Details

analyze322.0ms (5.8%)

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 (0.9%)

Algorithm

1×

intervals

Results

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

Compiler

Compiled 47 to 47 computations (0% saved)

simplify317.0ms (5.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (154.0ms)

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: 0.3b

Counts

2 → 1

Compiler

Compiled 32 to 32 computations (0% saved)

localize14.0ms (0.3%)

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

rewrite27.0ms (0.5%)

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:

8.0ms	(.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)))

series581.0ms (10.5%)

Counts

4 → 12

Calls

4 calls:

241.0ms	(+.f64 1/2 (.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
157.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
147.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
35.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify73.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5077	1090

prune113.0ms (2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	61	10	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	10	72

Merged error: 0.0b

Counts

72 → 10

Compiler

Compiled 1664 to 1311 computations (21.2% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (neg.f64 (log.f64 u1)))
0.2b	(.f64 (.f64 2 PI.f64) u2)
0.3b	(.f64 1/6 (.f64 (cos.f64 (.f64 (.f64 2 PI.f64) u2)) (*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))))
0.4b	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))

rewrite41.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`sqrt-prod_binary64`
27×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
20×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
19×	`associate-l_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
12×	`pow-prod-down_binary64`
10×	`cbrt-unprod_binary64` `associate-r_binary64` `prod-exp_binary64`
8×	`distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_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 → 100

Calls

4 calls:

13.0ms	(.f64 1/6 (.f64 (cos.f64 (.f64 (.f64 2 PI.f64) u2)) (*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))))
10.0ms	(*.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)))

series569.0ms (10.3%)

Counts

4 → 12

Calls

4 calls:

228.0ms	(.f64 1/6 (.f64 (cos.f64 (.f64 (.f64 2 PI.f64) u2)) (*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))))
183.0ms	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))
118.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
39.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify62.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5516	1752

prune149.0ms (2.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	109	3	112
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	114	8	122

Merged error: 0b

Counts

122 → 8

Compiler

Compiled 2657 to 1847 computations (30.5% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1/2 (.f64 1/6 (.f64 (cos.f64 (.f64 (.f64 2 PI.f64) u2)) (sqrt.f64 (*.f64 (log.f64 u1) -2)))))
0.1b	(sqrt.f64 (*.f64 (log.f64 u1) -2))
0.2b	(.f64 (.f64 2 PI.f64) u2)
0.3b	(.f64 1/6 (.f64 (cos.f64 (.f64 (.f64 2 PI.f64) u2)) (sqrt.f64 (*.f64 (log.f64 u1) -2))))

rewrite26.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`pow1_binary64`
14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`pow-prod-down_binary64`
6×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `add-cube-cbrt_binary64` `prod-exp_binary64` `add-sqr-sqrt_binary64`
4×	`associate-r_binary64` `associate-l_binary64`
2×	`sqrt-pow1_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `+-commutative_binary64` `sqrt-prod_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 58

Calls

4 calls:

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

series549.0ms (9.9%)

Counts

4 → 12

Calls

4 calls:

198.0ms	(+.f64 1/2 (.f64 1/6 (.f64 (cos.f64 (.f64 (.f64 2 PI.f64) u2)) (sqrt.f64 (*.f64 (log.f64 u1) -2)))))
180.0ms	(.f64 1/6 (.f64 (cos.f64 (.f64 (.f64 2 PI.f64) u2)) (sqrt.f64 (*.f64 (log.f64 u1) -2))))
134.0ms	(sqrt.f64 (*.f64 (log.f64 u1) -2))
37.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify68.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4918	1318
1	4918	1318

prune88.0ms (1.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	70	8	78

Merged error: 0b

Counts

78 → 8

Compiler

Compiled 1595 to 1248 computations (21.8% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite35.0ms (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)))
8.0ms	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))
5.0ms	(.f64 (.f64 2 PI.f64) u2)
3.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))

series560.0ms (10.1%)

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)))
169.0ms	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))
132.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
42.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify70.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5073	1122

prune126.0ms (2.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	93	8	101

Merged error: 0b

Counts

101 → 8

Compiler

Compiled 2093 to 1680 computations (19.7% saved)

regimes138.0ms (2.5%)

Compiler: Compiled 1126 to 1112 computations (1.2% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	30
1	31	30

end0.0ms (0%)

sample1.5s (26.9%)

Algorithm

1×

intervals

Results

865.0ms	8000×	body	128	valid
203.0ms	8000×	pre	128	true

Compiler

Compiled 208 to 204 computations (1.9% saved)

Details

analyze322.0ms (5.8%)

sample50.0ms (0.9%)

simplify317.0ms (5.7%)

prune14.0ms (0.2%)

localize14.0ms (0.3%)

rewrite27.0ms (0.5%)

series581.0ms (10.5%)

simplify73.0ms (1.3%)

prune113.0ms (2%)

localize15.0ms (0.3%)

rewrite41.0ms (0.7%)

series569.0ms (10.3%)

simplify62.0ms (1.1%)

prune149.0ms (2.7%)

localize16.0ms (0.3%)

rewrite26.0ms (0.5%)

series549.0ms (9.9%)

simplify68.0ms (1.2%)

prune88.0ms (1.6%)

localize15.0ms (0.3%)

rewrite35.0ms (0.6%)

series560.0ms (10.1%)

simplify70.0ms (1.3%)

prune126.0ms (2.3%)

regimes138.0ms (2.5%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.5s (26.9%)

Profiling