3b	(+.f64 (fma.f64 (sqrt.f64 2) (.f64 1/6 (sqrt.f64 (neg.f64 (log.f64 u1)))) 1/2) (.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (neg.f64 (log.f64 u1)))) (+.f64 (.f64 1/9 (.f64 (pow.f64 u2 4) (pow.f64 (PI.f64) 4))) (.f64 (pow.f64 (PI.f64) 2) (.f64 u2 (.f64 u2 -1/3))))))
	0.3b	(+.f64 (.f64 (sqrt.f64 (expm1.f64 (log1p.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)

Compiler

Compiled 2616 to 1877 computations (28.2% saved)

localize22.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(fma.f64 (sqrt.f64 2) (*.f64 1/6 (sqrt.f64 (neg.f64 (log.f64 u1)))) 1/2)
✓	0.4b	(*.f64 (sqrt.f64 2) (sqrt.f64 (neg.f64 (log.f64 u1))))
✓	0.4b	(*.f64 1/6 (sqrt.f64 (neg.f64 (log.f64 u1))))
✓	1.6b	(pow.f64 (PI.f64) 4)

series72.0ms (1.3%)

Counts

4 → 28

Calls

4 calls:

25.0ms	(fma.f64 (sqrt.f64 2) (*.f64 1/6 (sqrt.f64 (neg.f64 (log.f64 u1)))) 1/2)
23.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (neg.f64 (log.f64 u1))))
23.0ms	(*.f64 1/6 (sqrt.f64 (neg.f64 (log.f64 u1))))
0.0ms	(pow.f64 (PI.f64) 4)

rewrite50.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

558×	`log-prod_binary64`
224×	`expm1-udef_binary64`
224×	`log1p-udef_binary64`
201×	`log-pow_binary64`
137×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	41
1	307	35
2	3324	33

Stop Event

1×	node limit

Counts

4 → 80

Calls

4 calls:

49.0ms	(fma.f64 (sqrt.f64 2) (*.f64 1/6 (sqrt.f64 (neg.f64 (log.f64 u1)))) 1/2)
49.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (neg.f64 (log.f64 u1))))
49.0ms	(*.f64 1/6 (sqrt.f64 (neg.f64 (log.f64 u1))))
49.0ms	(pow.f64 (PI.f64) 4)

simplify54.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

884×	`fma-neg_binary64`
689×	`fma-def_binary64`
646×	`distribute-rgt-in_binary64`
448×	`distribute-lft-in_binary64`
265×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	368
1	55	368
2	79	368
3	116	368
4	168	368
5	332	368
6	483	368
7	1121	368
8	2274	368
9	2932	368
10	3470	368
11	4053	368
12	4732	368

Stop Event

1×	node limit

Counts

108 → 90

prune97.0ms (1.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	90	5	95

Error

Counts

95 → 5

Alt Table

Status	Error	Program
✓	0.3b	(fma.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (.f64 u2 (PI.f64)))))) 1/2)
	0.5b	(-.f64 (/.f64 (.f64 (.f64 (log.f64 u1) -1/18) (pow.f64 (cos.f64 (.f64 2 (.f64 (PI.f64) u2))) 2)) (fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 2 (.f64 (PI.f64) u2))) -1/2)) (/.f64 1/4 (fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 2 (.f64 (PI.f64) u2))) -1/2)))
✓	0.3b	(+.f64 (fma.f64 (sqrt.f64 2) (.f64 1/6 (sqrt.f64 (neg.f64 (log.f64 u1)))) 1/2) (.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (neg.f64 (log.f64 u1)))) (+.f64 (.f64 1/9 (.f64 (pow.f64 u2 4) (pow.f64 (PI.f64) 4))) (.f64 (pow.f64 (PI.f64) 2) (.f64 u2 (.f64 u2 -1/3))))))
	0.3b	(+.f64 (.f64 (sqrt.f64 (expm1.f64 (log1p.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)

Compiler

Compiled 3883 to 2768 computations (28.7% saved)

regimes1.5s (26.6%)

Accuracy

Total 0.5b remaining (96.7%)

Threshold costs 0.5b (96.7%)

Counts

121 → 1

Compiler

Compiled 30092 to 25802 computations (14.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
3×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	62
1	42	62
2	44	62
3	45	62

Stop Event

1×

saturated

end125.0ms (2.2%)

Compiler: Compiled 220 to 175 computations (20.5% saved)

Details

analyze90.0ms (1.6%)

sample2.0s (34.1%)

simplify50.0ms (0.9%)

prune4.0ms (0.1%)

localize15.0ms (0.3%)

series400.0ms (7%)

rewrite65.0ms (1.1%)

simplify58.0ms (1%)

prune186.0ms (3.3%)

localize11.0ms (0.2%)

series183.0ms (3.2%)

rewrite61.0ms (1.1%)

simplify49.0ms (0.8%)

prune129.0ms (2.3%)

localize13.0ms (0.2%)

series310.0ms (5.4%)

rewrite58.0ms (1%)

simplify57.0ms (1%)

prune84.0ms (1.5%)

localize22.0ms (0.4%)

series72.0ms (1.3%)

rewrite50.0ms (0.9%)

simplify54.0ms (0.9%)

prune97.0ms (1.7%)

regimes1.5s (26.6%)

simplify3.0ms (0%)

end125.0ms (2.2%)

Profiling