Details

Time bar (total: 9.2s)

analyze1.4s (14.7%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
0%100%0%3
0%100%0%4
0%100%0%5
0%100%0%6
0%100%0%7
0%100%0%8
0%100%0%9
0%100%0%10
0%100%0%11
0%100%0%12
0%100%0%13
0.1%99.9%0%14
Compiler

Compiled 10 to 7 computations (30% saved)

sample191.0ms (2.1%)

Algorithm
1×intervals
Results
123.0ms54×body2048valid
41.0ms110×body1024valid
9.0ms43×body512valid
4.0ms25×body256valid
3.0ms2×body4096valid
2.0ms22×body128valid
Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify240.0ms (2.6%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (70.0ms)

IterNodesCost
099014
199014

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 30.3b

Counts
2 → 1
Compiler

Compiled 18 to 12 computations (33.3% saved)

localize17.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
2.7b
(-.f64 x (tan.f64 x))
2.7b
(-.f64 x (sin.f64 x))

rewrite30.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
45×*-un-lft-identity_binary64 add-sqr-sqrt_binary64
25×times-frac_binary64
17×add-cube-cbrt_binary64
14×difference-of-squares_binary64 distribute-lft-out--_binary64
7×add-log-exp_binary64
6×cancel-sign-sub-inv_binary64
5×associate-/r*_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 associate-/l*_binary64
4×flip3--_binary64 flip--_binary64
3×pow1_binary64
2×associate-/l/_binary64 sub-neg_binary64 diff-log_binary64 associate-/r/_binary64
1×cbrt-undiv_binary64 div-sub_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64
Counts
3 → 84
Calls

3 calls:

10.0ms
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
6.0ms
(-.f64 x (sin.f64 x))
4.0ms
(-.f64 x (tan.f64 x))

series267.0ms (2.9%)

Counts
3 → 9
Calls

3 calls:

114.0ms
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
100.0ms
(-.f64 x (tan.f64 x))
53.0ms
(-.f64 x (sin.f64 x))

simplify75.0ms (0.8%)

Algorithm
1×egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
048771847
148771847

prune124.0ms (1.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New91293
Fresh000
Picked011
Done000
Total91394

Merged error: 0b

Counts
94 → 3
Compiler

Compiled 2363 to 735 computations (68.9% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.7b
(-.f64 x (tan.f64 x))
2.7b
(-.f64 x (sin.f64 x))
2.7b
(-.f64 x (sin.f64 x))
2.7b
(-.f64 x (sin.f64 x))

rewrite27.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
16×*-un-lft-identity_binary64 add-sqr-sqrt_binary64
12×add-log-exp_binary64 cancel-sign-sub-inv_binary64
8×add-cube-cbrt_binary64
4×sub-neg_binary64 pow1_binary64 flip3--_binary64 diff-log_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 difference-of-squares_binary64 distribute-lft-out--_binary64 flip--_binary64
Counts
4 → 64
Calls

4 calls:

5.0ms
(-.f64 x (sin.f64 x))
5.0ms
(-.f64 x (sin.f64 x))
5.0ms
(-.f64 x (sin.f64 x))
4.0ms
(-.f64 x (tan.f64 x))

series215.0ms (2.3%)

Counts
4 → 12
Calls

4 calls:

86.0ms
(-.f64 x (tan.f64 x))
49.0ms
(-.f64 x (sin.f64 x))
41.0ms
(-.f64 x (sin.f64 x))
38.0ms
(-.f64 x (sin.f64 x))

simplify99.0ms (1.1%)

Algorithm
1×egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 0 (84.0ms)

IterNodesCost
04784838
14784838

prune82.0ms (0.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New76076
Fresh011
Picked011
Done011
Total76379

Merged error: 0b

Counts
79 → 3
Compiler

Compiled 3027 to 353 computations (88.3% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b
(*.f64 (*.f64 x x) 9/40)
0.1b
(*.f64 27/2800 (pow.f64 x 4))
18.8b
(-.f64 (*.f64 (*.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))

rewrite29.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
14×add-sqr-sqrt_binary64
13×add-exp-log_binary64
10×associate-*r*_binary64 add-cbrt-cube_binary64
8×*-un-lft-identity_binary64 add-log-exp_binary64 pow1_binary64 add-cube-cbrt_binary64
6×prod-exp_binary64
4×cbrt-unprod_binary64 associate-*l*_binary64 unswap-sqr_binary64 unpow-prod-down_binary64
3×pow-prod-down_binary64 cancel-sign-sub-inv_binary64
2×diff-log_binary64 sqr-pow_binary64 *-commutative_binary64
1×pow-to-exp_binary64 sub-neg_binary64 associate--r+_binary64 flip3--_binary64 flip--_binary64 pow-exp_binary64 sum-log_binary64
Counts
3 → 60
Calls

3 calls:

11.0ms
(-.f64 (*.f64 (*.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
7.0ms
(*.f64 (*.f64 x x) 9/40)
6.0ms
(*.f64 27/2800 (pow.f64 x 4))

series135.0ms (1.5%)

Counts
3 → 9
Calls

3 calls:

49.0ms
(-.f64 (*.f64 (*.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
48.0ms
(*.f64 27/2800 (pow.f64 x 4))
38.0ms
(*.f64 (*.f64 x x) 9/40)

simplify58.0ms (0.6%)

Algorithm
1×egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
05488873

prune73.0ms (0.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New69069
Fresh000
Picked011
Done022
Total69372

Merged error: 0b

Counts
72 → 3
Compiler

Compiled 1178 to 859 computations (27.1% saved)

regimes35.0ms (0.4%)

Compiler

Compiled 134 to 72 computations (46.3% saved)

bsearch54.0ms (0.6%)

Steps
ItersRangePoint
10
6.797883803840714e-07
508494.9946227883
0.029376914368532816
9
-2720.4178659984177
-8.181101991936199e-07
-0.028311968525913885
Compiler

Compiled 1 to 1 computations (0% saved)

simplify3.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
08847
18847

end0.0ms (0%)

sample6.1s (66%)

Algorithm
1×intervals
Results
4.0s2022×body2048valid
1.2s3074×body1024valid
294.0ms1426×body512valid
130.0ms105×body4096valid
107.0ms755×body256valid
52.0ms618×body128valid
Compiler

Compiled 98 to 60 computations (38.8% saved)

Profiling

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