Details

Time bar (total: 1.4min)

analyze271.0ms (0.3%)

Algorithm
1×search
Search
TrueOtherFalseIter
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
24.0ms256×body128valid
7.0ms256×pre128true
Compiler

Compiled 47 to 47 computations (0% saved)

simplify292.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (175.0ms)

IterNodesCost
0564426

prune6.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.4b
Counts
2 → 2
Compiler

Compiled 16 to 16 computations (0% saved)

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

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

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

series504.0ms (0.6%)

Counts
4 → 18
Calls

4 calls:

292.0ms
(+.f64 1/2 (*.f64 (*.f64 1/6 (sqrt.f64 (*.f64 -2 (log.f64 u1)))) (cos.f64 (*.f64 (*.f64 2 PI.f64) u2))))
107.0ms
(*.f64 1/6 (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 628 to 611 computations (2.7% saved)

simplify68.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
051161290

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

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

rewrite38.0ms (0%)

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

series533.0ms (0.6%)

Counts
4 → 18
Calls

4 calls:

276.0ms
(+.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)
137.0ms
(pow.f64 (*.f64 -2 (log.f64 u1)) 1/2)
92.0ms
(*.f64 (/.f64 1 6) (pow.f64 (*.f64 -2 (log.f64 u1)) 1/2))
28.0ms
(*.f64 (*.f64 2 PI.f64) u2)
Compiler

Compiled 658 to 641 computations (2.6% saved)

simplify79.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
049271909
149271909

prune1.0s (1.2%)

Pruning

74 alts after pruning (72 fresh and 2 done)

PrunedKeptTotal
New12172193
Fresh000
Picked000
Done022
Total12174195
Error
0.0b
Counts
195 → 74
Compiler

Compiled 4678 to 3916 computations (16.3% saved)

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

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

rewrite27.0ms (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)
2.0ms
(sqrt.f64 (*.f64 -2 (log.f64 u1)))
0.0ms
(*.f64 (/.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 6) (cos.f64 (*.f64 (*.f64 2 PI.f64) u2)))

series512.0ms (0.6%)

Counts
4 → 18
Calls

4 calls:

312.0ms
(+.f64 (*.f64 (/.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 6) (cos.f64 (*.f64 (*.f64 2 PI.f64) u2))) 1/2)
96.0ms
(/.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 6)
77.0ms
(sqrt.f64 (*.f64 -2 (log.f64 u1)))
26.0ms
(*.f64 (*.f64 2 PI.f64) u2)
Compiler

Compiled 628 to 611 computations (2.7% saved)

simplify69.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
050711602

localize10.0ms (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)))
0.0b
(+.f64 1/2 (*.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 1/6))
0.0b
(+.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)

rewrite14.0ms (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)))

series269.0ms (0.3%)

Counts
3 → 9
Calls

3 calls:

97.0ms
(+.f64 1/2 (*.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 1/6))
92.0ms
(*.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 1/6)
80.0ms
(sqrt.f64 (*.f64 -2 (log.f64 u1)))
Compiler

Compiled 210 to 228 computations (-8.6% saved)

simplify102.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
50 → 50
Iterations

Useful iterations: 0 (91.0ms)

IterNodesCost
04751672
14751672

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(sqrt.f64 (*.f64 -2 (log.f64 u1)))
0.0b
(+.f64 1/2 (*.f64 (cbrt.f64 (pow.f64 (*.f64 1/6 (sqrt.f64 (*.f64 -2 (log.f64 u1)))) 3)) (cos.f64 (*.f64 (*.f64 2 PI.f64) u2))))
0.0b
(cos.f64 (*.f64 (*.f64 2 PI.f64) u2))
0.0b
(*.f64 (cbrt.f64 (pow.f64 (*.f64 1/6 (sqrt.f64 (*.f64 -2 (log.f64 u1)))) 3)) (cos.f64 (*.f64 (*.f64 2 PI.f64) u2)))
0.2b
(*.f64 (*.f64 2 PI.f64) u2)
0.4b
(*.f64 1/6 (sqrt.f64 (*.f64 -2 (log.f64 u1))))
0.5b
(cbrt.f64 (pow.f64 (*.f64 1/6 (sqrt.f64 (*.f64 -2 (log.f64 u1)))) 3))
0.8b
(pow.f64 (*.f64 1/6 (sqrt.f64 (*.f64 -2 (log.f64 u1)))) 3)

rewrite27.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
14×pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
11×add-sqr-sqrt_binary64
9×*-un-lft-identity_binary64 add-cube-cbrt_binary64
8×cbrt-prod_binary64
7×associate-*r*_binary64
5×pow-prod-down_binary64 cbrt-unprod_binary64 prod-exp_binary64
4×add-log-exp_binary64 associate-*l*_binary64
3×pow-unpow_binary64
2×pow-pow_binary64 sqr-pow_binary64 rem-cube-cbrt_binary64 unpow-prod-down_binary64 cube-prod_binary64 pow-exp_binary64 unpow3_binary64 *-commutative_binary64 cube-mult_binary64
1×pow-to-exp_binary64 rem-cbrt-cube_binary64 pow1/3_binary64 unswap-sqr_binary64 sqrt-prod_binary64
Counts
4 → 76
Calls

8 calls:

7.0ms
(*.f64 1/6 (sqrt.f64 (*.f64 -2 (log.f64 u1))))
6.0ms
(pow.f64 (*.f64 1/6 (sqrt.f64 (*.f64 -2 (log.f64 u1)))) 3)
5.0ms
(*.f64 (*.f64 2 PI.f64) u2)
3.0ms
(cbrt.f64 (pow.f64 (*.f64 1/6 (sqrt.f64 (*.f64 -2 (log.f64 u1)))) 3))
0.0ms
(*.f64 (cbrt.f64 (pow.f64 (*.f64 1/6 (sqrt.f64 (*.f64 -2 (log.f64 u1)))) 3)) (cos.f64 (*.f64 (*.f64 2 PI.f64) u2)))

series370.0ms (0.4%)

Counts
4 → 12
Calls

4 calls:

147.0ms
(pow.f64 (*.f64 1/6 (sqrt.f64 (*.f64 -2 (log.f64 u1)))) 3)
104.0ms
(cbrt.f64 (pow.f64 (*.f64 1/6 (sqrt.f64 (*.f64 -2 (log.f64 u1)))) 3))
89.0ms
(*.f64 1/6 (sqrt.f64 (*.f64 -2 (log.f64 u1))))
29.0ms
(*.f64 (*.f64 2 PI.f64) u2)
Compiler

Compiled 496 to 496 computations (0% saved)

simplify86.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 0 (69.0ms)

IterNodesCost
048131083
148131083

localize23.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b
(*.f64 (*.f64 2 PI.f64) u2)
0.0b
(+.f64 (*.f64 (*.f64 (/.f64 1 6) (pow.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) (sqrt.f64 1/2)) (sqrt.f64 1/2))) (cos.f64 (*.f64 (*.f64 2 PI.f64) u2))) 1/2)
0.0b
(cos.f64 (*.f64 (*.f64 2 PI.f64) u2))
0.0b
(*.f64 (*.f64 (/.f64 1 6) (pow.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) (sqrt.f64 1/2)) (sqrt.f64 1/2))) (cos.f64 (*.f64 (*.f64 2 PI.f64) u2)))
0.2b
(*.f64 (*.f64 2 PI.f64) u2)
0.4b
(*.f64 (/.f64 1 6) (pow.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) (sqrt.f64 1/2)) (sqrt.f64 1/2)))
1.2b
(pow.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) (sqrt.f64 1/2)) (sqrt.f64 1/2))
1.5b
(pow.f64 (*.f64 -2 (log.f64 u1)) (sqrt.f64 1/2))

rewrite41.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
66×add-exp-log_binary64
41×add-sqr-sqrt_binary64
33×prod-exp_binary64
32×pow-exp_binary64
23×*-un-lft-identity_binary64
19×add-cube-cbrt_binary64 unpow-prod-down_binary64
17×times-frac_binary64
14×add-cbrt-cube_binary64 associate-*l*_binary64
12×pow-unpow_binary64 pow1_binary64 associate-*r*_binary64 unswap-sqr_binary64 div-exp_binary64
11×pow-to-exp_binary64 sqr-pow_binary64
6×1-exp_binary64 rec-exp_binary64 sqrt-prod_binary64
5×cbrt-unprod_binary64
4×pow-prod-down_binary64 add-log-exp_binary64
3×pow-pow_binary64
2×*-commutative_binary64
1×cbrt-undiv_binary64 div-inv_binary64 associate-*l/_binary64
Counts
4 → 132
Calls

8 calls:

13.0ms
(*.f64 (/.f64 1 6) (pow.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) (sqrt.f64 1/2)) (sqrt.f64 1/2)))
5.0ms
(*.f64 (*.f64 2 PI.f64) u2)
4.0ms
(pow.f64 (*.f64 -2 (log.f64 u1)) (sqrt.f64 1/2))
4.0ms
(pow.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) (sqrt.f64 1/2)) (sqrt.f64 1/2))
0.0ms
(*.f64 (*.f64 (/.f64 1 6) (pow.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) (sqrt.f64 1/2)) (sqrt.f64 1/2))) (cos.f64 (*.f64 (*.f64 2 PI.f64) u2)))

series692.0ms (0.8%)

Counts
4 → 12
Calls

4 calls:

272.0ms
(*.f64 (/.f64 1 6) (pow.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) (sqrt.f64 1/2)) (sqrt.f64 1/2)))
249.0ms
(pow.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) (sqrt.f64 1/2)) (sqrt.f64 1/2))
143.0ms
(pow.f64 (*.f64 -2 (log.f64 u1)) (sqrt.f64 1/2))
28.0ms
(*.f64 (*.f64 2 PI.f64) u2)
Compiler

Compiled 582 to 582 computations (0% saved)

simplify90.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
049002704
149002704

localize21.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(pow.f64 (*.f64 -2 (log.f64 u1)) 1/4)
0.0b
(+.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 1/6) (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4)) (*.f64 (sqrt.f64 1/6) (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4))) (cos.f64 (*.f64 (*.f64 2 PI.f64) u2))) 1/2)
0.0b
(cos.f64 (*.f64 (*.f64 2 PI.f64) u2))
0.0b
(*.f64 (*.f64 (*.f64 (sqrt.f64 1/6) (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4)) (*.f64 (sqrt.f64 1/6) (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4))) (cos.f64 (*.f64 (*.f64 2 PI.f64) u2)))
0.2b
(*.f64 (*.f64 2 PI.f64) u2)
0.3b
(*.f64 (sqrt.f64 1/6) (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4))
0.3b
(*.f64 (sqrt.f64 1/6) (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4))
0.5b
(*.f64 (*.f64 (sqrt.f64 1/6) (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4)) (*.f64 (sqrt.f64 1/6) (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4)))

rewrite44.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
115×add-exp-log_binary64
88×prod-exp_binary64
25×add-cbrt-cube_binary64
24×pow-exp_binary64
23×add-sqr-sqrt_binary64
16×pow1_binary64
14×associate-*r*_binary64 associate-*l*_binary64
13×cbrt-unprod_binary64
12×pow-to-exp_binary64
11×*-un-lft-identity_binary64 add-cube-cbrt_binary64
10×sqrt-prod_binary64
8×unswap-sqr_binary64
6×sqr-pow_binary64
4×pow-prod-down_binary64 add-log-exp_binary64 *-commutative_binary64
2×unpow-prod-down_binary64
1×swap-sqr_binary64 pow-prod-up_binary64 pow-plus_binary64 pow-sqr_binary64 pow2_binary64
Counts
4 → 119
Calls

8 calls:

11.0ms
(*.f64 (*.f64 (sqrt.f64 1/6) (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4)) (*.f64 (sqrt.f64 1/6) (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4)))
7.0ms
(*.f64 (sqrt.f64 1/6) (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4))
7.0ms
(*.f64 (sqrt.f64 1/6) (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4))
5.0ms
(*.f64 (*.f64 2 PI.f64) u2)
0.0ms
(*.f64 (*.f64 (*.f64 (sqrt.f64 1/6) (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4)) (*.f64 (sqrt.f64 1/6) (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4))) (cos.f64 (*.f64 (*.f64 2 PI.f64) u2)))

series506.0ms (0.6%)

Counts
4 → 12
Calls

4 calls:

175.0ms
(*.f64 (sqrt.f64 1/6) (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4))
172.0ms
(*.f64 (sqrt.f64 1/6) (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4))
131.0ms
(*.f64 (*.f64 (sqrt.f64 1/6) (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4)) (*.f64 (sqrt.f64 1/6) (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4)))
28.0ms
(*.f64 (*.f64 2 PI.f64) u2)
Compiler

Compiled 662 to 634 computations (4.2% saved)

simplify66.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
052991869

prune6.4s (7.7%)

Pruning

234 alts after pruning (227 fresh and 7 done)

PrunedKeptTotal
New331171502
Fresh115667
Picked000
Done077
Total342234576
Error
0.0b
Counts
576 → 234
Compiler

Compiled 13886 to 11962 computations (13.9% saved)

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

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

rewrite30.0ms (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:

10.0ms
(+.f64 (*.f64 (*.f64 1 (/.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 6)) (cos.f64 (*.f64 (*.f64 2 PI.f64) u2))) 1/2)
6.0ms
(/.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 6)
5.0ms
(*.f64 (*.f64 2 PI.f64) u2)
2.0ms
(sqrt.f64 (*.f64 -2 (log.f64 u1)))
0.0ms
(*.f64 (*.f64 1 (/.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 6)) (cos.f64 (*.f64 (*.f64 2 PI.f64) u2)))

series488.0ms (0.6%)

Counts
4 → 18
Calls

4 calls:

290.0ms
(+.f64 (*.f64 (*.f64 1 (/.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 6)) (cos.f64 (*.f64 (*.f64 2 PI.f64) u2))) 1/2)
93.0ms
(/.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 6)
70.0ms
(sqrt.f64 (*.f64 -2 (log.f64 u1)))
33.0ms
(*.f64 (*.f64 2 PI.f64) u2)
Compiler

Compiled 664 to 647 computations (2.6% saved)

simplify71.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
050391602

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

rewrite23.0ms (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
(/.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 6)

series270.0ms (0.3%)

Counts
3 → 9
Calls

3 calls:

101.0ms
(+.f64 (/.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 6) 1/2)
89.0ms
(/.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 6)
80.0ms
(sqrt.f64 (*.f64 -2 (log.f64 u1)))
Compiler

Compiled 210 to 228 computations (-8.6% saved)

simplify62.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
63 → 63
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
04978987
14978987

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(sqrt.f64 (*.f64 -2 (log.f64 u1)))
0.0b
(+.f64 1/2 (*.f64 (cbrt.f64 (*.f64 (*.f64 1/6 (sqrt.f64 (*.f64 -2 (log.f64 u1)))) (*.f64 (log.f64 u1) -1/18))) (cos.f64 (*.f64 (*.f64 2 PI.f64) u2))))
0.0b
(cos.f64 (*.f64 (*.f64 2 PI.f64) u2))
0.0b
(*.f64 (cbrt.f64 (*.f64 (*.f64 1/6 (sqrt.f64 (*.f64 -2 (log.f64 u1)))) (*.f64 (log.f64 u1) -1/18))) (cos.f64 (*.f64 (*.f64 2 PI.f64) u2)))
0.4b
(*.f64 (*.f64 1/6 (sqrt.f64 (*.f64 -2 (log.f64 u1)))) (*.f64 (log.f64 u1) -1/18))
0.4b
(*.f64 1/6 (sqrt.f64 (*.f64 -2 (log.f64 u1))))
0.5b
(*.f64 (log.f64 u1) -1/18)
0.5b
(cbrt.f64 (*.f64 (*.f64 1/6 (sqrt.f64 (*.f64 -2 (log.f64 u1)))) (*.f64 (log.f64 u1) -1/18)))

rewrite35.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
21×pow1_binary64
20×add-exp-log_binary64 add-cbrt-cube_binary64
12×add-sqr-sqrt_binary64
10×pow-prod-down_binary64 cbrt-unprod_binary64 prod-exp_binary64
8×*-un-lft-identity_binary64 associate-*r*_binary64 add-cube-cbrt_binary64 associate-*l*_binary64
4×add-log-exp_binary64
3×*-commutative_binary64
2×unswap-sqr_binary64
1×pow1/3_binary64 log-pow_binary64 sqrt-prod_binary64 cbrt-prod_binary64
Counts
4 → 69
Calls

8 calls:

10.0ms
(*.f64 (*.f64 1/6 (sqrt.f64 (*.f64 -2 (log.f64 u1)))) (*.f64 (log.f64 u1) -1/18))
8.0ms
(cbrt.f64 (*.f64 (*.f64 1/6 (sqrt.f64 (*.f64 -2 (log.f64 u1)))) (*.f64 (log.f64 u1) -1/18)))
6.0ms
(*.f64 1/6 (sqrt.f64 (*.f64 -2 (log.f64 u1))))
4.0ms
(*.f64 (log.f64 u1) -1/18)
0.0ms
(*.f64 (cbrt.f64 (*.f64 (*.f64 1/6 (sqrt.f64 (*.f64 -2 (log.f64 u1)))) (*.f64 (log.f64 u1) -1/18))) (cos.f64 (*.f64 (*.f64 2 PI.f64) u2)))

series623.0ms (0.8%)

Counts
4 → 12
Calls

4 calls:

311.0ms
(cbrt.f64 (*.f64 (*.f64 1/6 (sqrt.f64 (*.f64 -2 (log.f64 u1)))) (*.f64 (log.f64 u1) -1/18)))
147.0ms
(*.f64 (*.f64 1/6 (sqrt.f64 (*.f64 -2 (log.f64 u1)))) (*.f64 (log.f64 u1) -1/18))
96.0ms
(*.f64 1/6 (sqrt.f64 (*.f64 -2 (log.f64 u1))))
68.0ms
(*.f64 (log.f64 u1) -1/18)
Compiler

Compiled 594 to 566 computations (4.7% saved)

simplify76.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
050341006

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(pow.f64 (*.f64 -2 (log.f64 u1)) 1/4)
0.0b
(+.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
(cos.f64 (*.f64 (*.f64 2 PI.f64) u2))
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)))
0.2b
(*.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))
0.5b
(*.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)))

rewrite103.0ms (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:

35.0ms
(*.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)))
9.0ms
(/.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)))

series573.0ms (0.7%)

Counts
4 → 12
Calls

4 calls:

194.0ms
(/.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4) (sqrt.f64 6))
194.0ms
(/.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) 1/4) (sqrt.f64 6))
153.0ms
(*.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)))
31.0ms
(*.f64 (*.f64 2 PI.f64) u2)
Compiler

Compiled 686 to 658 computations (4.1% saved)

simplify150.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
324 → 324
Iterations

Useful iterations: 0 (66.0ms)

IterNodesCost
049937770
149937770

localize25.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b
(*.f64 (*.f64 2 PI.f64) u2)
0.0b
(+.f64 (*.f64 (*.f64 (/.f64 1 6) (pow.f64 (pow.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) (sqrt.f64 (sqrt.f64 1/2))) (sqrt.f64 (sqrt.f64 1/2))) (sqrt.f64 1/2))) (cos.f64 (*.f64 (*.f64 2 PI.f64) u2))) 1/2)
0.0b
(cos.f64 (*.f64 (*.f64 2 PI.f64) u2))
0.0b
(*.f64 (*.f64 (/.f64 1 6) (pow.f64 (pow.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) (sqrt.f64 (sqrt.f64 1/2))) (sqrt.f64 (sqrt.f64 1/2))) (sqrt.f64 1/2))) (cos.f64 (*.f64 (*.f64 2 PI.f64) u2)))
1.0b
(sqrt.f64 (sqrt.f64 1/2))
1.2b
(pow.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) (sqrt.f64 (sqrt.f64 1/2))) (sqrt.f64 (sqrt.f64 1/2)))
1.2b
(pow.f64 (pow.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) (sqrt.f64 (sqrt.f64 1/2))) (sqrt.f64 (sqrt.f64 1/2))) (sqrt.f64 1/2))
1.4b
(pow.f64 (*.f64 -2 (log.f64 u1)) (sqrt.f64 (sqrt.f64 1/2)))

rewrite30.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
31×sqrt-prod_binary64
24×pow-unpow_binary64
22×unpow-prod-down_binary64
20×pow-exp_binary64
19×add-sqr-sqrt_binary64
17×*-un-lft-identity_binary64 add-cube-cbrt_binary64
16×add-exp-log_binary64
9×pow1_binary64
6×pow-to-exp_binary64 sqr-pow_binary64
4×add-log-exp_binary64 pow-pow_binary64 add-cbrt-cube_binary64 sqrt-pow1_binary64
3×prod-exp_binary64
2×pow1/2_binary64 rem-sqrt-square_binary64
1×pow-prod-down_binary64
Counts
4 → 101
Calls

8 calls:

6.0ms
(pow.f64 (pow.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) (sqrt.f64 (sqrt.f64 1/2))) (sqrt.f64 (sqrt.f64 1/2))) (sqrt.f64 1/2))
5.0ms
(pow.f64 (*.f64 -2 (log.f64 u1)) (sqrt.f64 (sqrt.f64 1/2)))
5.0ms
(pow.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) (sqrt.f64 (sqrt.f64 1/2))) (sqrt.f64 (sqrt.f64 1/2)))
2.0ms
(sqrt.f64 (sqrt.f64 1/2))
0.0ms
(*.f64 (*.f64 (/.f64 1 6) (pow.f64 (pow.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) (sqrt.f64 (sqrt.f64 1/2))) (sqrt.f64 (sqrt.f64 1/2))) (sqrt.f64 1/2))) (cos.f64 (*.f64 (*.f64 2 PI.f64) u2)))

series880.0ms (1.1%)

Counts
4 → 9
Calls

4 calls:

420.0ms
(pow.f64 (pow.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) (sqrt.f64 (sqrt.f64 1/2))) (sqrt.f64 (sqrt.f64 1/2))) (sqrt.f64 1/2))
288.0ms
(pow.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) (sqrt.f64 (sqrt.f64 1/2))) (sqrt.f64 (sqrt.f64 1/2)))
171.0ms
(pow.f64 (*.f64 -2 (log.f64 u1)) (sqrt.f64 (sqrt.f64 1/2)))
0.0ms
(sqrt.f64 (sqrt.f64 1/2))
Compiler

Compiled 546 to 546 computations (0% saved)

simplify100.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 0 (75.0ms)

IterNodesCost
049112271
149112271

prune14.4s (17.3%)

Pruning

423 alts after pruning (411 fresh and 12 done)

PrunedKeptTotal
New456211667
Fresh22200222
Picked000
Done01212
Total478423901
Error
0.0b
Counts
901 → 423
Compiler

Compiled 24129 to 21115 computations (12.5% saved)

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

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

rewrite36.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
36×times-frac_binary64
30×*-un-lft-identity_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64
16×distribute-lft-neg-in_binary64 distribute-rgt-neg-in_binary64
12×pow1_binary64 associate-/l*_binary64
11×add-exp-log_binary64 add-cbrt-cube_binary64
9×sqrt-prod_binary64
6×add-log-exp_binary64
4×pow-prod-down_binary64 neg-mul-1_binary64
3×associate-/r*_binary64 cbrt-unprod_binary64 associate-*r*_binary64 prod-exp_binary64
2×sqrt-pow1_binary64
1×flip3-+_binary64 pow1/2_binary64 neg-sub0_binary64 cbrt-undiv_binary64 associate-*l*_binary64 div-sub_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64 +-commutative_binary64 distribute-frac-neg_binary64 flip-+_binary64 sum-log_binary64 *-commutative_binary64
Counts
4 → 105
Calls

8 calls:

13.0ms
(+.f64 (*.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1)))) -6) (cos.f64 (*.f64 (*.f64 2 PI.f64) u2))) 1/2)
6.0ms
(/.f64 (neg.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1)))) -6)
5.0ms
(*.f64 (*.f64 2 PI.f64) u2)
2.0ms
(sqrt.f64 (*.f64 -2 (log.f64 u1)))
0.0ms
(*.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1)))) -6) (cos.f64 (*.f64 (*.f64 2 PI.f64) u2)))

series489.0ms (0.6%)

Counts
4 → 18
Calls

4 calls:

293.0ms
(+.f64 (*.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1)))) -6) (cos.f64 (*.f64 (*.f64 2 PI.f64) u2))) 1/2)
85.0ms
(/.f64 (neg.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1)))) -6)
82.0ms
(sqrt.f64 (*.f64 -2 (log.f64 u1)))
28.0ms
(*.f64 (*.f64 2 PI.f64) u2)
Compiler

Compiled 640 to 623 computations (2.7% saved)

simplify72.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
049602455
149602455

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

rewrite17.0ms (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)
4.0ms
(+.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)

series340.0ms (0.4%)

Counts
3 → 9
Calls

3 calls:

143.0ms
(pow.f64 (*.f64 -2 (log.f64 u1)) 1/2)
100.0ms
(+.f64 1/2 (*.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) 1/2) 1/6))
97.0ms
(*.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) 1/2) 1/6)
Compiler

Compiled 210 to 228 computations (-8.6% saved)

simplify79.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 0 (65.0ms)

IterNodesCost
04857813
14857813

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(sqrt.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 1/6) 1/2))
0.1b
(sqrt.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 1/6) 1/2))
0.0b
(+.f64 (*.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 1/6) 1/2)
0.0b
(+.f64 (*.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 1/6) 1/2)
0.1b
(sqrt.f64 (*.f64 -2 (log.f64 u1)))
0.4b
(*.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 1/6)
0.4b
(*.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 1/6)
0.5b
(*.f64 (sqrt.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 1/6) 1/2)) (sqrt.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 1/6) 1/2)))

rewrite44.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
34×add-sqr-sqrt_binary64
26×pow1_binary64
21×sqrt-prod_binary64
16×*-un-lft-identity_binary64 add-cube-cbrt_binary64
14×associate-*l*_binary64
12×associate-*r*_binary64 sqrt-div_binary64
10×add-exp-log_binary64 add-cbrt-cube_binary64 sqrt-pow1_binary64
9×pow1/2_binary64
8×swap-sqr_binary64
6×pow-prod-down_binary64 flip3-+_binary64 unswap-sqr_binary64 flip-+_binary64
5×pow-prod-up_binary64
4×add-log-exp_binary64 frac-times_binary64
3×cbrt-unprod_binary64 prod-exp_binary64 pow-sqr_binary64 *-commutative_binary64
2×associate-*r/_binary64 rem-sqrt-square_binary64 associate-*l/_binary64
1×rem-square-sqrt_binary64 pow-plus_binary64 sqrt-unprod_binary64 sqr-abs_binary64 pow2_binary64
Counts
4 → 107
Calls

8 calls:

18.0ms
(*.f64 (sqrt.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 1/6) 1/2)) (sqrt.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 1/6) 1/2)))
6.0ms
(*.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 1/6)
6.0ms
(*.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 1/6)
2.0ms
(sqrt.f64 (*.f64 -2 (log.f64 u1)))
0.0ms
(+.f64 (*.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 1/6) 1/2)

series364.0ms (0.4%)

Counts
4 → 12
Calls

4 calls:

100.0ms
(*.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 1/6)
96.0ms
(*.f64 (sqrt.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 1/6) 1/2)) (sqrt.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 1/6) 1/2)))
88.0ms
(*.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) 1/6)
80.0ms
(sqrt.f64 (*.f64 -2 (log.f64 u1)))
Compiler

Compiled 496 to 496 computations (0% saved)

simplify86.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
049191950
149191950

localize23.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b
(*.f64 (*.f64 2 PI.f64) u2)
0.0b
(+.f64 (*.f64 (*.f64 (/.f64 1 6) (pow.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) (sqrt.f64 (sqrt.f64 1/2))) (pow.f64 (sqrt.f64 (sqrt.f64 1/2)) 3))) (cos.f64 (*.f64 (*.f64 2 PI.f64) u2))) 1/2)
0.0b
(cos.f64 (*.f64 (*.f64 2 PI.f64) u2))
0.0b
(*.f64 (*.f64 (/.f64 1 6) (pow.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) (sqrt.f64 (sqrt.f64 1/2))) (pow.f64 (sqrt.f64 (sqrt.f64 1/2)) 3))) (cos.f64 (*.f64 (*.f64 2 PI.f64) u2)))
1.0b
(sqrt.f64 (sqrt.f64 1/2))
1.0b
(sqrt.f64 (sqrt.f64 1/2))
1.0b
(pow.f64 (sqrt.f64 (sqrt.f64 1/2)) 3)
1.4b
(pow.f64 (*.f64 -2 (log.f64 u1)) (sqrt.f64 (sqrt.f64 1/2)))

rewrite24.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
47×sqrt-prod_binary64
22×add-sqr-sqrt_binary64
18×*-un-lft-identity_binary64 add-cube-cbrt_binary64
14×pow1_binary64
12×pow-unpow_binary64 sqrt-pow1_binary64
10×unpow-prod-down_binary64
9×cube-prod_binary64
8×add-exp-log_binary64
7×pow-pow_binary64
6×pow1/2_binary64
5×add-cbrt-cube_binary64
4×add-log-exp_binary64 rem-sqrt-square_binary64
3×pow-exp_binary64
2×pow-to-exp_binary64 sqr-pow_binary64
1×pow-prod-down_binary64 sqrt-pow2_binary64 rem-cube-cbrt_binary64 prod-exp_binary64 unpow3_binary64 cube-mult_binary64
Counts
4 → 101
Calls

8 calls:

5.0ms
(pow.f64 (*.f64 -2 (log.f64 u1)) (sqrt.f64 (sqrt.f64 1/2)))
4.0ms
(pow.f64 (sqrt.f64 (sqrt.f64 1/2)) 3)
2.0ms
(sqrt.f64 (sqrt.f64 1/2))
2.0ms
(sqrt.f64 (sqrt.f64 1/2))
0.0ms
(*.f64 (*.f64 (/.f64 1 6) (pow.f64 (pow.f64 (*.f64 -2 (log.f64 u1)) (sqrt.f64 (sqrt.f64 1/2))) (pow.f64 (sqrt.f64 (sqrt.f64 1/2)) 3))) (cos.f64 (*.f64 (*.f64 2 PI.f64) u2)))

series176.0ms (0.2%)

Counts
4 → 3
Calls

4 calls:

176.0ms
(pow.f64 (*.f64 -2 (log.f64 u1)) (sqrt.f64 (sqrt.f64 1/2)))
0.0ms
(pow.f64 (sqrt.f64 (sqrt.f64 1/2)) 3)
0.0ms
(sqrt.f64 (sqrt.f64 1/2))
0.0ms
(sqrt.f64 (sqrt.f64 1/2))
Compiler

Compiled 176 to 176 computations (0% saved)

simplify81.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 0 (64.0ms)

IterNodesCost
04852985
14852985

localize25.0ms (0%)

Local error

Found 8 expressions with local error:

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

rewrite27.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
12×cbrt-prod_binary64
11×*-un-lft-identity_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64
9×add-exp-log_binary64 sqrt-prod_binary64
7×add-cbrt-cube_binary64
6×associate-/r*_binary64 times-frac_binary64
4×add-log-exp_binary64 pow1_binary64
3×pow1/3_binary64
2×cbrt-undiv_binary64 div-exp_binary64
1×cbrt-unprod_binary64 clear-num_binary64 prod-exp_binary64 frac-2neg_binary64 associate-/l*_binary64 div-inv_binary64
Counts
4 → 63
Calls

8 calls:

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

series786.0ms (0.9%)

Counts
4 → 12
Calls

4 calls:

262.0ms
(/.f64 (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1)))) (cbrt.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))))) (sqrt.f64 6))
178.0ms
(cbrt.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))))
175.0ms
(cbrt.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))))
171.0ms
(cbrt.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))))
Compiler

Compiled 962 to 894 computations (7.1% saved)

simplify78.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 0 (60.0ms)

IterNodesCost
050311131

prune14.5s (17.5%)

Pruning

534 alts after pruning (517 fresh and 17 done)

PrunedKeptTotal
New351131482
Fresh20386406
Picked000
Done01717
Total371534905
Error
0.0b
Counts
905 → 534
Compiler

Compiled 8492 to 6838 computations (19.5% saved)

simplify642.0ms (0.8%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
0498943119
1498943119

regimes12.3s (14.9%)

Compiler

Compiled 126482 to 118829 computations (6.1% saved)

bsearch1.0ms (0%)

regimes174.0ms (0.2%)

Compiler

Compiled 838 to 963 computations (-14.9% saved)

bsearch0.0ms (0%)

regimes19.0ms (0%)

Accuracy

Total 0.3b remaining (99.6%)

Threshold costs 0.3b (99.6%)

Compiler

Compiled 10 to 26 computations (-160% saved)

bsearch3.0ms (0%)

Compiler

Compiled 26 to 29 computations (-11.5% saved)

simplify3.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02641
12641

end0.0ms (0%)

sample22.1s (26.7%)

Algorithm
1×intervals
Results
800.0ms8000×body128valid
217.0ms8000×pre128true
Compiler

Compiled 18130 to 17044 computations (6% saved)

Pareto

0.3232538189112769

Profiling

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