Details

analyze263.0ms (4.7%)

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 28 to 26 computations (7.1% saved)

sample41.0ms (0.7%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	128	valid
7.0ms	256×	pre	128	true

Compiler

Compiled 47 to 47 computations (0% saved)

simplify265.0ms (4.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (160.0ms)

Iter	Nodes	Cost
0	5644	26

prune7.0ms (0.1%)

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

Error

0.3b

Counts

2 → 1

Compiler

Compiled 32 to 32 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)))
0.3b	(.f64 (.f64 2 PI.f64) u2)
0.4b	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))

rewrite25.0ms (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:

8.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
5.0ms	(.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))))
2.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))

series343.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

130.0ms	(+.f64 1/2 (.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
116.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
77.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
19.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify85.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4904	1090
1	4904	1090

prune107.0ms (1.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	63	8	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	8	72

Error

0.0b

Counts

72 → 8

Compiler

Compiled 1669 to 1306 computations (21.7% saved)

localize14.0ms (0.3%)

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

rewrite37.0ms (0.7%)

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:

11.0ms	(.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)
2.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))

series309.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

117.0ms	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (sqrt.f64 1/6)))
104.0ms	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))
66.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
21.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify78.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5026	1122

prune142.0ms (2.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	94	7	101

Error

Counts

101 → 7

Compiler

Compiled 2252 to 1831 computations (18.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (*.f64 (log.f64 u1) -1/3))
0.2b	(.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 (log.f64 u1) -1/3)))
0.3b	(.f64 (.f64 2 PI.f64) u2)
0.4b	(*.f64 (log.f64 u1) -1/3)

rewrite26.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`pow1_binary64`
16×	`add-sqr-sqrt_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`associate-l_binary64`
10×	`pow-prod-down_binary64` `-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
6×	`sqrt-pow1_binary64` `sqrt-prod_binary64`
5×	`cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64`
3×	`pow1/2_binary64` `unswap-sqr_binary64` `*-commutative_binary64`
1×	`log-pow_binary64` `sqrt-unprod_binary64`

Counts

4 → 75

Calls

4 calls:

8.0ms	(.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 (log.f64 u1) -1/3)))
5.0ms	(.f64 (.f64 2 PI.f64) u2)
4.0ms	(*.f64 (log.f64 u1) -1/3)
3.0ms	(sqrt.f64 (*.f64 (log.f64 u1) -1/3))

series239.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

91.0ms	(.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 (log.f64 u1) -1/3)))
72.0ms	(sqrt.f64 (*.f64 (log.f64 u1) -1/3))
54.0ms	(*.f64 (log.f64 u1) -1/3)
21.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify73.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5161	940

prune116.0ms (2.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	87	7	94

Error

Counts

94 → 7

Compiler

Compiled 1923 to 1515 computations (21.2% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

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))))
0.9b	(exp.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))))

rewrite21.0ms (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×	`pow1/2_binary64` `rem-exp-log_binary64` `unswap-sqr_binary64` `exp-to-pow_binary64` `exp-prod_binary64`

Counts

4 → 58

Calls

4 calls:

6.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
5.0ms	(.f64 (.f64 2 PI.f64) u2)
2.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
2.0ms	(exp.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))))

series304.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

128.0ms	(exp.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))))
89.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
68.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
19.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify88.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4884	772
1	4884	772

prune87.0ms (1.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	70	7	77

Error

Counts

77 → 7

Compiler

Compiled 1495 to 1176 computations (21.3% saved)

regimes810.0ms (14.6%)

Accuracy

Total 0.2b remaining (99.3%)

Threshold costs 0.2b (99.3%)

Compiler

Compiled 8860 to 8532 computations (3.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	23
1	20	23

end0.0ms (0%)

sample2.0s (36.6%)

Algorithm

1×

intervals

Results

743.0ms	8000×	body	128	valid
207.0ms	8000×	pre	128	true

Compiler

Compiled 855 to 823 computations (3.7% saved)

Details

analyze263.0ms (4.7%)

sample41.0ms (0.7%)

simplify265.0ms (4.8%)

prune7.0ms (0.1%)

localize14.0ms (0.2%)

rewrite25.0ms (0.4%)

series343.0ms (6.2%)

simplify85.0ms (1.5%)

prune107.0ms (1.9%)

localize14.0ms (0.3%)

rewrite37.0ms (0.7%)

series309.0ms (5.6%)

simplify78.0ms (1.4%)

prune142.0ms (2.6%)

localize13.0ms (0.2%)

rewrite26.0ms (0.5%)

series239.0ms (4.3%)

simplify73.0ms (1.3%)

prune116.0ms (2.1%)

localize15.0ms (0.3%)

rewrite21.0ms (0.4%)

series304.0ms (5.5%)

simplify88.0ms (1.6%)

prune87.0ms (1.6%)

regimes810.0ms (14.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.0s (36.6%)

Profiling