Details

analyze529.0ms (10%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4873	52
1	4873	52
0	2	2
1	2	2

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)

sample49.0ms (0.9%)

Algorithm

1×

intervals

Results

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

Compiler

Compiled 47 to 47 computations (0% saved)

simplify166.0ms (3.1%)

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

0.4b

Counts

2 → 1

Compiler

Compiled 32 to 32 computations (0% saved)

localize14.0ms (0.3%)

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))))

rewrite24.0ms (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)
3.0ms	(+.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)))

series323.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

126.0ms	(+.f64 1/2 (.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
110.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
65.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
21.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify85.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4904	1090
1	4904	1090

prune105.0ms (2%)

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

Error

Counts

72 → 9

Compiler

Compiled 1674 to 1313 computations (21.6% 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)
0.2b	(.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))

rewrite35.0ms (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))
8.0ms	(.f64 (.f64 2 PI.f64) u2)
2.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))

series299.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

110.0ms	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (sqrt.f64 1/6)))
95.0ms	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))
73.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
21.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify76.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5026	1122

prune138.0ms (2.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	95	7	102

Error

Counts

102 → 7

Compiler

Compiled 2212 to 1797 computations (18.8% saved)

localize14.0ms (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)
0.4b	(.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))

rewrite34.0ms (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:

10.0ms	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))
8.0ms	(.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)))
5.0ms	(.f64 (.f64 2 PI.f64) u2)
3.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))

series275.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

101.0ms	(.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)))
92.0ms	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))
63.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
19.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify51.0ms (1%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4949	1396
1	4949	1396

prune123.0ms (2.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	109	7	116

Error

Counts

116 → 7

Compiler

Compiled 2490 to 1699 computations (31.8% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite27.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`pow1_binary64`
14×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64`
10×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
7×	`associate-r_binary64`
6×	`pow-prod-down_binary64`
5×	`prod-exp_binary64` `exp-prod_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `log-pow_binary64` `associate-l_binary64`
2×	`log-prod_binary64` `rem-log-exp_binary64` `*-commutative_binary64`
1×	`rem-exp-log_binary64` `unswap-sqr_binary64` `exp-sum_binary64` `sqrt-prod_binary64`

Counts

4 → 63

Calls

4 calls:

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

series449.0ms (8.5%)

Counts

4 → 12

Calls

4 calls:

171.0ms	(exp.f64 (log.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))))
169.0ms	(log.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))))
91.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
18.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify68.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4959	905
1	4959	905

prune91.0ms (1.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	75	7	82

Error

Counts

82 → 7

Compiler

Compiled 1613 to 1267 computations (21.5% saved)

regimes523.0ms (9.9%)

Accuracy

Total 0.2b remaining (99.2%)

Threshold costs 0.2b (99.2%)

Compiler

Compiled 5642 to 5358 computations (5% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	26
1	23	26

end0.0ms (0%)

sample1.8s (33.1%)

Algorithm

1×

intervals

Results

755.0ms	8000×	body	128	valid
197.0ms	8000×	pre	128	true

Compiler

Compiled 594 to 564 computations (5.1% saved)

Details

analyze529.0ms (10%)

sample49.0ms (0.9%)

simplify166.0ms (3.1%)

prune7.0ms (0.1%)

localize14.0ms (0.3%)

rewrite24.0ms (0.4%)

series323.0ms (6.1%)

simplify85.0ms (1.6%)

prune105.0ms (2%)

localize15.0ms (0.3%)

rewrite35.0ms (0.7%)

series299.0ms (5.7%)

simplify76.0ms (1.4%)

prune138.0ms (2.6%)

localize14.0ms (0.3%)

rewrite34.0ms (0.6%)

series275.0ms (5.2%)

simplify51.0ms (1%)

prune123.0ms (2.3%)

localize16.0ms (0.3%)

rewrite27.0ms (0.5%)

series449.0ms (8.5%)

simplify68.0ms (1.3%)

prune91.0ms (1.7%)

regimes523.0ms (9.9%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.8s (33.1%)

Profiling