Details

Time bar (total: 7.0min)

analyze892.0ms (0.2%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
0%75%25%3
0%62.5%37.5%4
0%56.2%43.8%5
3.1%46.9%50%6
3.1%45.3%51.6%7
3.1%44.5%52.4%8
3.5%44.1%52.4%9
3.7%43.9%52.4%10
3.8%43.8%52.4%11
3.8%43.8%52.4%12
3.8%43.8%52.4%13
3.8%43.7%52.4%14
Compiler

Compiled 38 to 31 computations (18.4% saved)

sample217.0ms (0.1%)

Algorithm
1×intervals
Results
69.0ms129×body1024valid
54.0ms112×body1024nan
21.0ms58×body512valid
16.0ms48×body512nan
12.0ms11×body2048valid
10.0ms36×body256valid
6.0ms27×body256nan
4.0ms22×body128valid
Compiler

Compiled 78 to 66 computations (15.4% saved)

simplify182.0ms (0%)

Algorithm
1×egg-herbie
Counts
3 → 3
Iterations

Useful iterations: 0 (76.0ms)

IterNodesCost
0479557
1479557

prune6.0ms (0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New033
Fresh033
Picked000
Done000
Total066
Error
52.0b
Counts
6 → 4
Compiler

Compiled 34 to 26 computations (23.5% saved)

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(exp.f64 (*.f64 (/.f64 PI.f64 4) f))
0.0b
(exp.f64 (neg.f64 (*.f64 (/.f64 PI.f64 4) f)))
0.0b
(exp.f64 (neg.f64 (*.f64 (/.f64 PI.f64 4) f)))
0.0b
(+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 PI.f64 4) f))))
0.3b
(*.f64 (/.f64 PI.f64 4) f)
0.3b
(log.f64 (/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 PI.f64 4) f)))) (-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 PI.f64 4) f))))))
0.8b
(/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 PI.f64 4) f)))) (-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 PI.f64 4) f)))))
6.0b
(-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 PI.f64 4) f))))

rewrite67.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
88×*-un-lft-identity_binary64
70×times-frac_binary64
67×add-sqr-sqrt_binary64
38×add-cube-cbrt_binary64
36×log-prod_binary64
14×add-exp-log_binary64
13×distribute-lft-out_binary64 cosh-undef_binary64 associate-*l*_binary64
12×sinh-undef_binary64 difference-of-squares_binary64 distribute-lft-out--_binary64
11×add-cbrt-cube_binary64
7×pow1_binary64
6×associate-/r*_binary64 add-log-exp_binary64
5×associate-/l*_binary64
4×associate-/r/_binary64
3×flip3--_binary64 associate-*r*_binary64 cancel-sign-sub-inv_binary64 div-inv_binary64 div-exp_binary64 flip--_binary64
2×associate-/l/_binary64 cbrt-unprod_binary64 cbrt-undiv_binary64 rem-log-exp_binary64 unswap-sqr_binary64 prod-exp_binary64
1×pow-prod-down_binary64 flip3-+_binary64 sub-neg_binary64 diff-log_binary64 log-pow_binary64 clear-num_binary64 frac-2neg_binary64 log-div_binary64 flip-+_binary64 associate-*l/_binary64 *-commutative_binary64
Counts
4 → 153
Calls

8 calls:

11.0ms
(/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 PI.f64 4) f)))) (-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 PI.f64 4) f)))))
10.0ms
(log.f64 (/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 PI.f64 4) f)))) (-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 PI.f64 4) f))))))
7.0ms
(*.f64 (/.f64 PI.f64 4) f)
7.0ms
(-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 PI.f64 4) f))))
0.0ms
(+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 PI.f64 4) f))))

series516.0ms (0.1%)

Counts
4 → 21
Calls

4 calls:

282.0ms
(log.f64 (/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 PI.f64 4) f)))) (-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 PI.f64 4) f))))))
132.0ms
(/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 PI.f64 4) f)))) (-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 PI.f64 4) f)))))
71.0ms
(-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 PI.f64 4) f))))
30.0ms
(*.f64 (/.f64 PI.f64 4) f)
Compiler

Compiled 1050 to 832 computations (20.8% saved)

simplify125.0ms (0%)

Algorithm
1×egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
048948577
148948577

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(exp.f64 (*.f64 (/.f64 PI.f64 4) f))
0.0b
(pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))
0.0b
(pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))
0.0b
(+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))
0.3b
(*.f64 (/.f64 PI.f64 4) f)
0.3b
(log.f64 (/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))) (-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))))
0.8b
(/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))) (-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))
6.0b
(-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))

rewrite67.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
94×add-sqr-sqrt_binary64
89×*-un-lft-identity_binary64
66×times-frac_binary64
39×add-cube-cbrt_binary64
34×log-prod_binary64
30×difference-of-squares_binary64
15×distribute-lft-out_binary64
14×add-exp-log_binary64
13×associate-*l*_binary64 unpow-prod-down_binary64
11×sqr-pow_binary64 add-cbrt-cube_binary64
10×distribute-lft-out--_binary64
7×associate-/r*_binary64 pow1_binary64 cancel-sign-sub-inv_binary64
6×add-log-exp_binary64
4×associate-/r/_binary64 associate-/l*_binary64
3×flip3--_binary64 associate-*r*_binary64 div-inv_binary64 div-exp_binary64 flip--_binary64
2×associate-/l/_binary64 cbrt-unprod_binary64 cbrt-undiv_binary64 rem-log-exp_binary64 unswap-sqr_binary64 prod-exp_binary64
1×pow-prod-down_binary64 flip3-+_binary64 sub-neg_binary64 diff-log_binary64 log-pow_binary64 clear-num_binary64 frac-2neg_binary64 log-div_binary64 flip-+_binary64 associate-*l/_binary64 *-commutative_binary64
Counts
4 → 154
Calls

8 calls:

17.0ms
(/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))) (-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))
13.0ms
(log.f64 (/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))) (-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))))
7.0ms
(*.f64 (/.f64 PI.f64 4) f)
7.0ms
(-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))
0.0ms
(+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))

series538.0ms (0.1%)

Counts
4 → 12
Calls

4 calls:

330.0ms
(log.f64 (/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))) (-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))))
137.0ms
(/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))) (-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))
42.0ms
(-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))
29.0ms
(*.f64 (/.f64 PI.f64 4) f)
Compiler

Compiled 988 to 782 computations (20.9% saved)

simplify121.0ms (0%)

Algorithm
1×egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
050058522

prune5.1s (1.2%)

Pruning

177 alts after pruning (175 fresh and 2 done)

PrunedKeptTotal
New167173340
Fresh022
Picked000
Done022
Total167177344
Error
0.6b
Counts
344 → 177
Compiler

Compiled 20835 to 15444 computations (25.9% saved)

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b
(*.f64 (/.f64 PI.f64 4) f)
0.3b
(*.f64 (/.f64 PI.f64 4) f)
0.0b
(sinh.f64 (*.f64 (/.f64 PI.f64 4) f))
0.0b
(cosh.f64 (*.f64 (/.f64 PI.f64 4) f))
0.3b
(*.f64 (/.f64 PI.f64 4) f)
0.3b
(log.f64 (/.f64 (cosh.f64 (*.f64 (/.f64 PI.f64 4) f)) (sinh.f64 (*.f64 (/.f64 PI.f64 4) f))))
0.4b
(*.f64 (/.f64 1 (/.f64 PI.f64 4)) (+.f64 (log.f64 1) (log.f64 (/.f64 (cosh.f64 (*.f64 (/.f64 PI.f64 4) f)) (sinh.f64 (*.f64 (/.f64 PI.f64 4) f))))))
1.0b
(/.f64 (cosh.f64 (*.f64 (/.f64 PI.f64 4) f)) (sinh.f64 (*.f64 (/.f64 PI.f64 4) f)))

rewrite59.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
100×times-frac_binary64
82×add-sqr-sqrt_binary64
69×*-un-lft-identity_binary64
63×add-cube-cbrt_binary64
57×associate-*l*_binary64
33×add-exp-log_binary64
20×add-cbrt-cube_binary64
14×log-prod_binary64
13×pow1_binary64
10×associate-*r*_binary64 div-exp_binary64
9×prod-exp_binary64
7×unswap-sqr_binary64 div-inv_binary64
5×cbrt-unprod_binary64 cbrt-undiv_binary64 log-pow_binary64
4×add-log-exp_binary64 distribute-lft-out_binary64
3×associate-/r*_binary64 associate-/r/_binary64 associate-/l*_binary64
2×pow-prod-down_binary64 flip3-+_binary64 sinh-def_binary64 1-exp_binary64 rem-log-exp_binary64 associate-*r/_binary64 rec-exp_binary64 flip-+_binary64 frac-times_binary64 associate-*l/_binary64 *-commutative_binary64
1×associate-/l/_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 clear-num_binary64 frac-2neg_binary64 log-div_binary64 cosh-def_binary64
Counts
4 → 168
Calls

8 calls:

21.0ms
(*.f64 (/.f64 1 (/.f64 PI.f64 4)) (+.f64 (log.f64 1) (log.f64 (/.f64 (cosh.f64 (*.f64 (/.f64 PI.f64 4) f)) (sinh.f64 (*.f64 (/.f64 PI.f64 4) f))))))
7.0ms
(*.f64 (/.f64 PI.f64 4) f)
7.0ms
(/.f64 (cosh.f64 (*.f64 (/.f64 PI.f64 4) f)) (sinh.f64 (*.f64 (/.f64 PI.f64 4) f)))
3.0ms
(log.f64 (/.f64 (cosh.f64 (*.f64 (/.f64 PI.f64 4) f)) (sinh.f64 (*.f64 (/.f64 PI.f64 4) f))))
0.0ms
(cosh.f64 (*.f64 (/.f64 PI.f64 4) f))

series886.0ms (0.2%)

Counts
4 → 21
Calls

4 calls:

361.0ms
(*.f64 (/.f64 1 (/.f64 PI.f64 4)) (+.f64 (log.f64 1) (log.f64 (/.f64 (cosh.f64 (*.f64 (/.f64 PI.f64 4) f)) (sinh.f64 (*.f64 (/.f64 PI.f64 4) f))))))
317.0ms
(log.f64 (/.f64 (cosh.f64 (*.f64 (/.f64 PI.f64 4) f)) (sinh.f64 (*.f64 (/.f64 PI.f64 4) f))))
181.0ms
(/.f64 (cosh.f64 (*.f64 (/.f64 PI.f64 4) f)) (sinh.f64 (*.f64 (/.f64 PI.f64 4) f)))
26.0ms
(*.f64 (/.f64 PI.f64 4) f)
Compiler

Compiled 952 to 763 computations (19.9% saved)

simplify144.0ms (0%)

Algorithm
1×egg-herbie
Counts
189 → 189
Iterations

Useful iterations: 0 (85.0ms)

IterNodesCost
049226381
149226381

localize9.0ms (0%)

Local error

Found 8 expressions with local error:

0.4b
(*.f64 (log.f64 (/.f64 2 (*.f64 PI.f64 (*.f64 1/2 f)))) (/.f64 -4 PI.f64))
0.3b
(*.f64 PI.f64 (*.f64 1/2 f))
0.3b
(/.f64 2 (*.f64 PI.f64 (*.f64 1/2 f)))
0.0b
(log.f64 (/.f64 2 (*.f64 PI.f64 (*.f64 1/2 f))))
0.0b
(log.f64 (/.f64 2 (*.f64 PI.f64 (*.f64 1/2 f))))
0.3b
(/.f64 2 (*.f64 PI.f64 (*.f64 1/2 f)))
0.3b
(*.f64 PI.f64 (*.f64 1/2 f))
0.4b
(*.f64 (log.f64 (/.f64 2 (*.f64 PI.f64 (*.f64 1/2 f)))) (/.f64 -4 PI.f64))

rewrite37.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
33×add-exp-log_binary64
23×add-cbrt-cube_binary64
22×add-sqr-sqrt_binary64
17×*-un-lft-identity_binary64 add-cube-cbrt_binary64
16×times-frac_binary64
14×associate-*r*_binary64
13×pow1_binary64
11×prod-exp_binary64
8×cbrt-unprod_binary64
7×log-prod_binary64 associate-*l*_binary64 div-exp_binary64
4×pow-prod-down_binary64 add-log-exp_binary64 cbrt-undiv_binary64 rem-log-exp_binary64
3×associate-/l*_binary64 div-inv_binary64
2×log-pow_binary64 unswap-sqr_binary64 *-commutative_binary64
1×associate-/r*_binary64 associate-*r/_binary64 clear-num_binary64 frac-2neg_binary64 log-div_binary64
Counts
4 → 94
Calls

8 calls:

10.0ms
(*.f64 (log.f64 (/.f64 2 (*.f64 PI.f64 (*.f64 1/2 f)))) (/.f64 -4 PI.f64))
9.0ms
(/.f64 2 (*.f64 PI.f64 (*.f64 1/2 f)))
5.0ms
(log.f64 (/.f64 2 (*.f64 PI.f64 (*.f64 1/2 f))))
5.0ms
(*.f64 PI.f64 (*.f64 1/2 f))
0.0ms
(log.f64 (/.f64 2 (*.f64 PI.f64 (*.f64 1/2 f))))

series235.0ms (0.1%)

Counts
4 → 12
Calls

4 calls:

108.0ms
(*.f64 (log.f64 (/.f64 2 (*.f64 PI.f64 (*.f64 1/2 f)))) (/.f64 -4 PI.f64))
71.0ms
(log.f64 (/.f64 2 (*.f64 PI.f64 (*.f64 1/2 f))))
32.0ms
(/.f64 2 (*.f64 PI.f64 (*.f64 1/2 f)))
24.0ms
(*.f64 PI.f64 (*.f64 1/2 f))
Compiler

Compiled 280 to 256 computations (8.6% saved)

simplify74.0ms (0%)

Algorithm
1×egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
049481498
149481498

localize22.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(exp.f64 (*.f64 (/.f64 PI.f64 4) f))
0.0b
(pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))
0.0b
(pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))
0.0b
(+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))
0.4b
(-.f64 (log.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))) (log.f64 (-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))))
0.7b
(log.f64 (-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))
0.7b
(log.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))
6.0b
(-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))

rewrite47.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
28×add-sqr-sqrt_binary64
25×*-un-lft-identity_binary64
22×log-prod_binary64
11×pow1_binary64 add-cube-cbrt_binary64 cancel-sign-sub-inv_binary64
10×difference-of-squares_binary64
8×log-div_binary64
7×associate--r+_binary64 log-pow_binary64 distribute-lft-out--_binary64
6×add-log-exp_binary64 add-exp-log_binary64 unpow-prod-down_binary64
4×flip3--_binary64 sqr-pow_binary64 add-cbrt-cube_binary64 flip--_binary64 associate--l+_binary64
2×flip3-+_binary64 sub-neg_binary64 associate--l-_binary64 diff-log_binary64 distribute-lft-out_binary64 associate--r-_binary64 rem-log-exp_binary64 flip-+_binary64
Counts
4 → 90
Calls

8 calls:

16.0ms
(-.f64 (log.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))) (log.f64 (-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))))
7.0ms
(-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))
6.0ms
(log.f64 (-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))
6.0ms
(log.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))
0.0ms
(+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))

series514.0ms (0.1%)

Counts
4 → 12
Calls

4 calls:

247.0ms
(-.f64 (log.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))) (log.f64 (-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))))
121.0ms
(log.f64 (-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))
100.0ms
(log.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))
46.0ms
(-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))
Compiler

Compiled 920 to 727 computations (21% saved)

simplify116.0ms (0%)

Algorithm
1×egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 0 (76.0ms)

IterNodesCost
048973958
148973958

localize26.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))
0.0b
(sqrt.f64 (exp.f64 (/.f64 (*.f64 PI.f64 f) 1)))
0.0b
(+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))
0.0b
(+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))
0.6b
(log.f64 (/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))) (/.f64 (-.f64 (sqrt.f64 (exp.f64 (/.f64 (*.f64 PI.f64 f) 1))) (pow.f64 (exp.f64 -1/4) (*.f64 (*.f64 PI.f64 f) 2))) (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))))
0.6b
(/.f64 (-.f64 (sqrt.f64 (exp.f64 (/.f64 (*.f64 PI.f64 f) 1))) (pow.f64 (exp.f64 -1/4) (*.f64 (*.f64 PI.f64 f) 2))) (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))
0.8b
(/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))) (/.f64 (-.f64 (sqrt.f64 (exp.f64 (/.f64 (*.f64 PI.f64 f) 1))) (pow.f64 (exp.f64 -1/4) (*.f64 (*.f64 PI.f64 f) 2))) (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))))
6.2b
(-.f64 (sqrt.f64 (exp.f64 (/.f64 (*.f64 PI.f64 f) 1))) (pow.f64 (exp.f64 -1/4) (*.f64 (*.f64 PI.f64 f) 2)))

rewrite258.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
768×times-frac_binary64
723×*-un-lft-identity_binary64
671×add-sqr-sqrt_binary64
252×difference-of-squares_binary64
251×add-cube-cbrt_binary64
194×distribute-lft-out_binary64
189×log-prod_binary64
126×sqrt-prod_binary64
87×unpow-prod-down_binary64
85×sqr-pow_binary64
50×associate-/r*_binary64
42×distribute-lft-out--_binary64
22×associate-/r/_binary64
17×add-exp-log_binary64
14×associate-/l*_binary64
12×div-inv_binary64
11×flip3-+_binary64 add-cbrt-cube_binary64 flip-+_binary64
7×cancel-sign-sub-inv_binary64 div-exp_binary64
6×add-log-exp_binary64
5×pow1_binary64
4×associate-/l/_binary64 cbrt-undiv_binary64
3×rem-log-exp_binary64
2×flip3--_binary64 clear-num_binary64 frac-2neg_binary64 flip--_binary64
1×sub-neg_binary64 diff-log_binary64 log-pow_binary64 div-sub_binary64 log-div_binary64
Counts
4 → 548
Calls

8 calls:

35.0ms
(log.f64 (/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))) (/.f64 (-.f64 (sqrt.f64 (exp.f64 (/.f64 (*.f64 PI.f64 f) 1))) (pow.f64 (exp.f64 -1/4) (*.f64 (*.f64 PI.f64 f) 2))) (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))))
32.0ms
(/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))) (/.f64 (-.f64 (sqrt.f64 (exp.f64 (/.f64 (*.f64 PI.f64 f) 1))) (pow.f64 (exp.f64 -1/4) (*.f64 (*.f64 PI.f64 f) 2))) (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))))
19.0ms
(/.f64 (-.f64 (sqrt.f64 (exp.f64 (/.f64 (*.f64 PI.f64 f) 1))) (pow.f64 (exp.f64 -1/4) (*.f64 (*.f64 PI.f64 f) 2))) (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))
11.0ms
(-.f64 (sqrt.f64 (exp.f64 (/.f64 (*.f64 PI.f64 f) 1))) (pow.f64 (exp.f64 -1/4) (*.f64 (*.f64 PI.f64 f) 2)))
0.0ms
(+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))

series810.0ms (0.2%)

Counts
4 → 12
Calls

4 calls:

428.0ms
(log.f64 (/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))) (/.f64 (-.f64 (sqrt.f64 (exp.f64 (/.f64 (*.f64 PI.f64 f) 1))) (pow.f64 (exp.f64 -1/4) (*.f64 (*.f64 PI.f64 f) 2))) (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))))
188.0ms
(/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))) (/.f64 (-.f64 (sqrt.f64 (exp.f64 (/.f64 (*.f64 PI.f64 f) 1))) (pow.f64 (exp.f64 -1/4) (*.f64 (*.f64 PI.f64 f) 2))) (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))))
131.0ms
(/.f64 (-.f64 (sqrt.f64 (exp.f64 (/.f64 (*.f64 PI.f64 f) 1))) (pow.f64 (exp.f64 -1/4) (*.f64 (*.f64 PI.f64 f) 2))) (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))
63.0ms
(-.f64 (sqrt.f64 (exp.f64 (/.f64 (*.f64 PI.f64 f) 1))) (pow.f64 (exp.f64 -1/4) (*.f64 (*.f64 PI.f64 f) 2)))
Compiler

Compiled 1236 to 987 computations (20.1% saved)

simplify542.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
560 → 560
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
0507262562

localize32.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(sqrt.f64 (/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))) (-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))))
0.0b
(sqrt.f64 (/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))) (-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))))
0.0b
(+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))
0.0b
(+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))
0.8b
(/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))) (-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))
0.8b
(/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))) (-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))
6.0b
(-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))
6.0b
(-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))

rewrite80.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
94×add-sqr-sqrt_binary64
90×*-un-lft-identity_binary64
56×times-frac_binary64
36×difference-of-squares_binary64
34×add-cube-cbrt_binary64
18×unpow-prod-down_binary64
16×distribute-lft-out_binary64
14×associate-/r*_binary64 sqr-pow_binary64 cancel-sign-sub-inv_binary64
12×distribute-lft-out--_binary64
8×add-log-exp_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 associate-/l*_binary64
4×associate-/l/_binary64 pow1_binary64 flip3--_binary64 associate-/r/_binary64 flip--_binary64
2×flip3-+_binary64 sub-neg_binary64 diff-log_binary64 cbrt-undiv_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64 flip-+_binary64
Counts
4 → 154
Calls

8 calls:

14.0ms
(/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))) (-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))
14.0ms
(/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))) (-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))
7.0ms
(-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))
7.0ms
(-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))
0.0ms
(+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))

series391.0ms (0.1%)

Counts
4 → 12
Calls

4 calls:

147.0ms
(/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))) (-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))
146.0ms
(/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))) (-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))
49.0ms
(-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))
48.0ms
(-.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))
Compiler

Compiled 1672 to 1240 computations (25.8% saved)

simplify124.0ms (0%)

Algorithm
1×egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
056659312

prune48.7s (11.6%)

Pruning

529 alts after pruning (522 fresh and 7 done)

PrunedKeptTotal
New7563671123
Fresh15155170
Picked000
Done077
Total7715291300
Error
0.3b
Counts
1300 → 529
Compiler

Compiled 66991 to 46247 computations (31% saved)

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b
(*.f64 (/.f64 PI.f64 4) f)
0.3b
(/.f64 (+.f64 (log.f64 (/.f64 (cosh.f64 (*.f64 (/.f64 PI.f64 4) f)) (sinh.f64 (*.f64 (/.f64 PI.f64 4) f)))) (log.f64 1)) (/.f64 PI.f64 4))
0.0b
(sinh.f64 (*.f64 (/.f64 PI.f64 4) f))
0.0b
(cosh.f64 (*.f64 (/.f64 PI.f64 4) f))
0.3b
(*.f64 (/.f64 PI.f64 4) f)
0.3b
(*.f64 (/.f64 PI.f64 4) f)
0.3b
(log.f64 (/.f64 (cosh.f64 (*.f64 (/.f64 PI.f64 4) f)) (sinh.f64 (*.f64 (/.f64 PI.f64 4) f))))
1.0b
(/.f64 (cosh.f64 (*.f64 (/.f64 PI.f64 4) f)) (sinh.f64 (*.f64 (/.f64 PI.f64 4) f)))

rewrite37.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
45×add-sqr-sqrt_binary64
38×times-frac_binary64
35×*-un-lft-identity_binary64 add-cube-cbrt_binary64
26×associate-*l*_binary64
19×add-exp-log_binary64
16×add-cbrt-cube_binary64
14×log-prod_binary64
9×pow1_binary64
6×associate-*r*_binary64
4×add-log-exp_binary64 cbrt-unprod_binary64 unswap-sqr_binary64 prod-exp_binary64 div-inv_binary64 div-exp_binary64
3×associate-/r*_binary64 cbrt-undiv_binary64 associate-/l*_binary64
2×pow-prod-down_binary64 sinh-def_binary64 rem-log-exp_binary64 associate-/r/_binary64 associate-*l/_binary64 *-commutative_binary64
1×associate-/l/_binary64 log-pow_binary64 clear-num_binary64 frac-2neg_binary64 log-div_binary64 cosh-def_binary64
Counts
4 → 118
Calls

8 calls:

7.0ms
(*.f64 (/.f64 PI.f64 4) f)
7.0ms
(*.f64 (/.f64 PI.f64 4) f)
5.0ms
(/.f64 (cosh.f64 (*.f64 (/.f64 PI.f64 4) f)) (sinh.f64 (*.f64 (/.f64 PI.f64 4) f)))
3.0ms
(log.f64 (/.f64 (cosh.f64 (*.f64 (/.f64 PI.f64 4) f)) (sinh.f64 (*.f64 (/.f64 PI.f64 4) f))))
0.0ms
(cosh.f64 (*.f64 (/.f64 PI.f64 4) f))

series545.0ms (0.1%)

Counts
4 → 18
Calls

4 calls:

309.0ms
(log.f64 (/.f64 (cosh.f64 (*.f64 (/.f64 PI.f64 4) f)) (sinh.f64 (*.f64 (/.f64 PI.f64 4) f))))
176.0ms
(/.f64 (cosh.f64 (*.f64 (/.f64 PI.f64 4) f)) (sinh.f64 (*.f64 (/.f64 PI.f64 4) f)))
33.0ms
(*.f64 (/.f64 PI.f64 4) f)
26.0ms
(*.f64 (/.f64 PI.f64 4) f)
Compiler

Compiled 790 to 642 computations (18.7% saved)

simplify91.0ms (0%)

Algorithm
1×egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
049553001
149553001

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

0.4b
(*.f64 (log.f64 (/.f64 4 (*.f64 PI.f64 f))) (/.f64 -4 PI.f64))
0.3b
(*.f64 PI.f64 f)
0.3b
(/.f64 4 (*.f64 PI.f64 f))
0.0b
(log.f64 (/.f64 4 (*.f64 PI.f64 f)))
0.0b
(log.f64 (/.f64 4 (*.f64 PI.f64 f)))
0.3b
(/.f64 4 (*.f64 PI.f64 f))
0.3b
(*.f64 PI.f64 f)
0.4b
(*.f64 (log.f64 (/.f64 4 (*.f64 PI.f64 f))) (/.f64 -4 PI.f64))

rewrite27.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
25×add-sqr-sqrt_binary64
22×add-exp-log_binary64
18×*-un-lft-identity_binary64 add-cube-cbrt_binary64
16×associate-*r*_binary64 add-cbrt-cube_binary64 times-frac_binary64
10×pow1_binary64
7×log-prod_binary64 associate-*l*_binary64
5×prod-exp_binary64 div-exp_binary64
4×add-log-exp_binary64 cbrt-unprod_binary64
3×cbrt-undiv_binary64 rem-log-exp_binary64 unswap-sqr_binary64 associate-/l*_binary64 div-inv_binary64
2×pow-prod-down_binary64 log-pow_binary64 *-commutative_binary64
1×associate-/r*_binary64 associate-*r/_binary64 clear-num_binary64 frac-2neg_binary64 log-div_binary64
Counts
4 → 91
Calls

8 calls:

9.0ms
(*.f64 (log.f64 (/.f64 4 (*.f64 PI.f64 f))) (/.f64 -4 PI.f64))
4.0ms
(/.f64 4 (*.f64 PI.f64 f))
4.0ms
(log.f64 (/.f64 4 (*.f64 PI.f64 f)))
4.0ms
(*.f64 PI.f64 f)
0.0ms
(log.f64 (/.f64 4 (*.f64 PI.f64 f)))

series229.0ms (0.1%)

Counts
4 → 12
Calls

4 calls:

103.0ms
(*.f64 (log.f64 (/.f64 4 (*.f64 PI.f64 f))) (/.f64 -4 PI.f64))
75.0ms
(log.f64 (/.f64 4 (*.f64 PI.f64 f)))
27.0ms
(/.f64 4 (*.f64 PI.f64 f))
23.0ms
(*.f64 PI.f64 f)
Compiler

Compiled 268 to 244 computations (9% saved)

simplify79.0ms (0%)

Algorithm
1×egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
049641399
149641399

localize22.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b
(*.f64 (/.f64 PI.f64 4) f)
0.3b
(*.f64 (/.f64 PI.f64 4) f)
0.0b
(sinh.f64 (*.f64 (/.f64 PI.f64 4) f))
0.0b
(cosh.f64 (*.f64 (/.f64 PI.f64 4) f))
1.0b
(cbrt.f64 (/.f64 1 (/.f64 PI.f64 4)))
1.0b
(cbrt.f64 (/.f64 1 (/.f64 PI.f64 4)))
1.0b
(*.f64 (cbrt.f64 (/.f64 1 (/.f64 PI.f64 4))) (cbrt.f64 (/.f64 1 (/.f64 PI.f64 4))))
1.0b
(/.f64 (cosh.f64 (*.f64 (/.f64 PI.f64 4) f)) (sinh.f64 (*.f64 (/.f64 PI.f64 4) f)))

rewrite151.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
477×times-frac_binary64
346×add-sqr-sqrt_binary64
328×cbrt-prod_binary64
252×*-un-lft-identity_binary64
226×add-cube-cbrt_binary64
49×swap-sqr_binary64
47×associate-*r*_binary64 associate-*l*_binary64
36×unswap-sqr_binary64
27×div-inv_binary64
11×pow1_binary64
8×pow1/3_binary64 add-exp-log_binary64
7×associate-/r/_binary64
6×cbrt-div_binary64 add-cbrt-cube_binary64
4×add-log-exp_binary64
3×associate-/r*_binary64 associate-/l*_binary64
2×pow-prod-down_binary64 pow-prod-up_binary64 pow-sqr_binary64
1×associate-/l/_binary64 sinh-def_binary64 cbrt-unprod_binary64 cbrt-undiv_binary64 associate-*r/_binary64 pow-plus_binary64 clear-num_binary64 prod-exp_binary64 frac-2neg_binary64 div-exp_binary64 frac-times_binary64 pow2_binary64 cosh-def_binary64 associate-*l/_binary64 *-commutative_binary64
Counts
4 → 335
Calls

8 calls:

65.0ms
(*.f64 (cbrt.f64 (/.f64 1 (/.f64 PI.f64 4))) (cbrt.f64 (/.f64 1 (/.f64 PI.f64 4))))
6.0ms
(cbrt.f64 (/.f64 1 (/.f64 PI.f64 4)))
6.0ms
(cbrt.f64 (/.f64 1 (/.f64 PI.f64 4)))
5.0ms
(/.f64 (cosh.f64 (*.f64 (/.f64 PI.f64 4) f)) (sinh.f64 (*.f64 (/.f64 PI.f64 4) f)))
0.0ms
(cosh.f64 (*.f64 (/.f64 PI.f64 4) f))

series183.0ms (0%)

Counts
4 → 6
Calls

4 calls:

182.0ms
(/.f64 (cosh.f64 (*.f64 (/.f64 PI.f64 4) f)) (sinh.f64 (*.f64 (/.f64 PI.f64 4) f)))
0.0ms
(*.f64 (cbrt.f64 (/.f64 1 (/.f64 PI.f64 4))) (cbrt.f64 (/.f64 1 (/.f64 PI.f64 4))))
0.0ms
(cbrt.f64 (/.f64 1 (/.f64 PI.f64 4)))
0.0ms
(cbrt.f64 (/.f64 1 (/.f64 PI.f64 4)))
Compiler

Compiled 378 to 306 computations (19% saved)

simplify166.0ms (0%)

Algorithm
1×egg-herbie
Counts
341 → 341
Iterations

Useful iterations: 0 (73.0ms)

IterNodesCost
049489151
149489151

localize37.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(exp.f64 (neg.f64 (*.f64 (/.f64 PI.f64 4) f)))
0.0b
(+.f64 (pow.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) -2) 1)
0.0b
(+.f64 (pow.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) 2) (+.f64 (pow.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) -2) 1))
0.0b
(+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 PI.f64 4) f))))
0.7b
(log.f64 (+.f64 (pow.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) 2) (+.f64 (pow.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) -2) 1)))
0.7b
(log.f64 (/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 PI.f64 4) f)))) (-.f64 (pow.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) 3) (pow.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) -3))))
0.8b
(/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 PI.f64 4) f)))) (-.f64 (pow.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) 3) (pow.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) -3)))
5.6b
(-.f64 (pow.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) 3) (pow.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) -3))

rewrite129.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
256×add-sqr-sqrt_binary64
160×times-frac_binary64
147×*-un-lft-identity_binary64
144×difference-of-squares_binary64
91×log-prod_binary64
87×unpow-prod-down_binary64
85×sqr-pow_binary64
52×add-cube-cbrt_binary64
36×distribute-lft-out_binary64 cube-prod_binary64
33×cosh-undef_binary64
16×associate-/r*_binary64
12×distribute-lft-out--_binary64
10×add-exp-log_binary64
7×cancel-sign-sub-inv_binary64
6×add-log-exp_binary64 pow1_binary64 add-cbrt-cube_binary64
5×associate-/l*_binary64
4×associate-/r/_binary64
3×flip3--_binary64 rem-log-exp_binary64 log-div_binary64 flip--_binary64
2×flip3-+_binary64 associate-/l/_binary64 log-pow_binary64 div-inv_binary64 div-exp_binary64 flip-+_binary64
1×sub-neg_binary64 diff-log_binary64 cbrt-undiv_binary64 clear-num_binary64 frac-2neg_binary64
Counts
4 → 261
Calls

8 calls:

20.0ms
(log.f64 (/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 PI.f64 4) f)))) (-.f64 (pow.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) 3) (pow.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) -3))))
19.0ms
(/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 PI.f64 4) f)))) (-.f64 (pow.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) 3) (pow.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) -3)))
14.0ms
(log.f64 (+.f64 (pow.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) 2) (+.f64 (pow.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) -2) 1)))
11.0ms
(-.f64 (pow.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) 3) (pow.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) -3))
0.0ms
(+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 PI.f64 4) f))))

series1.2s (0.3%)

Counts
4 → 24
Calls

4 calls:

473.0ms
(log.f64 (/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 PI.f64 4) f)))) (-.f64 (pow.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) 3) (pow.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) -3))))
304.0ms
(/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 PI.f64 4) f)))) (-.f64 (pow.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) 3) (pow.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) -3)))
261.0ms
(log.f64 (+.f64 (pow.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) 2) (+.f64 (pow.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) -2) 1)))
195.0ms
(-.f64 (pow.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) 3) (pow.f64 (exp.f64 (*.f64 (/.f64 PI.f64 4) f)) -3))
Compiler

Compiled 1882 to 1522 computations (19.1% saved)

simplify266.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
285 → 285
Iterations

Useful iterations: 0 (87.0ms)

IterNodesCost
0602922345

localize38.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(sqrt.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)) (exp.f64 (*.f64 f (/.f64 PI.f64 4)))))
0.0b
(sqrt.f64 (exp.f64 (*.f64 PI.f64 f)))
0.0b
(+.f64 (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)) (exp.f64 (*.f64 f (/.f64 PI.f64 4))))
0.0b
(+.f64 (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)) (exp.f64 (*.f64 f (/.f64 PI.f64 4))))
1.1b
(log.f64 (*.f64 (*.f64 (-.f64 (pow.f64 (exp.f64 (/.f64 PI.f64 4)) (*.f64 f 2)) (pow.f64 (exp.f64 -1/4) (*.f64 (*.f64 PI.f64 f) 2))) (/.f64 (sqrt.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)) (exp.f64 (*.f64 f (/.f64 PI.f64 4))))) (-.f64 (sqrt.f64 (exp.f64 (*.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (*.f64 (*.f64 PI.f64 f) 2))))) (/.f64 (sqrt.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)) (exp.f64 (*.f64 f (/.f64 PI.f64 4))))) (-.f64 (exp.f64 (*.f64 f (/.f64 PI.f64 4))) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))))
6.0b
(-.f64 (exp.f64 (*.f64 f (/.f64 PI.f64 4))) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))
6.2b
(-.f64 (sqrt.f64 (exp.f64 (*.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (*.f64 (*.f64 PI.f64 f) 2)))
6.2b
(-.f64 (pow.f64 (exp.f64 (/.f64 PI.f64 4)) (*.f64 f 2)) (pow.f64 (exp.f64 -1/4) (*.f64 (*.f64 PI.f64 f) 2)))

rewrite105.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
37×add-sqr-sqrt_binary64
26×add-exp-log_binary64
21×cancel-sign-sub-inv_binary64
18×unpow-prod-down_binary64 difference-of-squares_binary64
16×*-un-lft-identity_binary64
12×sqr-pow_binary64
11×log-div_binary64
10×add-log-exp_binary64 pow1_binary64 add-cube-cbrt_binary64 prod-exp_binary64
9×frac-times_binary64 associate-*l/_binary64
7×flip3--_binary64 rem-log-exp_binary64 flip--_binary64
5×div-exp_binary64
4×add-cbrt-cube_binary64
3×pow-prod-down_binary64 sub-neg_binary64 diff-log_binary64 associate-*r/_binary64 log-pow_binary64 distribute-lft-out--_binary64 sqrt-prod_binary64
1×log-prod_binary64
Counts
4 → 104
Calls

8 calls:

49.0ms
(log.f64 (*.f64 (*.f64 (-.f64 (pow.f64 (exp.f64 (/.f64 PI.f64 4)) (*.f64 f 2)) (pow.f64 (exp.f64 -1/4) (*.f64 (*.f64 PI.f64 f) 2))) (/.f64 (sqrt.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)) (exp.f64 (*.f64 f (/.f64 PI.f64 4))))) (-.f64 (sqrt.f64 (exp.f64 (*.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (*.f64 (*.f64 PI.f64 f) 2))))) (/.f64 (sqrt.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)) (exp.f64 (*.f64 f (/.f64 PI.f64 4))))) (-.f64 (exp.f64 (*.f64 f (/.f64 PI.f64 4))) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))))
13.0ms
(-.f64 (sqrt.f64 (exp.f64 (*.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (*.f64 (*.f64 PI.f64 f) 2)))
12.0ms
(-.f64 (pow.f64 (exp.f64 (/.f64 PI.f64 4)) (*.f64 f 2)) (pow.f64 (exp.f64 -1/4) (*.f64 (*.f64 PI.f64 f) 2)))
7.0ms
(-.f64 (exp.f64 (*.f64 f (/.f64 PI.f64 4))) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))
0.0ms
(+.f64 (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)) (exp.f64 (*.f64 f (/.f64 PI.f64 4))))

series2.2s (0.5%)

Counts
4 → 12
Calls

4 calls:

2.1s
(log.f64 (*.f64 (*.f64 (-.f64 (pow.f64 (exp.f64 (/.f64 PI.f64 4)) (*.f64 f 2)) (pow.f64 (exp.f64 -1/4) (*.f64 (*.f64 PI.f64 f) 2))) (/.f64 (sqrt.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)) (exp.f64 (*.f64 f (/.f64 PI.f64 4))))) (-.f64 (sqrt.f64 (exp.f64 (*.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (*.f64 (*.f64 PI.f64 f) 2))))) (/.f64 (sqrt.f64 (+.f64 (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)) (exp.f64 (*.f64 f (/.f64 PI.f64 4))))) (-.f64 (exp.f64 (*.f64 f (/.f64 PI.f64 4))) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))))
73.0ms
(-.f64 (pow.f64 (exp.f64 (/.f64 PI.f64 4)) (*.f64 f 2)) (pow.f64 (exp.f64 -1/4) (*.f64 (*.f64 PI.f64 f) 2)))
64.0ms
(-.f64 (sqrt.f64 (exp.f64 (*.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (*.f64 (*.f64 PI.f64 f) 2)))
49.0ms
(-.f64 (exp.f64 (*.f64 f (/.f64 PI.f64 4))) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))
Compiler

Compiled 3586 to 2880 computations (19.7% saved)

simplify106.0ms (0%)

Algorithm
1×egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
050785440

prune1.3min (18%)

Pruning

871 alts after pruning (862 fresh and 9 done)

PrunedKeptTotal
New601380981
Fresh35482517
Picked000
Done3912
Total6398711510
Error
0.3b
Counts
1510 → 871
Compiler

Compiled 88298 to 66882 computations (24.3% saved)

localize22.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b
(sqrt.f64 (*.f64 (/.f64 PI.f64 4) f))
0.2b
(sqrt.f64 (*.f64 (/.f64 PI.f64 4) f))
0.0b
(sinh.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 PI.f64 4) f)) (sqrt.f64 (*.f64 (/.f64 PI.f64 4) f))))
0.0b
(cosh.f64 (*.f64 (/.f64 PI.f64 4) f))
0.3b
(*.f64 (/.f64 PI.f64 4) f)
0.5b
(*.f64 (sqrt.f64 (*.f64 (/.f64 PI.f64 4) f)) (sqrt.f64 (*.f64 (/.f64 PI.f64 4) f)))
1.0b
(/.f64 (cosh.f64 (*.f64 (/.f64 PI.f64 4) f)) (sinh.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 PI.f64 4) f)) (sqrt.f64 (*.f64 (/.f64 PI.f64 4) f)))))
1.1b
(log.f64 (/.f64 (cosh.f64 (*.f64 (/.f64 PI.f64 4) f)) (sinh.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 PI.f64 4) f)) (sqrt.f64 (*.f64 (/.f64 PI.f64 4) f))))))

rewrite50.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
56×pow1_binary64
38×add-sqr-sqrt_binary64
31×*-un-lft-identity_binary64 add-cube-cbrt_binary64
28×sqrt-pow1_binary64 times-frac_binary64
21×pow-prod-down_binary64
17×associate-*l*_binary64
16×add-exp-log_binary64
14×log-prod_binary64
13×add-cbrt-cube_binary64
10×pow1/2_binary64 pow-prod-up_binary64
7×associate-*r*_binary64
6×pow-sqr_binary64 associate-*l/_binary64
4×add-log-exp_binary64 swap-sqr_binary64 sqrt-prod_binary64 sqrt-div_binary64
3×associate-/r*_binary64 cbrt-unprod_binary64 unswap-sqr_binary64 prod-exp_binary64 associate-/l*_binary64 div-inv_binary64 div-exp_binary64
2×sinh-def_binary64 cbrt-undiv_binary64 rem-log-exp_binary64 associate-/r/_binary64 *-commutative_binary64
1×associate-/l/_binary64 rem-square-sqrt_binary64 associate-*r/_binary64 log-pow_binary64 pow-plus_binary64 sqrt-unprod_binary64 clear-num_binary64 frac-2neg_binary64 log-div_binary64 frac-times_binary64 pow2_binary64 cosh-def_binary64
Counts
4 → 138
Calls

8 calls:

14.0ms
(*.f64 (sqrt.f64 (*.f64 (/.f64 PI.f64 4) f)) (sqrt.f64 (*.f64 (/.f64 PI.f64 4) f)))
8.0ms
(*.f64 (/.f64 PI.f64 4) f)
6.0ms
(/.f64 (cosh.f64 (*.f64 (/.f64 PI.f64 4) f)) (sinh.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 PI.f64 4) f)) (sqrt.f64 (*.f64 (/.f64 PI.f64 4) f)))))
5.0ms
(log.f64 (/.f64 (cosh.f64 (*.f64 (/.f64 PI.f64 4) f)) (sinh.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 PI.f64 4) f)) (sqrt.f64 (*.f64 (/.f64 PI.f64 4) f))))))
0.0ms
(cosh.f64 (*.f64 (/.f64 PI.f64 4) f))

series773.0ms (0.2%)

Counts
4 → 18
Calls

4 calls:

445.0ms
(log.f64 (/.f64 (cosh.f64 (*.f64 (/.f64 PI.f64 4) f)) (sinh.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 PI.f64 4) f)) (sqrt.f64 (*.f64 (/.f64 PI.f64 4) f))))))
270.0ms
(/.f64 (cosh.f64 (*.f64 (/.f64 PI.f64 4) f)) (sinh.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 PI.f64 4) f)) (sqrt.f64 (*.f64 (/.f64 PI.f64 4) f)))))
30.0ms
(*.f64 (sqrt.f64 (*.f64 (/.f64 PI.f64 4) f)) (sqrt.f64 (*.f64 (/.f64 PI.f64 4) f)))
28.0ms
(*.f64 (/.f64 PI.f64 4) f)
Compiler

Compiled 1353 to 1080 computations (20.2% saved)

simplify103.0ms (0%)

Algorithm
1×egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
049373152
149373152

localize8.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b
(*.f64 PI.f64 f)
0.3b
(/.f64 4 (*.f64 PI.f64 f))
0.3b
(/.f64 (*.f64 (log.f64 (/.f64 4 (*.f64 PI.f64 f))) -4) PI.f64)
0.0b
(log.f64 (/.f64 4 (*.f64 PI.f64 f)))
0.0b
(log.f64 (/.f64 4 (*.f64 PI.f64 f)))
0.3b
(/.f64 (*.f64 (log.f64 (/.f64 4 (*.f64 PI.f64 f))) -4) PI.f64)
0.3b
(/.f64 4 (*.f64 PI.f64 f))
0.3b
(*.f64 PI.f64 f)

rewrite24.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
22×add-exp-log_binary64
16×add-cbrt-cube_binary64
14×add-sqr-sqrt_binary64
12×*-un-lft-identity_binary64 add-cube-cbrt_binary64
9×times-frac_binary64
7×pow1_binary64 log-prod_binary64
6×div-exp_binary64
4×associate-/r*_binary64 add-log-exp_binary64 cbrt-undiv_binary64 prod-exp_binary64 associate-/l*_binary64
3×cbrt-unprod_binary64 associate-*r*_binary64 rem-log-exp_binary64 associate-*l*_binary64 div-inv_binary64
2×clear-num_binary64 frac-2neg_binary64
1×pow-prod-down_binary64 log-pow_binary64 unswap-sqr_binary64 log-div_binary64 *-commutative_binary64
Counts
4 → 79
Calls

8 calls:

6.0ms
(/.f64 (*.f64 (log.f64 (/.f64 4 (*.f64 PI.f64 f))) -4) PI.f64)
4.0ms
(/.f64 4 (*.f64 PI.f64 f))
4.0ms
(*.f64 PI.f64 f)
4.0ms
(log.f64 (/.f64 4 (*.f64 PI.f64 f)))
0.0ms
(log.f64 (/.f64 4 (*.f64 PI.f64 f)))

series222.0ms (0.1%)

Counts
4 → 12
Calls

4 calls:

111.0ms
(/.f64 (*.f64 (log.f64 (/.f64 4 (*.f64 PI.f64 f))) -4) PI.f64)
68.0ms
(log.f64 (/.f64 4 (*.f64 PI.f64 f)))
26.0ms
(/.f64 4 (*.f64 PI.f64 f))
17.0ms
(*.f64 PI.f64 f)
Compiler

Compiled 268 to 244 computations (9% saved)

simplify77.0ms (0%)

Algorithm
1×egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
049751118
149751118

localize23.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b
(*.f64 (/.f64 PI.f64 4) f)
0.3b
(*.f64 (/.f64 PI.f64 4) f)
0.0b
(sinh.f64 (*.f64 (/.f64 PI.f64 4) f))
0.0b
(cosh.f64 (*.f64 (/.f64 PI.f64 4) f))
1.0b
(cbrt.f64 (/.f64 PI.f64 4))
1.0b
(cbrt.f64 (/.f64 4 PI.f64))
1.0b
(cbrt.f64 (/.f64 4 PI.f64))
1.0b
(/.f64 (cosh.f64 (*.f64 (/.f64 PI.f64 4) f)) (sinh.f64 (*.f64 (/.f64 PI.f64 4) f)))

rewrite24.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
39×cbrt-prod_binary64
36×times-frac_binary64
33×*-un-lft-identity_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64
6×add-exp-log_binary64 add-cbrt-cube_binary64
4×add-log-exp_binary64 pow1_binary64 div-inv_binary64
3×cbrt-div_binary64 associate-/r*_binary64 pow1/3_binary64 associate-/l*_binary64
1×associate-/l/_binary64 sinh-def_binary64 cbrt-undiv_binary64 associate-/r/_binary64 clear-num_binary64 frac-2neg_binary64 div-exp_binary64 cosh-def_binary64
Counts
4 → 95
Calls

8 calls:

5.0ms
(/.f64 (cosh.f64 (*.f64 (/.f64 PI.f64 4) f)) (sinh.f64 (*.f64 (/.f64 PI.f64 4) f)))
2.0ms
(cbrt.f64 (/.f64 4 PI.f64))
2.0ms
(cbrt.f64 (/.f64 PI.f64 4))
2.0ms
(cbrt.f64 (/.f64 4 PI.f64))
0.0ms
(cosh.f64 (*.f64 (/.f64 PI.f64 4) f))

series181.0ms (0%)

Counts
4 → 6
Calls

4 calls:

181.0ms
(/.f64 (cosh.f64 (*.f64 (/.f64 PI.f64 4) f)) (sinh.f64 (*.f64 (/.f64 PI.f64 4) f)))
0.0ms
(cbrt.f64 (/.f64 4 PI.f64))
0.0ms
(cbrt.f64 (/.f64 4 PI.f64))
0.0ms
(cbrt.f64 (/.f64 PI.f64 4))
Compiler

Compiled 370 to 298 computations (19.5% saved)

simplify75.0ms (0%)

Algorithm
1×egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
054832119

localize28.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(sinh.f64 (*.f64 (/.f64 PI.f64 4) f))
0.0b
(sinh.f64 (*.f64 (/.f64 PI.f64 4) f))
0.0b
(cosh.f64 (*.f64 (/.f64 PI.f64 4) f))
0.0b
(cosh.f64 (*.f64 (/.f64 PI.f64 4) f))
1.0b
(cbrt.f64 (/.f64 4 PI.f64))
1.0b
(*.f64 (cbrt.f64 (/.f64 1 (/.f64 PI.f64 4))) (cbrt.f64 (/.f64 1 (/.f64 PI.f64 4))))
1.0b
(/.f64 (sqrt.f64 (cosh.f64 (*.f64 (/.f64 PI.f64 4) f))) (sqrt.f64 (sinh.f64 (*.f64 (/.f64 PI.f64 4) f))))
1.0b
(/.f64 (sqrt.f64 (cosh.f64 (*.f64 (/.f64 PI.f64 4) f))) (sqrt.f64 (sinh.f64 (*.f64 (/.f64 PI.f64 4) f))))

rewrite162.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
417×times-frac_binary64
331×add-sqr-sqrt_binary64
253×cbrt-prod_binary64
237×*-un-lft-identity_binary64
211×add-cube-cbrt_binary64
84×sqrt-prod_binary64
49×swap-sqr_binary64
47×associate-*r*_binary64 associate-*l*_binary64
36×unswap-sqr_binary64
21×div-inv_binary64
12×associate-/r*_binary64 associate-/l*_binary64
11×pow1_binary64
10×add-exp-log_binary64
8×add-cbrt-cube_binary64
7×pow1/3_binary64
6×associate-/r/_binary64
5×cbrt-div_binary64
4×add-log-exp_binary64 sqrt-div_binary64
2×pow-prod-down_binary64 associate-/l/_binary64 sinh-def_binary64 pow-prod-up_binary64 cbrt-undiv_binary64 sqrt-undiv_binary64 clear-num_binary64 frac-2neg_binary64 div-exp_binary64 pow-sqr_binary64 cosh-def_binary64
1×cbrt-unprod_binary64 associate-*r/_binary64 pow-plus_binary64 prod-exp_binary64 frac-times_binary64 pow2_binary64 associate-*l/_binary64 *-commutative_binary64
Counts
4 → 348
Calls

8 calls:

61.0ms
(*.f64 (cbrt.f64 (/.f64 1 (/.f64 PI.f64 4))) (cbrt.f64 (/.f64 1 (/.f64 PI.f64 4))))
7.0ms
(/.f64 (sqrt.f64 (cosh.f64 (*.f64 (/.f64 PI.f64 4) f))) (sqrt.f64 (sinh.f64 (*.f64 (/.f64 PI.f64 4) f))))
7.0ms
(/.f64 (sqrt.f64 (cosh.f64 (*.f64 (/.f64 PI.f64 4) f))) (sqrt.f64 (sinh.f64 (*.f64 (/.f64 PI.f64 4) f))))
3.0ms
(cbrt.f64 (/.f64 4 PI.f64))
0.0ms
(cosh.f64 (*.f64 (/.f64 PI.f64 4) f))

series298.0ms (0.1%)

Counts
4 → 6
Calls

4 calls:

154.0ms
(/.f64 (sqrt.f64 (cosh.f64 (*.f64 (/.f64 PI.f64 4) f))) (sqrt.f64 (sinh.f64 (*.f64 (/.f64 PI.f64 4) f))))
144.0ms
(/.f64 (sqrt.f64 (cosh.f64 (*.f64 (/.f64 PI.f64 4) f))) (sqrt.f64 (sinh.f64 (*.f64 (/.f64 PI.f64 4) f))))
0.0ms
(*.f64 (cbrt.f64 (/.f64 1 (/.f64 PI.f64 4))) (cbrt.f64 (/.f64 1 (/.f64 PI.f64 4))))
0.0ms
(cbrt.f64 (/.f64 4 PI.f64))
Compiler

Compiled 744 to 586 computations (21.2% saved)

simplify173.0ms (0%)

Algorithm
1×egg-herbie
Counts
354 → 354
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
0550211705

localize38.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b
(*.f64 (/.f64 PI.f64 4) f)
0.3b
(*.f64 (/.f64 PI.f64 4) f)
0.0b
(sinh.f64 (*.f64 (/.f64 PI.f64 4) f))
0.0b
(cosh.f64 (*.f64 (/.f64 PI.f64 4) f))
1.0b
(*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))
1.0b
(*.f64 (cbrt.f64 4) (cbrt.f64 4))
1.0b
(*.f64 (cbrt.f64 4) (cbrt.f64 4))
1.0b
(/.f64 (cosh.f64 (*.f64 (/.f64 PI.f64 4) f)) (sinh.f64 (*.f64 (/.f64 PI.f64 4) f)))

rewrite55.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
60×add-sqr-sqrt_binary64
48×cbrt-prod_binary64
36×*-un-lft-identity_binary64 add-cube-cbrt_binary64
25×pow1_binary64
18×swap-sqr_binary64 associate-*r*_binary64 pow1/3_binary64 associate-*l*_binary64
12×add-exp-log_binary64 unswap-sqr_binary64
9×times-frac_binary64
6×pow-prod-down_binary64 pow-prod-up_binary64 add-cbrt-cube_binary64 pow-sqr_binary64
4×add-log-exp_binary64
3×associate-/r*_binary64 cbrt-unprod_binary64 pow-plus_binary64 prod-exp_binary64 associate-/l*_binary64 pow2_binary64 *-commutative_binary64
1×associate-/l/_binary64 sinh-def_binary64 cbrt-undiv_binary64 associate-/r/_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64 cosh-def_binary64
Counts
4 → 149
Calls

8 calls:

8.0ms
(*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))
7.0ms
(*.f64 (cbrt.f64 4) (cbrt.f64 4))
7.0ms
(*.f64 (cbrt.f64 4) (cbrt.f64 4))
5.0ms
(/.f64 (cosh.f64 (*.f64 (/.f64 PI.f64 4) f)) (sinh.f64 (*.f64 (/.f64 PI.f64 4) f)))
0.0ms
(cosh.f64 (*.f64 (/.f64 PI.f64 4) f))

series182.0ms (0%)

Counts
4 → 6
Calls

4 calls:

182.0ms
(/.f64 (cosh.f64 (*.f64 (/.f64 PI.f64 4) f)) (sinh.f64 (*.f64 (/.f64 PI.f64 4) f)))
0.0ms
(*.f64 (cbrt.f64 4) (cbrt.f64 4))
0.0ms
(*.f64 (cbrt.f64 4) (cbrt.f64 4))
0.0ms
(*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))
Compiler

Compiled 586 to 434 computations (25.9% saved)

simplify93.0ms (0%)

Algorithm
1×egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
049972281
149972281

prune1.7min (24.7%)

Pruning

1077 alts after pruning (1065 fresh and 12 done)

PrunedKeptTotal
New610247857
Fresh39818857
Picked000
Done21214
Total65110771728
Error
0.3b
Counts
1728 → 1077
Compiler

Compiled 30237 to 23170 computations (23.4% saved)

simplify3.1s (0.7%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
09045193237

regimes44.8s (10.7%)

Compiler

Compiled 702756 to 546772 computations (22.2% saved)

bsearch0.0ms (0%)

regimes5.1s (1.2%)

Compiler

Compiled 71793 to 60173 computations (16.2% saved)

bsearch0.0ms (0%)

regimes2.6s (0.6%)

Compiler

Compiled 32899 to 28126 computations (14.5% saved)

bsearch0.0ms (0%)

regimes510.0ms (0.1%)

Compiler

Compiled 4672 to 4062 computations (13.1% saved)

bsearch0.0ms (0%)

regimes197.0ms (0%)

Compiler

Compiled 1636 to 1463 computations (10.6% saved)

bsearch0.0ms (0%)

regimes116.0ms (0%)

Compiler

Compiled 942 to 864 computations (8.3% saved)

bsearch0.0ms (0%)

regimes68.0ms (0%)

Compiler

Compiled 527 to 485 computations (8% saved)

bsearch0.0ms (0%)

regimes12.0ms (0%)

Compiler

Compiled 25 to 26 computations (-4% saved)

bsearch0.0ms (0%)

regimes8.0ms (0%)

Accuracy

Total 1.6b remaining (85.7%)

Threshold costs 0b (0%)

Compiler

Compiled 5 to 8 computations (-60% saved)

bsearch10.0ms (0%)

Compiler

Compiled 162 to 137 computations (15.4% saved)

simplify6.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0193273
1193273

end0.0ms (0%)

sample1.9min (27.2%)

Algorithm
1×intervals
Results
2.0s3902×body1024valid
1.9s3982×body1024nan
735.0ms1995×body512valid
647.0ms1916×body512nan
534.0ms500×body2048valid
248.0ms977×body256valid
227.0ms990×body256nan
88.0ms626×body128valid
1.0ms2×body2048nan
0.0ms3×body128overflowed
Compiler

Compiled 107896 to 83528 computations (22.6% saved)

Pareto

0.8631940589658339

Profiling

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