Details

analyze325.0ms (4.4%)

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)

sample52.0ms (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)

simplify330.0ms (4.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (151.0ms)

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))))
0.1b	(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))))

rewrite26.0ms (0.3%)

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)))

series560.0ms (7.5%)

Counts

4 → 12

Calls

4 calls:

231.0ms	(+.f64 1/2 (.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
166.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
127.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
36.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify72.0ms (1%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5077	1090

prune112.0ms (1.5%)

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

Merged error: 0b

Counts

72 → 8

Compiler

Compiled 1682 to 1315 computations (21.8% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (neg.f64 (log.f64 u1)))
0.3b	(.f64 (.f64 2 PI.f64) u2)
0.4b	(.f64 1/6 (.f64 (cos.f64 (.f64 (.f64 2 PI.f64) u2)) (*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))))
0.5b	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))

rewrite40.0ms (0.5%)

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)))

series586.0ms (7.9%)

Counts

4 → 12

Calls

4 calls:

244.0ms	(.f64 1/6 (.f64 (cos.f64 (.f64 (.f64 2 PI.f64) u2)) (*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))))
175.0ms	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))
129.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
38.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify63.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5516	1752

prune149.0ms (2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	114	6	120

Merged error: 0b

Counts

120 → 6

Compiler

Compiled 2663 to 1841 computations (30.9% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 2 PI.f64) u2)
0.4b	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
0.4b	(*.f64 (log.f64 u1) -1/18)
0.5b	(/.f64 (-.f64 1/4 (.f64 (.f64 (log.f64 u1) -1/18) (.f64 (cos.f64 (.f64 (.f64 2 PI.f64) u2)) (cos.f64 (.f64 (.f64 2 PI.f64) u2))))) (-.f64 1/2 (.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)))))

rewrite36.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
15×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`pow1_binary64`
10×	`associate-r_binary64`
9×	`times-frac_binary64`
8×	`associate-l_binary64`
5×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64` `*-commutative_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `flip--_binary64`
1×	`cbrt-undiv_binary64` `log-pow_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `sqrt-prod_binary64`

Counts

4 → 88

Calls

4 calls:

7.0ms	(/.f64 (-.f64 1/4 (.f64 (.f64 (log.f64 u1) -1/18) (.f64 (cos.f64 (.f64 (.f64 2 PI.f64) u2)) (cos.f64 (.f64 (.f64 2 PI.f64) u2))))) (-.f64 1/2 (.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)))))
6.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
5.0ms	(.f64 (.f64 2 PI.f64) u2)
4.0ms	(*.f64 (log.f64 u1) -1/18)

series1.1s (14.9%)

Counts

4 → 12

Calls

4 calls:

815.0ms	(/.f64 (-.f64 1/4 (.f64 (.f64 (log.f64 u1) -1/18) (.f64 (cos.f64 (.f64 (.f64 2 PI.f64) u2)) (cos.f64 (.f64 (.f64 2 PI.f64) u2))))) (-.f64 1/2 (.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)))))
152.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
99.0ms	(*.f64 (log.f64 u1) -1/18)
40.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify55.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4917	3229
1	4917	3229

prune260.0ms (3.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	100	6	106

Merged error: 0b

Counts

106 → 6

Compiler

Compiled 4716 to 3543 computations (24.9% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite28.0ms (0.4%)

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:

7.0ms	(.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)))))

series856.0ms (11.5%)

Counts

4 → 12

Calls

4 calls:

340.0ms	(exp.f64 (log.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))))
304.0ms	(log.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))))
174.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
37.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify65.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5001	905

prune93.0ms (1.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	75	6	81

Merged error: 0b

Counts

81 → 6

Compiler

Compiled 1613 to 1267 computations (21.5% saved)

regimes595.0ms (8%)

Compiler: Compiled 6239 to 5945 computations (4.7% 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%)

sample1.9s (26.1%)

Algorithm

1×

intervals

Results

898.0ms	8000×	body	128	valid
210.0ms	8000×	pre	128	true

Compiler

Compiled 613 to 584 computations (4.7% saved)

Details

analyze325.0ms (4.4%)

sample52.0ms (0.7%)

simplify330.0ms (4.4%)

prune14.0ms (0.2%)

localize15.0ms (0.2%)

rewrite26.0ms (0.3%)

series560.0ms (7.5%)

simplify72.0ms (1%)

prune112.0ms (1.5%)

localize15.0ms (0.2%)

rewrite40.0ms (0.5%)

series586.0ms (7.9%)

simplify63.0ms (0.9%)

prune149.0ms (2%)

localize24.0ms (0.3%)

rewrite36.0ms (0.5%)

series1.1s (14.9%)

simplify55.0ms (0.7%)

prune260.0ms (3.5%)

localize17.0ms (0.2%)

rewrite28.0ms (0.4%)

series856.0ms (11.5%)

simplify65.0ms (0.9%)

prune93.0ms (1.2%)

regimes595.0ms (8%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.9s (26.1%)

Profiling