Details

analyze330.0ms (5.1%)

Algorithm

1×

Search

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

Compiler

Compiled 28 to 26 computations (7.1% saved)

sample50.0ms (0.8%)

Algorithm

1×

intervals

Results

31.0ms	256×	body	128	valid
7.0ms	256×	pre	128	true

Compiler

Compiled 47 to 47 computations (0% saved)

simplify323.0ms (5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (159.0ms)

Iter	Nodes	Cost
0	5644	26

prune13.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.4b

Counts

2 → 1

Compiler

Compiled 32 to 32 computations (0% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1/2 (.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
0.1b	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
0.3b	(.f64 (.f64 2 PI.f64) u2)
0.4b	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`pow1_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64`
5×	`pow-prod-down_binary64`
4×	`cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64`
2×	`sqrt-pow1_binary64` `sqrt-prod_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `unswap-sqr_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 59

Calls

4 calls:

9.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
6.0ms	(.f64 (.f64 2 PI.f64) u2)
4.0ms	(+.f64 1/2 (.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
3.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))

series653.0ms (10.2%)

Counts

4 → 12

Calls

4 calls:

238.0ms	(+.f64 1/2 (.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
204.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
156.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
54.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify75.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5089	1090

prune106.0ms (1.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	65	6	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	6	72

Merged error: 0.0b

Counts

72 → 6

Compiler

Compiled 1598 to 1242 computations (22.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (neg.f64 (log.f64 u1)))
0.3b	(.f64 (.f64 2 PI.f64) u2)
0.4b	(.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)))
0.4b	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))

rewrite37.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`sqrt-prod_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`pow1_binary64`
19×	`associate-l_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`associate-r_binary64`
9×	`pow-prod-down_binary64`
8×	`distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
7×	`cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64` `log-pow_binary64` `unswap-sqr_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64` `*-commutative_binary64`
2×	`neg-mul-1_binary64`
1×	`sqrt-unprod_binary64` `rem-sqrt-square_binary64`

Counts

4 → 97

Calls

4 calls:

11.0ms	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))
9.0ms	(.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)))
6.0ms	(.f64 (.f64 2 PI.f64) u2)
3.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))

series517.0ms (8%)

Counts

4 → 12

Calls

4 calls:

189.0ms	(.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)))
156.0ms	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))
134.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
37.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify52.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4970	1396
1	4970	1396

prune139.0ms (2.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	108	7	115

Merged error: 0b

Counts

115 → 7

Compiler

Compiled 2528 to 1730 computations (31.6% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (neg.f64 (log.f64 u1)))
0.3b	(.f64 (.f64 2 PI.f64) u2)
0.3b	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) 1/6)
0.4b	(.f64 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) 1/6) (sqrt.f64 2))

rewrite34.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`sqrt-prod_binary64`
21×	`pow1_binary64`
20×	`add-sqr-sqrt_binary64`
17×	`associate-l_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
12×	`associate-r_binary64`
8×	`distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
7×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64` `log-pow_binary64`
3×	`*-commutative_binary64`
2×	`neg-mul-1_binary64` `unswap-sqr_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 92

Calls

4 calls:

9.0ms	(.f64 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) 1/6) (sqrt.f64 2))
8.0ms	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) 1/6)
6.0ms	(.f64 (.f64 2 PI.f64) u2)
3.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))

series477.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

199.0ms	(.f64 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) 1/6) (sqrt.f64 2))
133.0ms	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) 1/6)
109.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
36.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify66.0ms (1%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5206	1249

prune132.0ms (2.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	104	7	111

Merged error: 0b

Counts

111 → 7

Compiler

Compiled 2391 to 1629 computations (31.9% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
0.2b	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (sqrt.f64 1/6)))
0.3b	(.f64 (.f64 2 PI.f64) u2)
0.3b	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))

rewrite36.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`pow1_binary64`
19×	`pow-prod-down_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`add-sqr-sqrt_binary64`
12×	`sqrt-pow1_binary64`
11×	`associate-l_binary64`
10×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
9×	`sqrt-prod_binary64`
7×	`cbrt-unprod_binary64` `prod-exp_binary64`
6×	`pow1/2_binary64`
4×	`add-log-exp_binary64`
3×	`sqrt-unprod_binary64` `*-commutative_binary64`
2×	`unswap-sqr_binary64`

Counts

4 → 81

Calls

4 calls:

12.0ms	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (sqrt.f64 1/6)))
9.0ms	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))
6.0ms	(.f64 (.f64 2 PI.f64) u2)
3.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))

series563.0ms (8.8%)

Counts

4 → 12

Calls

4 calls:

211.0ms	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (sqrt.f64 1/6)))
184.0ms	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))
130.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
38.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify90.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4929	1122
1	4929	1122

prune124.0ms (1.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	1	3	4
Picked	0	1	1
Done	1	1	2
Total	94	6	100

Merged error: 0b

Counts

100 → 6

Compiler

Compiled 2093 to 1680 computations (19.7% saved)

regimes583.0ms (9.1%)

Compiler: Compiled 6042 to 5768 computations (4.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	26
1	23	26

end0.0ms (0%)

sample1.9s (30.2%)

Algorithm

1×

intervals

Results

857.0ms	8000×	body	128	valid
215.0ms	8000×	pre	128	true

Compiler

Compiled 634 to 605 computations (4.6% saved)

Details

analyze330.0ms (5.1%)

sample50.0ms (0.8%)

simplify323.0ms (5%)

prune13.0ms (0.2%)

localize14.0ms (0.2%)

rewrite27.0ms (0.4%)

series653.0ms (10.2%)

simplify75.0ms (1.2%)

prune106.0ms (1.6%)

localize14.0ms (0.2%)

rewrite37.0ms (0.6%)

series517.0ms (8%)

simplify52.0ms (0.8%)

prune139.0ms (2.2%)

localize14.0ms (0.2%)

rewrite34.0ms (0.5%)

series477.0ms (7.4%)

simplify66.0ms (1%)

prune132.0ms (2.1%)

localize14.0ms (0.2%)

rewrite36.0ms (0.6%)

series563.0ms (8.8%)

simplify90.0ms (1.4%)

prune124.0ms (1.9%)

regimes583.0ms (9.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.9s (30.2%)

Profiling