Details

analyze321.0ms (4.7%)

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)

sample51.0ms (0.7%)

Algorithm

1×

intervals

Results

32.0ms	256×	body	128	valid
7.0ms	256×	pre	128	true

Compiler

Compiled 47 to 47 computations (0% saved)

simplify327.0ms (4.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (162.0ms)

Iter	Nodes	Cost
0	5644	26

prune14.0ms (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)

localize15.0ms (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))))
0.2b	(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)))

series568.0ms (8.3%)

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))))
163.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
130.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
37.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify80.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5089	1090

prune111.0ms (1.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	64	7	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	7	72

Merged error: 0.0b

Counts

72 → 7

Compiler

Compiled 1622 to 1263 computations (22.1% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(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))

rewrite37.0ms (0.5%)

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)))

series588.0ms (8.6%)

Counts

4 → 12

Calls

4 calls:

217.0ms	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (sqrt.f64 1/6)))
190.0ms	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))
146.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
36.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify91.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4929	1122
1	4929	1122

prune134.0ms (2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

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

Merged error: 0.0b

Counts

100 → 6

Compiler

Compiled 2210 to 1787 computations (19.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1/2 (.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
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)

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

6.0ms	(.f64 (.f64 -2 (log.f64 u1)) 1/36)
6.0ms	(.f64 (.f64 2 PI.f64) u2)
4.0ms	(sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36))
3.0ms	(+.f64 1/2 (.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))

series495.0ms (7.3%)

Counts

4 → 12

Calls

4 calls:

223.0ms	(+.f64 1/2 (.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
129.0ms	(sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36))
103.0ms	(.f64 (.f64 -2 (log.f64 u1)) 1/36)
40.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify102.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4819	920
1	4819	920

prune89.0ms (1.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	3	1	4
Picked	0	1	1
Done	0	1	1
Total	72	5	77

Merged error: 0.0b

Counts

77 → 5

Compiler

Compiled 1419 to 1076 computations (24.2% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1/2 (.f64 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 1/18)) (cos.f64 (.f64 (.f64 2 PI.f64) u2))))
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))) (sqrt.f64 1/18))

rewrite30.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`sqrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
18×	`pow1_binary64`
16×	`associate-l_binary64`
14×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`associate-r_binary64`
8×	`distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
6×	`pow-prod-down_binary64` `add-log-exp_binary64`
4×	`cbrt-unprod_binary64` `log-pow_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64`
2×	`neg-mul-1_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `sqrt-unprod_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 90

Calls

4 calls:

11.0ms	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 1/18))
5.0ms	(.f64 (.f64 2 PI.f64) u2)
4.0ms	(+.f64 1/2 (.f64 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 1/18)) (cos.f64 (.f64 (.f64 2 PI.f64) u2))))
3.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))

series600.0ms (8.8%)

Counts

4 → 12

Calls

4 calls:

254.0ms	(+.f64 1/2 (.f64 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 1/18)) (cos.f64 (.f64 (.f64 2 PI.f64) u2))))
179.0ms	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 1/18))
130.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
37.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify69.0ms (1%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4939	1565
1	4939	1565

prune115.0ms (1.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	102	5	107

Merged error: 0.0b

Counts

107 → 5

Compiler

Compiled 2127 to 1363 computations (35.9% saved)

regimes811.0ms (11.9%)

Compiler: Compiled 8632 to 8208 computations (4.9% saved)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	23
1	19	23

end0.0ms (0%)

sample2.1s (30.4%)

Algorithm

1×

intervals

Results

862.0ms	8000×	body	128	valid
221.0ms	8000×	pre	128	true

Compiler

Compiled 774 to 736 computations (4.9% saved)

Details

analyze321.0ms (4.7%)

sample51.0ms (0.7%)

simplify327.0ms (4.8%)

prune14.0ms (0.2%)

localize15.0ms (0.2%)

rewrite27.0ms (0.4%)

series568.0ms (8.3%)

simplify80.0ms (1.2%)

prune111.0ms (1.6%)

localize16.0ms (0.2%)

rewrite37.0ms (0.5%)

series588.0ms (8.6%)

simplify91.0ms (1.3%)

prune134.0ms (2%)

localize13.0ms (0.2%)

rewrite24.0ms (0.3%)

series495.0ms (7.3%)

simplify102.0ms (1.5%)

prune89.0ms (1.3%)

localize16.0ms (0.2%)

rewrite30.0ms (0.4%)

series600.0ms (8.8%)

simplify69.0ms (1%)

prune115.0ms (1.7%)

regimes811.0ms (11.9%)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample2.1s (30.4%)

Profiling