Details

analyze320.0ms (5%)

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)

simplify337.0ms (5.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (160.0ms)

Iter	Nodes	Cost
0	5644	26

prune10.0ms (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 67 to 67 computations (0% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(+.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)
0.4b	(.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)))

series601.0ms (9.3%)

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))))
193.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
130.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
36.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify73.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5089	1090

prune317.0ms (4.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	62	9	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	9	72

Merged error: 0b

Counts

72 → 9

Compiler

Compiled 4938 to 4377 computations (11.4% saved)

localize15.0ms (0.2%)

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

rewrite37.0ms (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)))

series592.0ms (9.2%)

Counts

4 → 12

Calls

4 calls:

228.0ms	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (sqrt.f64 1/6)))
189.0ms	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))
136.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
38.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify92.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4929	1122
1	4929	1122

prune233.0ms (3.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	90	3	93
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	95	7	102

Merged error: 0b

Counts

102 → 7

Compiler

Compiled 3760 to 3257 computations (13.4% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite30.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

10.0ms	(.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 1/6 (sqrt.f64 2)))
6.0ms	(.f64 (.f64 2 PI.f64) u2)
4.0ms	(+.f64 1/2 (.f64 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 1/6 (sqrt.f64 2))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
3.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))

series669.0ms (10.4%)

Counts

4 → 12

Calls

4 calls:

280.0ms	(+.f64 1/2 (.f64 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 1/6 (sqrt.f64 2))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
205.0ms	(.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 1/6 (sqrt.f64 2)))
138.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
45.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify82.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4894	1531
1	4894	1531

prune131.0ms (2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	93	7	100

Merged error: 0b

Counts

100 → 7

Compiler

Compiled 2410 to 1706 computations (29.2% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 1/2 (.f64 (pow.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36) 1/2) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
0.1b	(pow.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36) 1/2)
0.2b	(.f64 (.f64 2 PI.f64) u2)
0.4b	(.f64 (.f64 -2 (log.f64 u1)) 1/36)

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`pow1_binary64` `add-exp-log_binary64`
14×	`add-cbrt-cube_binary64`
9×	`pow-prod-down_binary64` `prod-exp_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
6×	`add-log-exp_binary64` `cbrt-unprod_binary64` `associate-r_binary64`
3×	`pow-unpow_binary64` `pow-pow_binary64` `pow-exp_binary64`
2×	`associate-l_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `sqr-pow_binary64` `unpow1/2_binary64` `unpow-prod-down_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 67

Calls

4 calls:

6.0ms	(.f64 (.f64 -2 (log.f64 u1)) 1/36)
6.0ms	(pow.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36) 1/2)
6.0ms	(.f64 (.f64 2 PI.f64) u2)
5.0ms	(+.f64 1/2 (.f64 (pow.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36) 1/2) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))

series641.0ms (10%)

Counts

4 → 12

Calls

4 calls:

288.0ms	(pow.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36) 1/2)
222.0ms	(+.f64 1/2 (.f64 (pow.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36) 1/2) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
92.0ms	(.f64 (.f64 -2 (log.f64 u1)) 1/36)
38.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify62.0ms (1%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4868	1005
1	4868	1005

prune181.0ms (2.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	77	2	79
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	80	6	86

Merged error: 0b

Counts

86 → 6

Compiler

Compiled 2839 to 2418 computations (14.8% saved)

regimes131.0ms (2%)

Compiler: Compiled 940 to 914 computations (2.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	24
1	19	24

end0.0ms (0%)

sample1.7s (26.8%)

Algorithm

1×

intervals

Results

983.0ms	8000×	body	128	valid
226.0ms	8000×	pre	128	true

Compiler

Compiled 167 to 161 computations (3.6% saved)

Details

analyze320.0ms (5%)

sample50.0ms (0.8%)

simplify337.0ms (5.2%)

prune10.0ms (0.2%)

localize14.0ms (0.2%)

rewrite27.0ms (0.4%)

series601.0ms (9.3%)

simplify73.0ms (1.1%)

prune317.0ms (4.9%)

localize15.0ms (0.2%)

rewrite37.0ms (0.6%)

series592.0ms (9.2%)

simplify92.0ms (1.4%)

prune233.0ms (3.6%)

localize15.0ms (0.2%)

rewrite30.0ms (0.5%)

series669.0ms (10.4%)

simplify82.0ms (1.3%)

prune131.0ms (2%)

localize18.0ms (0.3%)

rewrite29.0ms (0.5%)

series641.0ms (10%)

simplify62.0ms (1%)

prune181.0ms (2.8%)

regimes131.0ms (2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.7s (26.8%)

Profiling