Details

analyze318.0ms (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)

simplify325.0ms (5.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (157.0ms)

Iter	Nodes	Cost
0	5644	26

prune15.0ms (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: 0.4b

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

rewrite46.0ms (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:

13.0ms	(+.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)
12.0ms	(.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2))
6.0ms	(.f64 (.f64 2 PI.f64) u2)
4.0ms	(pow.f64 (*.f64 -2 (log.f64 u1)) 1/2)

series697.0ms (11%)

Counts

4 → 12

Calls

4 calls:

264.0ms	(pow.f64 (*.f64 -2 (log.f64 u1)) 1/2)
223.0ms	(+.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)
174.0ms	(.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2))
36.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify90.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4883	1685
1	4883	1685

prune407.0ms (6.4%)

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 6345 to 5683 computations (10.4% saved)

localize13.0ms (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)))
0.3b	(.f64 (.f64 2 PI.f64) u2)
0.3b	(/.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 6)

rewrite31.0ms (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:

10.0ms	(+.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)))

series585.0ms (9.2%)

Counts

4 → 12

Calls

4 calls:

225.0ms	(+.f64 (.f64 (/.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 6) (cos.f64 (.f64 (.f64 2 PI.f64) u2))) 1/2)
174.0ms	(/.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 6)
146.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
40.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify63.0ms (1%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5142	1393

prune184.0ms (2.9%)

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 3066 to 2604 computations (15.1% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite45.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`pow1_binary64`
21×	`associate-l_binary64`
20×	`add-sqr-sqrt_binary64`
19×	`pow-prod-down_binary64` `sqrt-prod_binary64`
16×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`sqrt-pow1_binary64`
10×	`associate-r_binary64`
9×	`times-frac_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`
1×	`div-inv_binary64` `sqrt-div_binary64` `associate-*l/_binary64`

Counts

4 → 92

Calls

4 calls:

16.0ms	(.f64 (sqrt.f64 (/.f64 1 6)) (.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (sqrt.f64 1/6)))
11.0ms	(.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)))

series580.0ms (9.1%)

Counts

4 → 12

Calls

4 calls:

217.0ms	(.f64 (sqrt.f64 (/.f64 1 6)) (.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (sqrt.f64 1/6)))
187.0ms	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))
139.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
37.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify77.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4984	1333
1	4984	1333

prune228.0ms (3.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	103	9	112

Merged error: 0b

Counts

112 → 9

Compiler

Compiled 3666 to 3175 computations (13.4% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 (pow.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36) 1/2) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))) 1/2)
0.1b	(pow.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36) 1/2)
0.3b	(.f64 (.f64 2 PI.f64) u2)
0.4b	(.f64 (.f64 -2 (log.f64 u1)) 1/36)

rewrite32.0ms (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:

8.0ms	(+.f64 (.f64 (pow.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36) 1/2) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))) 1/2)
6.0ms	(pow.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36) 1/2)
6.0ms	(.f64 (.f64 2 PI.f64) u2)
6.0ms	(.f64 (.f64 -2 (log.f64 u1)) 1/36)

series620.0ms (9.8%)

Counts

4 → 12

Calls

4 calls:

268.0ms	(pow.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36) 1/2)
208.0ms	(+.f64 (.f64 (pow.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36) 1/2) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))) 1/2)
106.0ms	(.f64 (.f64 -2 (log.f64 u1)) 1/36)
38.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify79.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4872	1005
1	4872	1005

prune194.0ms (3.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	77	2	79
Fresh	3	3	6
Picked	1	0	1
Done	0	2	2
Total	81	7	88

Merged error: 0b

Counts

88 → 7

Compiler

Compiled 2981 to 2578 computations (13.5% saved)

regimes145.0ms (2.3%)

Compiler: Compiled 1097 to 1081 computations (1.5% 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%)

sample1.5s (23.2%)

Algorithm

1×

intervals

Results

855.0ms	8000×	body	128	valid
209.0ms	8000×	pre	128	true

Compiler

Compiled 182 to 178 computations (2.2% saved)

Details

analyze318.0ms (5%)

sample50.0ms (0.8%)

simplify325.0ms (5.1%)

prune15.0ms (0.2%)

localize18.0ms (0.3%)

rewrite46.0ms (0.7%)

series697.0ms (11%)

simplify90.0ms (1.4%)

prune407.0ms (6.4%)

localize13.0ms (0.2%)

rewrite31.0ms (0.5%)

series585.0ms (9.2%)

simplify63.0ms (1%)

prune184.0ms (2.9%)

localize17.0ms (0.3%)

rewrite45.0ms (0.7%)

series580.0ms (9.1%)

simplify77.0ms (1.2%)

prune228.0ms (3.6%)

localize18.0ms (0.3%)

rewrite32.0ms (0.5%)

series620.0ms (9.8%)

simplify79.0ms (1.2%)

prune194.0ms (3.1%)

regimes145.0ms (2.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.5s (23.2%)

Profiling