Details

analyze324.0ms (5.4%)

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)

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)

simplify330.0ms (5.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (158.0ms)

Iter	Nodes	Cost
0	5644	26

prune10.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.3b

Counts

2 → 1

Compiler

Compiled 70 to 70 computations (0% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite43.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-exp-log_binary64`
25×	`add-sqr-sqrt_binary64`
24×	`prod-exp_binary64`
16×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
13×	`times-frac_binary64`
12×	`pow1_binary64`
10×	`pow-exp_binary64`
8×	`associate-r_binary64` `div-exp_binary64`
6×	`add-log-exp_binary64` `unswap-sqr_binary64`
5×	`pow-to-exp_binary64` `cbrt-unprod_binary64` `sqr-pow_binary64`
4×	`pow-prod-down_binary64` `1-exp_binary64` `rec-exp_binary64`
3×	`pow-unpow_binary64`
2×	`pow-pow_binary64` `unpow-prod-down_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `cbrt-undiv_binary64` `unpow1/2_binary64` `div-inv_binary64` `+-commutative_binary64` `flip-+_binary64` `associate-*l/_binary64` `sum-log_binary64`

Counts

4 → 98

Calls

4 calls:

12.0ms	(+.f64 (.f64 (.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2)) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))) 1/2)
11.0ms	(.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2))
5.0ms	(.f64 (.f64 2 PI.f64) u2)
4.0ms	(pow.f64 (*.f64 -2 (log.f64 u1)) 1/2)

series733.0ms (12.3%)

Counts

4 → 12

Calls

4 calls:

265.0ms	(pow.f64 (*.f64 -2 (log.f64 u1)) 1/2)
242.0ms	(+.f64 (.f64 (.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2)) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))) 1/2)
181.0ms	(.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2))
44.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify93.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4883	1685
1	4883	1685

prune452.0ms (7.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	102	8	110
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	8	111

Merged error: 0b

Counts

111 → 8

Compiler

Compiled 7116 to 6404 computations (10% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
12×	`pow1_binary64` `times-frac_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64`
5×	`sqrt-prod_binary64`
4×	`pow-prod-down_binary64` `associate-/l*_binary64`
3×	`associate-/r_binary64` `cbrt-unprod_binary64` `associate-r*_binary64` `prod-exp_binary64`
2×	`sqrt-pow1_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 71

Calls

4 calls:

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

series576.0ms (9.6%)

Counts

4 → 12

Calls

4 calls:

233.0ms	(+.f64 (.f64 (/.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 6) (cos.f64 (.f64 (.f64 2 PI.f64) u2))) 1/2)
170.0ms	(/.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 6)
127.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
45.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify65.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5142	1393

prune131.0ms (2.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	83	8	91

Merged error: 0b

Counts

91 → 8

Compiler

Compiled 2310 to 1876 computations (18.8% saved)

localize18.0ms (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 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)))
0.4b	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))

rewrite36.0ms (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:

11.0ms	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))
9.0ms	(.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)))

series507.0ms (8.5%)

Counts

4 → 12

Calls

4 calls:

179.0ms	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))
175.0ms	(.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)))
112.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
40.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify50.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4970	1396
1	4970	1396

prune146.0ms (2.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	110	7	117

Merged error: 0b

Counts

117 → 7

Compiler

Compiled 2681 to 1884 computations (29.7% saved)

localize14.0ms (0.2%)

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 (sqrt.f64 (neg.f64 (log.f64 u1))) 1/6)
0.4b	(.f64 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) 1/6) (sqrt.f64 2))

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`sqrt-prod_binary64`
21×	`pow1_binary64`
20×	`add-sqr-sqrt_binary64`
17×	`associate-l_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
12×	`associate-r_binary64`
8×	`distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
7×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64` `log-pow_binary64`
3×	`*-commutative_binary64`
2×	`neg-mul-1_binary64` `unswap-sqr_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 92

Calls

4 calls:

9.0ms	(.f64 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) 1/6) (sqrt.f64 2))
8.0ms	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) 1/6)
5.0ms	(.f64 (.f64 2 PI.f64) u2)
3.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))

series530.0ms (8.9%)

Counts

4 → 12

Calls

4 calls:

194.0ms	(.f64 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) 1/6) (sqrt.f64 2))
156.0ms	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) 1/6)
133.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
47.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify67.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5206	1249

prune121.0ms (2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	104	7	111

Merged error: 0b

Counts

111 → 7

Compiler

Compiled 2270 to 1517 computations (33.2% saved)

regimes110.0ms (1.8%)

Compiler: Compiled 842 to 842 computations (0% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	26
1	22	26

end0.0ms (0%)

sample1.5s (24.6%)

Algorithm

1×

intervals

Results

873.0ms	8000×	body	128	valid
204.0ms	8000×	pre	128	true

Compiler

Compiled 178 to 176 computations (1.1% saved)

Details

analyze324.0ms (5.4%)

sample50.0ms (0.8%)

simplify330.0ms (5.5%)

prune10.0ms (0.2%)

localize18.0ms (0.3%)

rewrite43.0ms (0.7%)

series733.0ms (12.3%)

simplify93.0ms (1.6%)

prune452.0ms (7.6%)

localize12.0ms (0.2%)

rewrite29.0ms (0.5%)

series576.0ms (9.6%)

simplify65.0ms (1.1%)

prune131.0ms (2.2%)

localize18.0ms (0.3%)

rewrite36.0ms (0.6%)

series507.0ms (8.5%)

simplify50.0ms (0.8%)

prune146.0ms (2.4%)

localize14.0ms (0.2%)

rewrite33.0ms (0.5%)

series530.0ms (8.9%)

simplify67.0ms (1.1%)

prune121.0ms (2%)

regimes110.0ms (1.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.5s (24.6%)

Profiling