Details

Time bar (total: 2.5min)

analyze108.0ms (0.1%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%50%50%4
0%50%50%5
12.5%37.5%50%6
18.7%31.2%50%7
28.1%21.9%50%8
32.8%17.2%50%9
38.2%11.7%50%10
41%9%50%11
43.9%6%50%12
45.4%4.6%50%13
46.9%3.1%50%14
Compiler

Compiled 29 to 22 computations (24.1% saved)

sample24.0ms (0%)

Algorithm
1×intervals
Results
17.0ms256×body80valid
Compiler

Compiled 57 to 45 computations (21.1% saved)

simplify66.0ms (0%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
0514340

prune7.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 0.4b

Counts
2 → 1
Compiler

Compiled 54 to 41 computations (24.1% saved)

localize15.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 5 (*.f64 v v))
0.2b
(*.f64 PI.f64 t)
0.3b
(/.f64 (-.f64 1 (*.f64 5 (*.f64 v v))) (*.f64 (*.f64 (*.f64 PI.f64 t) (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v)))))) (-.f64 1 (*.f64 v v))))
0.5b
(*.f64 (*.f64 PI.f64 t) (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v))))))

rewrite41.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
30×add-exp-log_binary64 add-cbrt-cube_binary64
18×associate-*r/_binary64
16×pow1_binary64
13×cbrt-unprod_binary64 prod-exp_binary64 add-sqr-sqrt_binary64
10×*-un-lft-identity_binary64 add-cube-cbrt_binary64
8×flip3--_binary64 associate-*r*_binary64 associate-/r/_binary64 flip--_binary64 sqrt-div_binary64
7×pow-prod-down_binary64 associate-*l*_binary64
4×add-log-exp_binary64 cbrt-undiv_binary64 div-exp_binary64 frac-times_binary64
3×associate-/l*_binary64 times-frac_binary64 *-commutative_binary64
2×associate-/l/_binary64 unswap-sqr_binary64 associate-*l/_binary64
1×associate-/r*_binary64 div-sub_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 sqrt-prod_binary64
Counts
4 → 94
Calls

4 calls:

18.0ms
(/.f64 (-.f64 1 (*.f64 5 (*.f64 v v))) (*.f64 (*.f64 (*.f64 PI.f64 t) (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v)))))) (-.f64 1 (*.f64 v v))))
10.0ms
(*.f64 (*.f64 PI.f64 t) (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v))))))
6.0ms
(*.f64 5 (*.f64 v v))
4.0ms
(*.f64 PI.f64 t)

series68.0ms (0%)

Counts
4 → 12
Calls

4 calls:

39.0ms
(/.f64 (-.f64 1 (*.f64 5 (*.f64 v v))) (*.f64 (*.f64 (*.f64 PI.f64 t) (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v)))))) (-.f64 1 (*.f64 v v))))
22.0ms
(*.f64 (*.f64 PI.f64 t) (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v))))))
3.0ms
(*.f64 5 (*.f64 v v))
3.0ms
(*.f64 PI.f64 t)

simplify67.0ms (0%)

Algorithm
1×egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
055642803

prune150.0ms (0.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New9610106
Fresh000
Picked101
Done000
Total9710107

Merged error: 0.1b

Counts
107 → 10
Compiler

Compiled 4180 to 2598 computations (37.8% saved)

localize19.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 5 (*.f64 v v))
0.2b
(*.f64 PI.f64 t)
0.3b
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 5 (*.f64 v v)))) (/.f64 (*.f64 (*.f64 PI.f64 t) (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v)))))) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 v v) 5))) (-.f64 1 (*.f64 v v)))))
0.5b
(*.f64 (*.f64 PI.f64 t) (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v))))))

rewrite78.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
708×times-frac_binary64
263×add-sqr-sqrt_binary64
260×*-un-lft-identity_binary64
232×sqrt-prod_binary64
218×add-cube-cbrt_binary64
84×difference-of-squares_binary64
45×add-exp-log_binary64 add-cbrt-cube_binary64
41×associate-/r*_binary64
22×associate-/r/_binary64
16×pow1_binary64 cbrt-undiv_binary64 div-exp_binary64
15×div-inv_binary64
13×cbrt-unprod_binary64 prod-exp_binary64
9×flip3--_binary64 flip--_binary64
8×associate-*r*_binary64
7×pow-prod-down_binary64 associate-*l*_binary64
6×associate-/l*_binary64
4×add-log-exp_binary64 associate-*r/_binary64 sqrt-div_binary64
3×*-commutative_binary64
2×associate-/l/_binary64 unswap-sqr_binary64
1×clear-num_binary64 frac-2neg_binary64
Counts
4 → 378
Calls

4 calls:

30.0ms
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 5 (*.f64 v v)))) (/.f64 (*.f64 (*.f64 PI.f64 t) (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v)))))) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 v v) 5))) (-.f64 1 (*.f64 v v)))))
10.0ms
(*.f64 (*.f64 PI.f64 t) (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v))))))
6.0ms
(*.f64 5 (*.f64 v v))
4.0ms
(*.f64 PI.f64 t)

series71.0ms (0%)

Counts
4 → 12
Calls

4 calls:

42.0ms
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 5 (*.f64 v v)))) (/.f64 (*.f64 (*.f64 PI.f64 t) (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v)))))) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 v v) 5))) (-.f64 1 (*.f64 v v)))))
22.0ms
(*.f64 (*.f64 PI.f64 t) (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v))))))
3.0ms
(*.f64 5 (*.f64 v v))
3.0ms
(*.f64 PI.f64 t)

simplify289.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
390 → 390
Iterations

Useful iterations: 0 (79.0ms)

IterNodesCost
0496727348
1496727348

prune1.4s (0.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New3873390
Fresh369
Picked011
Done000
Total39010400

Merged error: 0.0b

Counts
400 → 10
Compiler

Compiled 21679 to 13951 computations (35.6% saved)

localize19.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (*.f64 v v) 5)
0.2b
(*.f64 PI.f64 t)
0.3b
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 v v) 5))) (*.f64 (*.f64 PI.f64 t) (sqrt.f64 (-.f64 1 (*.f64 v v)))))
0.4b
(/.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 v v) 5))) (*.f64 (*.f64 PI.f64 t) (sqrt.f64 (-.f64 1 (*.f64 v v))))) (/.f64 (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v))))) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 v v) 5))) (sqrt.f64 (-.f64 1 (*.f64 v v))))))

rewrite525.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
9294×times-frac_binary64
4182×sqrt-prod_binary64
3215×add-sqr-sqrt_binary64
3212×*-un-lft-identity_binary64
2900×add-cube-cbrt_binary64
624×difference-of-squares_binary64
564×associate-/r/_binary64
552×sqrt-div_binary64
446×associate-*r/_binary64
289×div-inv_binary64
276×flip3--_binary64 flip--_binary64
222×associate-/r*_binary64
74×add-exp-log_binary64 add-cbrt-cube_binary64
36×cbrt-undiv_binary64 div-exp_binary64
18×associate-/l*_binary64
16×cbrt-unprod_binary64 prod-exp_binary64
11×pow1_binary64
6×associate-*r*_binary64
4×pow-prod-down_binary64 add-log-exp_binary64 associate-*l*_binary64
3×associate-/l/_binary64
2×unswap-sqr_binary64 clear-num_binary64 frac-2neg_binary64 *-commutative_binary64
Counts
4 → 2991
Calls

4 calls:

105.0ms
(/.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 v v) 5))) (*.f64 (*.f64 PI.f64 t) (sqrt.f64 (-.f64 1 (*.f64 v v))))) (/.f64 (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v))))) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 v v) 5))) (sqrt.f64 (-.f64 1 (*.f64 v v))))))
13.0ms
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 v v) 5))) (*.f64 (*.f64 PI.f64 t) (sqrt.f64 (-.f64 1 (*.f64 v v)))))
6.0ms
(*.f64 (*.f64 v v) 5)
4.0ms
(*.f64 PI.f64 t)

series71.0ms (0%)

Counts
4 → 12
Calls

4 calls:

44.0ms
(/.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 v v) 5))) (*.f64 (*.f64 PI.f64 t) (sqrt.f64 (-.f64 1 (*.f64 v v))))) (/.f64 (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v))))) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 v v) 5))) (sqrt.f64 (-.f64 1 (*.f64 v v))))))
20.0ms
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 v v) 5))) (*.f64 (*.f64 PI.f64 t) (sqrt.f64 (-.f64 1 (*.f64 v v)))))
3.0ms
(*.f64 (*.f64 v v) 5)
3.0ms
(*.f64 PI.f64 t)

simplify2.6s (1.7%)

Algorithm
1×egg-herbie
Counts
3003 → 3003
Iterations

Useful iterations: 0 (128.0ms)

IterNodesCost
05652365789

prune1.8min (71%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New300033003
Fresh358
Picked101
Done011
Total300493013

Merged error: 0.0b

Counts
3013 → 9
Compiler

Compiled 243384 to 159950 computations (34.3% saved)

localize20.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 PI.f64 t)
0.3b
(/.f64 1 (*.f64 (*.f64 PI.f64 t) (sqrt.f64 (-.f64 1 (*.f64 v v)))))
0.5b
(*.f64 (/.f64 1 (*.f64 (*.f64 PI.f64 t) (sqrt.f64 (-.f64 1 (*.f64 v v))))) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 v v) 5))) (/.f64 (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v))))) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 v v) 5))) (sqrt.f64 (-.f64 1 (*.f64 v v)))))))
1.0b
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 v v) 5))) (/.f64 (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v))))) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 v v) 5))) (sqrt.f64 (-.f64 1 (*.f64 v v))))))

rewrite859.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
7992×times-frac_binary64
4853×sqrt-prod_binary64
3490×add-sqr-sqrt_binary64
3432×*-un-lft-identity_binary64
3120×add-cube-cbrt_binary64
1334×associate-*r*_binary64
624×difference-of-squares_binary64
224×add-exp-log_binary64
222×associate-/r*_binary64
123×associate-/r/_binary64
110×sqrt-div_binary64
104×add-cbrt-cube_binary64
96×div-exp_binary64
86×prod-exp_binary64
69×div-inv_binary64
55×flip3--_binary64 flip--_binary64
45×cbrt-undiv_binary64
32×cbrt-unprod_binary64
15×1-exp_binary64 rec-exp_binary64
14×pow1_binary64 unswap-sqr_binary64
12×associate-*l*_binary64
9×associate-/l*_binary64
5×pow-prod-down_binary64 associate-*r/_binary64
4×add-log-exp_binary64
3×sqrt-undiv_binary64 pow-flip_binary64
2×associate-/l/_binary64 clear-num_binary64 frac-2neg_binary64 *-commutative_binary64
1×inv-pow_binary64 frac-times_binary64 associate-*l/_binary64
Counts
4 → 3047
Calls

4 calls:

382.0ms
(*.f64 (/.f64 1 (*.f64 (*.f64 PI.f64 t) (sqrt.f64 (-.f64 1 (*.f64 v v))))) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 v v) 5))) (/.f64 (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v))))) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 v v) 5))) (sqrt.f64 (-.f64 1 (*.f64 v v)))))))
67.0ms
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 v v) 5))) (/.f64 (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v))))) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 v v) 5))) (sqrt.f64 (-.f64 1 (*.f64 v v))))))
10.0ms
(/.f64 1 (*.f64 (*.f64 PI.f64 t) (sqrt.f64 (-.f64 1 (*.f64 v v)))))
4.0ms
(*.f64 PI.f64 t)

series116.0ms (0.1%)

Counts
4 → 12
Calls

4 calls:

73.0ms
(*.f64 (/.f64 1 (*.f64 (*.f64 PI.f64 t) (sqrt.f64 (-.f64 1 (*.f64 v v))))) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 v v) 5))) (/.f64 (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v))))) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 v v) 5))) (sqrt.f64 (-.f64 1 (*.f64 v v)))))))
23.0ms
(/.f64 1 (*.f64 (*.f64 PI.f64 t) (sqrt.f64 (-.f64 1 (*.f64 v v)))))
18.0ms
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 v v) 5))) (/.f64 (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v))))) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 v v) 5))) (sqrt.f64 (-.f64 1 (*.f64 v v))))))
3.0ms
(*.f64 PI.f64 t)

simplify1.8s (1.2%)

Algorithm
1×egg-herbie
Counts
3059 → 3059
Iterations

Useful iterations: 0 (83.0ms)

IterNodesCost
05309259060

prune35.2s (23.5%)

Profiling

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