Details

analyze64.0ms (0.1%)

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)

sample43.0ms (0.1%)

Algorithm

1×

intervals

Results

24.0ms	256×	body	128	valid
7.0ms	256×	pre	128	true

Compiler

Compiled 47 to 47 computations (0% saved)

simplify271.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (163.0ms)

Iter	Nodes	Cost
0	5644	26

prune6.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.4b

Counts

2 → 2

Compiler

Compiled 16 to 16 computations (0% saved)

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

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

rewrite50.0ms (0.1%)

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

8 calls:

11.0ms	(+.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)
0.0ms	(cos.f64 (.f64 (.f64 2 PI.f64) u2))

series563.0ms (0.7%)

Counts

4 → 18

Calls

4 calls:

290.0ms	(+.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)
146.0ms	(pow.f64 (*.f64 -2 (log.f64 u1)) 1/2)
100.0ms	(.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2))
26.0ms	(.f64 (.f64 2 PI.f64) u2)

Compiler

Compiled 658 to 641 computations (2.6% saved)

simplify80.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4927	1909
1	4927	1909

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

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

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

8 calls:

8.0ms	(.f64 (.f64 2 PI.f64) u2)
6.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
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)))
0.0ms	(cos.f64 (.f64 (.f64 2 PI.f64) u2))

series518.0ms (0.6%)

Counts

4 → 18

Calls

4 calls:

312.0ms	(+.f64 1/2 (.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))))
93.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
85.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
28.0ms	(.f64 (.f64 2 PI.f64) u2)

Compiler

Compiled 628 to 611 computations (2.7% saved)

simplify65.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5116	1290

prune1.1s (1.3%)

Pruning

72 alts after pruning (70 fresh and 2 done)

	Pruned	Kept	Total
New	123	70	193
Fresh	0	0	0
Picked	0	0	0
Done	0	2	2
Total	123	72	195

Error

Counts

195 → 72

Compiler

Compiled 4626 to 3864 computations (16.5% saved)

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

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

rewrite29.0ms (0%)

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

8 calls:

9.0ms	(+.f64 (.f64 (/.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 6) (cos.f64 (.f64 (.f64 2 PI.f64) u2))) 1/2)
5.0ms	(.f64 (.f64 2 PI.f64) u2)
5.0ms	(/.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 6)
3.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
0.0ms	(cos.f64 (.f64 (.f64 2 PI.f64) u2))

series499.0ms (0.6%)

Counts

4 → 18

Calls

4 calls:

299.0ms	(+.f64 (.f64 (/.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 6) (cos.f64 (.f64 (.f64 2 PI.f64) u2))) 1/2)
95.0ms	(/.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 6)
77.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
29.0ms	(.f64 (.f64 2 PI.f64) u2)

Compiler

Compiled 628 to 611 computations (2.7% saved)

simplify71.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5071	1602

localize7.0ms (0%)

Local error

Found 6 expressions with local error:

0.4b	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6)
0.1b	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
0.1b	(+.f64 1/2 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6))
0.1b	(+.f64 1/2 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6))
0.1b	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
0.4b	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6)

rewrite13.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`pow1_binary64`
7×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`associate-l_binary64`
3×	`associate-r_binary64`
2×	`pow-prod-down_binary64` `sqrt-pow1_binary64` `sqrt-prod_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

3 → 41

Calls

6 calls:

6.0ms	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6)
3.0ms	(+.f64 1/2 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6))
2.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
0.0ms	(+.f64 1/2 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6))
0.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))

series261.0ms (0.3%)

Counts

3 → 9

Calls

3 calls:

94.0ms	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6)
89.0ms	(+.f64 1/2 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6))
78.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))

Compiler

Compiled 210 to 228 computations (-8.6% saved)

simplify100.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4751	672
1	4751	672

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

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

rewrite27.0ms (0%)

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

8 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)))))
0.0ms	(cos.f64 (.f64 (.f64 2 PI.f64) u2))

series457.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

180.0ms	(exp.f64 (log.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))))
150.0ms	(log.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))))
100.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
26.0ms	(.f64 (.f64 2 PI.f64) u2)

Compiler

Compiled 480 to 480 computations (0% saved)

simplify67.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4959	905
1	4959	905

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(sqrt.f64 (.f64 (.f64 2 PI.f64) u2))
0.1b	(+.f64 (.f64 (.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2)) (cos.f64 (.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) u2)) (sqrt.f64 (.f64 (.f64 2 PI.f64) u2))))) 1/2)
0.0b	(.f64 (.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2)) (cos.f64 (.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) u2)) (sqrt.f64 (.f64 (.f64 2 PI.f64) u2)))))
0.0b	(cos.f64 (.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) u2)) (sqrt.f64 (.f64 (*.f64 2 PI.f64) u2))))
0.3b	(.f64 (.f64 2 PI.f64) u2)
0.3b	(.f64 (.f64 2 PI.f64) u2)
0.4b	(.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2))
0.5b	(.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) u2)) (sqrt.f64 (.f64 (*.f64 2 PI.f64) u2)))

rewrite52.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

141×	`pow1_binary64`
77×	`pow-prod-down_binary64`
60×	`sqrt-pow1_binary64`
52×	`add-exp-log_binary64`
31×	`add-sqr-sqrt_binary64`
27×	`prod-exp_binary64`
21×	`add-cbrt-cube_binary64`
20×	`*-un-lft-identity_binary64`
19×	`associate-l_binary64`
18×	`add-cube-cbrt_binary64`
17×	`pow-prod-up_binary64`
15×	`associate-r_binary64`
13×	`times-frac_binary64`
12×	`pow1/2_binary64`
11×	`pow-sqr_binary64`
9×	`cbrt-unprod_binary64`
8×	`div-exp_binary64` `pow-exp_binary64`
7×	`unswap-sqr_binary64`
4×	`pow-to-exp_binary64` `add-log-exp_binary64` `swap-sqr_binary64` `1-exp_binary64` `sqr-pow_binary64` `rec-exp_binary64` `sqrt-prod_binary64` `*-commutative_binary64`
1×	`cbrt-undiv_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `unpow-prod-down_binary64` `div-inv_binary64` `pow2_binary64` `associate-*l/_binary64`

Counts

4 → 153

Calls

8 calls:

15.0ms	(.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) u2)) (sqrt.f64 (.f64 (*.f64 2 PI.f64) u2)))
9.0ms	(.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2))
5.0ms	(.f64 (.f64 2 PI.f64) u2)
5.0ms	(.f64 (.f64 2 PI.f64) u2)
0.0ms	(cos.f64 (.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) u2)) (sqrt.f64 (.f64 (*.f64 2 PI.f64) u2))))

series217.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

100.0ms	(.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2))
51.0ms	(.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) u2)) (sqrt.f64 (.f64 (*.f64 2 PI.f64) u2)))
33.0ms	(.f64 (.f64 2 PI.f64) u2)
32.0ms	(.f64 (.f64 2 PI.f64) u2)

Compiler

Compiled 626 to 589 computations (5.9% saved)

simplify69.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4977	1731
1	4977	1731

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(pow.f64 (*.f64 -2 (log.f64 u1)) 1/4)
0.1b	(+.f64 (.f64 (.f64 (/.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4) (sqrt.f64 6)) (/.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4) (sqrt.f64 6))) (cos.f64 (.f64 (.f64 2 PI.f64) u2))) 1/2)
0.0b	(.f64 (.f64 (/.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4) (sqrt.f64 6)) (/.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4) (sqrt.f64 6))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)))
0.0b	(cos.f64 (.f64 (.f64 2 PI.f64) u2))
0.3b	(.f64 (.f64 2 PI.f64) u2)
0.5b	(/.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4) (sqrt.f64 6))
0.5b	(/.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4) (sqrt.f64 6))
0.6b	(.f64 (/.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4) (sqrt.f64 6)) (/.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4) (sqrt.f64 6)))

rewrite97.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

240×	`times-frac_binary64`
205×	`add-sqr-sqrt_binary64`
126×	`sqrt-prod_binary64`
115×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64`
62×	`sqr-pow_binary64`
48×	`div-exp_binary64`
44×	`swap-sqr_binary64`
42×	`unpow-prod-down_binary64`
40×	`prod-exp_binary64`
37×	`associate-r_binary64`
35×	`associate-l_binary64`
25×	`add-cbrt-cube_binary64` `unswap-sqr_binary64`
24×	`pow-exp_binary64`
16×	`pow1_binary64`
12×	`pow-to-exp_binary64` `associate-/r*_binary64`
10×	`associate-/l*_binary64`
7×	`cbrt-unprod_binary64`
6×	`cbrt-undiv_binary64` `div-inv_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`pow-prod-up_binary64` `associate-r/_binary64` `pow-plus_binary64` `pow-sqr_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64`

Counts

4 → 312

Calls

8 calls:

36.0ms	(.f64 (/.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4) (sqrt.f64 6)) (/.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4) (sqrt.f64 6)))
6.0ms	(/.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4) (sqrt.f64 6))
6.0ms	(/.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4) (sqrt.f64 6))
5.0ms	(.f64 (.f64 2 PI.f64) u2)
0.0ms	(.f64 (.f64 (/.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4) (sqrt.f64 6)) (/.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4) (sqrt.f64 6))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)))

series575.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

195.0ms	(/.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4) (sqrt.f64 6))
190.0ms	(/.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4) (sqrt.f64 6))
158.0ms	(.f64 (/.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4) (sqrt.f64 6)) (/.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4) (sqrt.f64 6)))
33.0ms	(.f64 (.f64 2 PI.f64) u2)

Compiler

Compiled 686 to 658 computations (4.1% saved)

simplify141.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

324 → 324

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4993	7770
1	4993	7770

prune9.4s (10.9%)

Pruning

264 alts after pruning (258 fresh and 6 done)

	Pruned	Kept	Total
New	498	205	703
Fresh	12	53	65
Picked	0	0	0
Done	1	6	7
Total	511	264	775

Error

Counts

775 → 264

Compiler

Compiled 18735 to 15906 computations (15.1% saved)

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(+.f64 (.f64 (/.f64 (log.f64 (exp.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))))) 6) (cos.f64 (.f64 (.f64 2 PI.f64) u2))) 1/2)
0.0b	(log.f64 (exp.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1)))))
0.0b	(.f64 (/.f64 (log.f64 (exp.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))))) 6) (cos.f64 (.f64 (.f64 2 PI.f64) u2)))
0.0b	(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)
0.3b	(/.f64 (log.f64 (exp.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))))) 6)
2.6b	(exp.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))))

rewrite24.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`times-frac_binary64`
23×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
20×	`log-pow_binary64` `exp-prod_binary64`
16×	`pow1_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`associate-/l*_binary64`
6×	`sqrt-prod_binary64`
5×	`add-log-exp_binary64`
4×	`pow-prod-down_binary64`
3×	`associate-/r_binary64` `cbrt-unprod_binary64` `associate-r*_binary64` `prod-exp_binary64`
2×	`sqrt-pow1_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `rem-exp-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `*-commutative_binary64`

Counts

4 → 88

Calls

8 calls:

5.0ms	(/.f64 (log.f64 (exp.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))))) 6)
5.0ms	(.f64 (.f64 2 PI.f64) u2)
3.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
2.0ms	(exp.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))))
0.0ms	(cos.f64 (.f64 (.f64 2 PI.f64) u2))

series380.0ms (0.4%)

Counts

4 → 12

Calls

4 calls:

178.0ms	(/.f64 (log.f64 (exp.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))))) 6)
95.0ms	(exp.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))))
79.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
27.0ms	(.f64 (.f64 2 PI.f64) u2)

Compiler

Compiled 480 to 480 computations (0% saved)

simplify72.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4895	1457
1	4895	1457

localize8.0ms (0%)

Local error

Found 6 expressions with local error:

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

rewrite20.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `times-frac_binary64`
6×	`pow1_binary64`
5×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64`
4×	`associate-/l*_binary64`
3×	`associate-/r*_binary64`
2×	`sqrt-pow1_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `pow1/2_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

3 → 54

Calls

6 calls:

9.0ms	(+.f64 (/.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 6) 1/2)
5.0ms	(/.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 6)
2.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
0.0ms	(+.f64 (/.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 6) 1/2)
0.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))

series268.0ms (0.3%)

Counts

3 → 9

Calls

3 calls:

93.0ms	(+.f64 (/.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 6) 1/2)
90.0ms	(/.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 6)
84.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))

Compiler

Compiled 210 to 228 computations (-8.6% saved)

simplify68.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4978	987
1	4978	987

localize21.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(sqrt.f64 (.f64 1 (.f64 (*.f64 2 PI.f64) u2)))
0.1b	(+.f64 (.f64 (.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2)) (cos.f64 (.f64 (sqrt.f64 (.f64 1 (.f64 (.f64 2 PI.f64) u2))) (sqrt.f64 (.f64 (*.f64 2 PI.f64) u2))))) 1/2)
0.0b	(.f64 (.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2)) (cos.f64 (.f64 (sqrt.f64 (.f64 1 (.f64 (.f64 2 PI.f64) u2))) (sqrt.f64 (.f64 (*.f64 2 PI.f64) u2)))))
0.0b	(cos.f64 (.f64 (sqrt.f64 (.f64 1 (.f64 (.f64 2 PI.f64) u2))) (sqrt.f64 (.f64 (.f64 2 PI.f64) u2))))
0.3b	(.f64 (.f64 2 PI.f64) u2)
0.3b	(.f64 (.f64 2 PI.f64) u2)
0.4b	(.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2))
0.5b	(.f64 (sqrt.f64 (.f64 1 (.f64 (.f64 2 PI.f64) u2))) (sqrt.f64 (.f64 (.f64 2 PI.f64) u2)))

rewrite48.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

70×	`pow1_binary64`
52×	`add-exp-log_binary64`
50×	`pow-prod-down_binary64`
29×	`add-sqr-sqrt_binary64`
27×	`prod-exp_binary64`
24×	`sqrt-pow1_binary64`
21×	`add-cbrt-cube_binary64`
19×	`associate-l_binary64`
18×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`
15×	`associate-r_binary64`
13×	`times-frac_binary64`
9×	`cbrt-unprod_binary64`
8×	`div-exp_binary64` `pow-exp_binary64`
7×	`unswap-sqr_binary64`
4×	`pow-to-exp_binary64` `add-log-exp_binary64` `1-exp_binary64` `sqr-pow_binary64` `rec-exp_binary64` `*-commutative_binary64`
2×	`pow1/2_binary64` `sqrt-prod_binary64`
1×	`cbrt-undiv_binary64` `sqrt-unprod_binary64` `unpow-prod-down_binary64` `div-inv_binary64` `associate-*l/_binary64`

Counts

4 → 121

Calls

8 calls:

14.0ms	(.f64 (sqrt.f64 (.f64 1 (.f64 (.f64 2 PI.f64) u2))) (sqrt.f64 (.f64 (.f64 2 PI.f64) u2)))
9.0ms	(.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2))
6.0ms	(.f64 (.f64 2 PI.f64) u2)
5.0ms	(.f64 (.f64 2 PI.f64) u2)
0.0ms	(cos.f64 (.f64 (sqrt.f64 (.f64 1 (.f64 (.f64 2 PI.f64) u2))) (sqrt.f64 (.f64 (.f64 2 PI.f64) u2))))

series216.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

96.0ms	(.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2))
58.0ms	(.f64 (sqrt.f64 (.f64 1 (.f64 (.f64 2 PI.f64) u2))) (sqrt.f64 (.f64 (.f64 2 PI.f64) u2)))
34.0ms	(.f64 (.f64 2 PI.f64) u2)
28.0ms	(.f64 (.f64 2 PI.f64) u2)

Compiler

Compiled 662 to 625 computations (5.6% saved)

simplify92.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4908	1690
1	4908	1690

localize25.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(pow.f64 (*.f64 -2 (log.f64 u1)) 1/4)
0.1b	(+.f64 (.f64 (.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4)) 1) (/.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4)) 3) 6)) (cos.f64 (.f64 (.f64 2 PI.f64) u2))) 1/2)
0.0b	(.f64 (.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4)) 1) (/.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4)) 3) 6)) (cos.f64 (.f64 (.f64 2 PI.f64) u2)))
0.0b	(cos.f64 (.f64 (.f64 2 PI.f64) u2))
0.3b	(/.f64 (pow.f64 (sqrt.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4)) 3) 6)
0.3b	(.f64 (.f64 2 PI.f64) u2)
0.5b	(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4)) 1) (/.f64 (pow.f64 (sqrt.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4)) 3) 6))
0.9b	(pow.f64 (sqrt.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4)) 3)

rewrite124.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

276×	`add-sqr-sqrt_binary64`
266×	`times-frac_binary64`
159×	`sqrt-prod_binary64`
133×	`*-un-lft-identity_binary64`
106×	`add-cube-cbrt_binary64`
104×	`unpow-prod-down_binary64`
85×	`cube-prod_binary64`
73×	`associate-r_binary64`
66×	`sqr-pow_binary64`
63×	`unswap-sqr_binary64`
49×	`add-exp-log_binary64`
29×	`associate-l_binary64`
24×	`add-cbrt-cube_binary64`
22×	`associate-/l*_binary64`
20×	`div-exp_binary64`
15×	`prod-exp_binary64`
12×	`pow1_binary64`
8×	`unpow3_binary64` `cube-mult_binary64`
7×	`cbrt-unprod_binary64`
5×	`pow-to-exp_binary64` `cbrt-undiv_binary64` `pow-exp_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `1-exp_binary64`
3×	`pow-unpow_binary64` `associate-/r*_binary64` `pow-pow_binary64` `div-inv_binary64`
2×	`*-commutative_binary64`
1×	`pow1/2_binary64` `sqrt-pow2_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `rem-cube-cbrt_binary64` `frac-2neg_binary64` `frac-times_binary64` `associate-l/_binary64`

Counts

4 → 348

Calls

8 calls:

47.0ms	(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4)) 1) (/.f64 (pow.f64 (sqrt.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4)) 3) 6))
10.0ms	(/.f64 (pow.f64 (sqrt.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4)) 3) 6)
9.0ms	(.f64 (.f64 2 PI.f64) u2)
4.0ms	(pow.f64 (sqrt.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4)) 3)
0.0ms	(cos.f64 (.f64 (.f64 2 PI.f64) u2))

series644.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

257.0ms	(/.f64 (pow.f64 (sqrt.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4)) 3) 6)
201.0ms	(pow.f64 (sqrt.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4)) 3)
152.0ms	(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4)) 1) (/.f64 (pow.f64 (sqrt.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4)) 3) 6))
33.0ms	(.f64 (.f64 2 PI.f64) u2)

Compiler

Compiled 680 to 652 computations (4.1% saved)

simplify169.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

360 → 360

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4935	9401
1	4935	9401

localize31.0ms (0%)

Local error

Found 8 expressions with local error:

0.5b	(/.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4) (sqrt.f64 6))
0.3b	(.f64 (.f64 2 PI.f64) u2)
0.1b	(pow.f64 (*.f64 -2 (log.f64 u1)) 1/4)
0.0b	(cos.f64 (.f64 (.f64 2 PI.f64) u2))
0.3b	(.f64 (.f64 2 PI.f64) u2)
0.5b	(/.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4) (sqrt.f64 6))
1.0b	(cbrt.f64 6)
1.0b	(cbrt.f64 6)

rewrite25.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`times-frac_binary64`
26×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
18×	`sqrt-prod_binary64`
17×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64`
9×	`pow1_binary64`
7×	`sqr-pow_binary64` `unpow-prod-down_binary64`
6×	`associate-/r*_binary64` `cbrt-prod_binary64`
5×	`associate-/l*_binary64`
4×	`add-log-exp_binary64` `prod-exp_binary64` `div-exp_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-r_binary64`
2×	`pow1/3_binary64` `pow-exp_binary64`
1×	`pow-to-exp_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `*-commutative_binary64`

Counts

4 → 96

Calls

8 calls:

6.0ms	(/.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4) (sqrt.f64 6))
5.0ms	(.f64 (.f64 2 PI.f64) u2)
1.0ms	(cbrt.f64 6)
1.0ms	(cbrt.f64 6)
0.0ms	(cos.f64 (.f64 (.f64 2 PI.f64) u2))

series212.0ms (0.2%)

Counts

4 → 6

Calls

4 calls:

179.0ms	(/.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4) (sqrt.f64 6))
32.0ms	(.f64 (.f64 2 PI.f64) u2)
0.0ms	(cbrt.f64 6)
0.0ms	(cbrt.f64 6)

Compiler

Compiled 446 to 426 computations (4.5% saved)

simplify88.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4916	1723
1	4916	1723

prune14.6s (16.9%)

Pruning

467 alts after pruning (457 fresh and 10 done)

	Pruned	Kept	Total
New	536	222	758
Fresh	18	235	253
Picked	0	0	0
Done	1	10	11
Total	555	467	1022

Error

Counts

1022 → 467

Compiler

Compiled 28090 to 24348 computations (13.3% saved)

localize22.0ms (0%)

Local error

Found 8 expressions with local error:

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

rewrite49.0ms (0.1%)

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

8 calls:

28.0ms	(+.f64 (.f64 (.f64 (/.f64 (sqrt.f64 1) (.f64 (cbrt.f64 1) (cbrt.f64 1))) (/.f64 (/.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 6) (cbrt.f64 1))) (cos.f64 (.f64 (.f64 2 PI.f64) u2))) 1/2)
6.0ms	(/.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 6)
6.0ms	(.f64 (.f64 2 PI.f64) u2)
3.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
0.0ms	(cos.f64 (.f64 (.f64 2 PI.f64) u2))

series524.0ms (0.6%)

Counts

4 → 18

Calls

4 calls:

306.0ms	(+.f64 (.f64 (.f64 (/.f64 (sqrt.f64 1) (.f64 (cbrt.f64 1) (cbrt.f64 1))) (/.f64 (/.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 6) (cbrt.f64 1))) (cos.f64 (.f64 (.f64 2 PI.f64) u2))) 1/2)
103.0ms	(/.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 6)
83.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
32.0ms	(.f64 (.f64 2 PI.f64) u2)

Compiler

Compiled 844 to 827 computations (2% saved)

simplify79.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4898	1622
1	4898	1622

localize9.0ms (0%)

Local error

Found 6 expressions with local error:

0.4b	(.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/2) 1/6)
0.1b	(pow.f64 (*.f64 -2 (log.f64 u1)) 1/2)
0.1b	(+.f64 1/2 (.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/2) 1/6))
0.1b	(+.f64 1/2 (.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/2) 1/6))
0.1b	(pow.f64 (*.f64 -2 (log.f64 u1)) 1/2)
0.4b	(.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/2) 1/6)

rewrite16.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-exp-log_binary64`
9×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `prod-exp_binary64`
5×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
4×	`pow-exp_binary64`
3×	`pow-unpow_binary64` `associate-r_binary64` `sqr-pow_binary64`
2×	`pow-to-exp_binary64` `pow-pow_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `unpow1/2_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

3 → 52

Calls

6 calls:

5.0ms	(.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/2) 1/6)
4.0ms	(pow.f64 (*.f64 -2 (log.f64 u1)) 1/2)
3.0ms	(+.f64 1/2 (.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/2) 1/6))
0.0ms	(+.f64 1/2 (.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/2) 1/6))
0.0ms	(pow.f64 (*.f64 -2 (log.f64 u1)) 1/2)

series326.0ms (0.4%)

Counts

3 → 9

Calls

3 calls:

134.0ms	(pow.f64 (*.f64 -2 (log.f64 u1)) 1/2)
97.0ms	(+.f64 1/2 (.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/2) 1/6))
95.0ms	(.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/2) 1/6)

Compiler

Compiled 210 to 228 computations (-8.6% saved)

simplify83.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4857	813
1	4857	813

localize21.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(sqrt.f64 (.f64 1 (.f64 (*.f64 2 PI.f64) u2)))
0.1b	(+.f64 (.f64 (.f64 1/6 (.f64 (sqrt.f64 2) (sqrt.f64 (neg.f64 (log.f64 u1))))) (cos.f64 (.f64 (sqrt.f64 (.f64 1 (.f64 (.f64 2 PI.f64) u2))) (sqrt.f64 (.f64 (*.f64 2 PI.f64) u2))))) 1/2)
0.0b	(.f64 (.f64 1/6 (.f64 (sqrt.f64 2) (sqrt.f64 (neg.f64 (log.f64 u1))))) (cos.f64 (.f64 (sqrt.f64 (.f64 1 (.f64 (.f64 2 PI.f64) u2))) (sqrt.f64 (.f64 (*.f64 2 PI.f64) u2)))))
0.0b	(cos.f64 (.f64 (sqrt.f64 (.f64 1 (.f64 (.f64 2 PI.f64) u2))) (sqrt.f64 (.f64 (.f64 2 PI.f64) u2))))
0.3b	(.f64 (.f64 2 PI.f64) u2)
0.4b	(.f64 1/6 (.f64 (sqrt.f64 2) (sqrt.f64 (neg.f64 (log.f64 u1)))))
0.4b	(*.f64 (sqrt.f64 2) (sqrt.f64 (neg.f64 (log.f64 u1))))
0.5b	(.f64 (sqrt.f64 (.f64 1 (.f64 (.f64 2 PI.f64) u2))) (sqrt.f64 (.f64 (.f64 2 PI.f64) u2)))

rewrite55.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`pow1_binary64`
53×	`pow-prod-down_binary64`
26×	`sqrt-pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`associate-r_binary64`
21×	`sqrt-prod_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`-un-lft-identity_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64`
8×	`cbrt-unprod_binary64` `prod-exp_binary64`
5×	`unswap-sqr_binary64`
4×	`add-log-exp_binary64` `pow1/2_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64` `*-commutative_binary64`
2×	`log-pow_binary64` `sqrt-unprod_binary64`
1×	`neg-mul-1_binary64`

Counts

4 → 109

Calls

8 calls:

18.0ms	(.f64 (sqrt.f64 (.f64 1 (.f64 (.f64 2 PI.f64) u2))) (sqrt.f64 (.f64 (.f64 2 PI.f64) u2)))
10.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (neg.f64 (log.f64 u1))))
8.0ms	(.f64 1/6 (.f64 (sqrt.f64 2) (sqrt.f64 (neg.f64 (log.f64 u1)))))
5.0ms	(.f64 (.f64 2 PI.f64) u2)
0.0ms	(cos.f64 (.f64 (sqrt.f64 (.f64 1 (.f64 (.f64 2 PI.f64) u2))) (sqrt.f64 (.f64 (.f64 2 PI.f64) u2))))

series291.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

111.0ms	(.f64 1/6 (.f64 (sqrt.f64 2) (sqrt.f64 (neg.f64 (log.f64 u1)))))
99.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (neg.f64 (log.f64 u1))))
49.0ms	(.f64 (sqrt.f64 (.f64 1 (.f64 (.f64 2 PI.f64) u2))) (sqrt.f64 (.f64 (.f64 2 PI.f64) u2)))
33.0ms	(.f64 (.f64 2 PI.f64) u2)

Compiler

Compiled 660 to 623 computations (5.6% saved)

simplify94.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4885	1598
1	4885	1598

localize29.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(pow.f64 (*.f64 -2 (log.f64 u1)) 1/4)
0.1b	(+.f64 (.f64 (.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4)) 1) (/.f64 (exp.f64 (.f64 3 (log.f64 (sqrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4))))) 6)) (cos.f64 (.f64 (*.f64 2 PI.f64) u2))) 1/2)
0.0b	(.f64 (.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4)) 1) (/.f64 (exp.f64 (.f64 3 (log.f64 (sqrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4))))) 6)) (cos.f64 (.f64 (*.f64 2 PI.f64) u2)))
0.0b	(cos.f64 (.f64 (.f64 2 PI.f64) u2))
0.3b	(.f64 3 (log.f64 (sqrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4))))
0.4b	(log.f64 (sqrt.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4)))
0.5b	(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4)) 1) (/.f64 (exp.f64 (.f64 3 (log.f64 (sqrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4))))) 6))
0.6b	(exp.f64 (.f64 3 (log.f64 (sqrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4)))))

rewrite109.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

223×	`add-sqr-sqrt_binary64`
178×	`times-frac_binary64`
130×	`log-prod_binary64` `sqrt-prod_binary64`
106×	`exp-sum_binary64`
90×	`*-un-lft-identity_binary64`
67×	`associate-r_binary64`
66×	`add-cube-cbrt_binary64`
61×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
57×	`unswap-sqr_binary64`
44×	`sqr-pow_binary64`
31×	`associate-l_binary64`
21×	`add-exp-log_binary64`
18×	`add-cbrt-cube_binary64`
14×	`unpow-prod-down_binary64`
10×	`pow1_binary64`
7×	`prod-exp_binary64` `div-exp_binary64`
6×	`add-log-exp_binary64` `log-pow_binary64`
5×	`cbrt-unprod_binary64`
4×	`cbrt-undiv_binary64`
2×	`pow-prod-down_binary64` `pow1/2_binary64` `1-exp_binary64` `sqrt-pow1_binary64` `div-inv_binary64` `*-commutative_binary64`
1×	`rem-log-exp_binary64` `associate-r/_binary64` `rem-exp-log_binary64` `exp-to-pow_binary64` `frac-times_binary64` `associate-l/_binary64` `exp-prod_binary64`

Counts

4 → 249

Calls

8 calls:

46.0ms	(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4)) 1) (/.f64 (exp.f64 (.f64 3 (log.f64 (sqrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4))))) 6))
7.0ms	(.f64 3 (log.f64 (sqrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4))))
5.0ms	(exp.f64 (.f64 3 (log.f64 (sqrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4)))))
3.0ms	(log.f64 (sqrt.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4)))
0.0ms	(cos.f64 (.f64 (.f64 2 PI.f64) u2))

series812.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

232.0ms	(.f64 3 (log.f64 (sqrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4))))
218.0ms	(log.f64 (sqrt.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4)))
197.0ms	(exp.f64 (.f64 3 (log.f64 (sqrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4)))))
164.0ms	(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4)) 1) (/.f64 (exp.f64 (.f64 3 (log.f64 (sqrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4))))) 6))

Compiler

Compiled 712 to 688 computations (3.4% saved)

simplify149.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

261 → 261

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4907	7690
1	4907	7690

localize35.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(pow.f64 (*.f64 -2 (log.f64 u1)) (/.f64 1/4 2))
0.0b	(pow.f64 (*.f64 -2 (log.f64 u1)) 1/8)
0.0b	(.f64 (.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) (/.f64 1/4 2))) (sqrt.f64 1)) (.f64 (sqrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/8)) (/.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4)) 3) 6))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)))
0.0b	(cos.f64 (.f64 (.f64 2 PI.f64) u2))
0.3b	(.f64 (.f64 2 PI.f64) u2)
0.3b	(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) (/.f64 1/4 2))) (sqrt.f64 1)) (.f64 (sqrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/8)) (/.f64 (pow.f64 (sqrt.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4)) 3) 6)))
0.4b	(.f64 (sqrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/8)) (/.f64 (pow.f64 (sqrt.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4)) 3) 6))
0.9b	(pow.f64 (sqrt.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4)) 3)

rewrite115.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

139×	`add-sqr-sqrt_binary64`
138×	`times-frac_binary64`
129×	`sqrt-prod_binary64`
79×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
74×	`associate-r_binary64`
61×	`associate-l_binary64`
57×	`add-exp-log_binary64`
56×	`unpow-prod-down_binary64`
41×	`cube-prod_binary64`
37×	`sqr-pow_binary64`
36×	`add-cbrt-cube_binary64`
27×	`unswap-sqr_binary64`
25×	`prod-exp_binary64`
17×	`pow1_binary64`
15×	`cbrt-unprod_binary64`
14×	`div-exp_binary64`
7×	`pow-prod-down_binary64`
6×	`cbrt-undiv_binary64`
4×	`pow-to-exp_binary64` `add-log-exp_binary64` `associate-*r/_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
3×	`pow-unpow_binary64` `pow-pow_binary64` `*-commutative_binary64`
2×	`div-inv_binary64`
1×	`pow1/2_binary64` `sqrt-pow2_binary64` `sqrt-pow1_binary64` `rem-cube-cbrt_binary64` `frac-times_binary64` `associate-*l/_binary64`

Counts

4 → 257

Calls

8 calls:

30.0ms	(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) (/.f64 1/4 2))) (sqrt.f64 1)) (.f64 (sqrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/8)) (/.f64 (pow.f64 (sqrt.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4)) 3) 6)))
30.0ms	(.f64 (sqrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/8)) (/.f64 (pow.f64 (sqrt.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4)) 3) 6))
5.0ms	(.f64 (.f64 2 PI.f64) u2)
4.0ms	(pow.f64 (sqrt.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4)) 3)
0.0ms	(cos.f64 (.f64 (.f64 2 PI.f64) u2))

series770.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

363.0ms	(.f64 (sqrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/8)) (/.f64 (pow.f64 (sqrt.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4)) 3) 6))
205.0ms	(pow.f64 (sqrt.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4)) 3)
166.0ms	(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) (/.f64 1/4 2))) (sqrt.f64 1)) (.f64 (sqrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/8)) (/.f64 (pow.f64 (sqrt.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4)) 3) 6)))
36.0ms	(.f64 (.f64 2 PI.f64) u2)

Compiler

Compiled 854 to 802 computations (6.1% saved)

simplify131.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

269 → 269

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5216	8280

prune25.5s (29.6%)

Pruning

687 alts after pruning (673 fresh and 14 done)

	Pruned	Kept	Total
New	532	269	801
Fresh	48	404	452
Picked	0	0	0
Done	1	14	15
Total	581	687	1268

Error

Counts

1268 → 687

Compiler

Compiled 17377 to 13993 computations (19.5% saved)

simplify860.0ms (1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5623	58004

regimes19.5s (22.6%)

Compiler: Compiled 216056 to 198091 computations (8.3% saved)

bsearch0.0ms (0%)

regimes2.0s (2.4%)

Compiler: Compiled 19592 to 19536 computations (0.3% saved)

bsearch0.0ms (0%)

regimes231.0ms (0.3%)

Compiler: Compiled 1289 to 1460 computations (-13.3% saved)

bsearch0.0ms (0%)

regimes166.0ms (0.2%)

Compiler: Compiled 843 to 968 computations (-14.8% saved)

bsearch0.0ms (0%)

regimes16.0ms (0%)

Compiler: Compiled 10 to 26 computations (-160% saved)

bsearch7.0ms (0%)

Compiler: Compiled 68 to 69 computations (-1.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	53	111
1	53	111

end0.0ms (0%)

sample2.0s (2.3%)

Algorithm

1×

intervals

Results

792.0ms	8000×	body	128	valid
208.0ms	8000×	pre	128	true

Compiler

Compiled 24976 to 22903 computations (8.3% saved)