Details

Time bar (total: 4.5s)

analyze352.0ms (7.8%)

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%99.9%0.1%4
50%50%0.1%5
50%50%0.1%6
50%37.5%12.6%7
50%37.5%12.6%8
50%31.2%18.8%9
50%31.2%18.8%10
50%28.1%22%11
50%28.1%22%12
50%26.5%23.5%13
50%26.5%23.5%14
Compiler

Compiled 12 to 11 computations (8.3% saved)

sample81.0ms (1.8%)

Algorithm
1×intervals
Results
24.0ms58×body1024valid
20.0ms75×body1024invalid
9.0ms153×body128valid
7.0ms33×body512valid
5.0ms28×body512invalid
2.0ms21×body256invalid
1.0ms12×body256valid
1.0ms21×body128invalid
Compiler

Compiled 23 to 23 computations (0% saved)

simplify255.0ms (5.6%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (97.0ms)

IterNodesCost
0488118
1488118

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.0b

Counts
2 → 1
Compiler

Compiled 22 to 20 computations (9.1% saved)

localize9.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.0b
(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

rewrite7.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
3×*-un-lft-identity_binary64_414 add-log-exp_binary64_450
1×pow1_binary64_472 flip3-+_binary64_417 add-cube-cbrt_binary64_446 +-commutative_binary64_346 add-exp-log_binary64_449 add-cbrt-cube_binary64_447 flip-+_binary64_388 distribute-lft-out_binary64_367 add-sqr-sqrt_binary64_435 sum-log_binary64_502
Counts
1 → 12
Calls

1 calls:

6.0ms
(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

series29.0ms (0.6%)

Counts
1 → 3
Calls

1 calls:

29.0ms
(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

simplify69.0ms (1.5%)

Algorithm
1×egg-herbie
Counts
15 → 15
Iterations

Useful iterations: 0 (62.0ms)

IterNodesCost
05106212

prune16.0ms (0.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New13215
Fresh000
Picked011
Done000
Total13316

Merged error: 0b

Counts
16 → 3
Compiler

Compiled 278 to 133 computations (52.2% saved)

localize23.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b
(pow.f64 (exp.f64 im) 2)
0.0b
(pow.f64 (exp.f64 im) -3)
0.0b
(pow.f64 (exp.f64 im) 3)
6.2b
(+.f64 (pow.f64 (exp.f64 im) 2) -1)

rewrite25.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
16×*-un-lft-identity_binary64_414 add-sqr-sqrt_binary64_435
14×add-cube-cbrt_binary64_446
12×pow-pow_binary64_483
10×unpow-prod-down_binary64_490
9×pow-unpow_binary64_488 exp-prod_binary64_463
7×pow1_binary64_472
6×add-log-exp_binary64_450
5×add-cbrt-cube_binary64_447
4×sqr-pow_binary64_386 add-exp-log_binary64_449 difference-of-sqr--1_binary64_385
3×cube-prod_binary64_439 pow-exp_binary64_479 pow-to-exp_binary64_480
2×unpow2_binary64_476
1×flip3-+_binary64_417 cube-mult_binary64_441 +-commutative_binary64_346 unpow3_binary64_477 flip-+_binary64_388 distribute-lft-out_binary64_367 sum-log_binary64_502 rem-cube-cbrt_binary64_436
Counts
4 → 83
Calls

4 calls:

6.0ms
(+.f64 (pow.f64 (exp.f64 im) 2) -1)
4.0ms
(pow.f64 (exp.f64 im) 3)
4.0ms
(pow.f64 (exp.f64 im) 2)
4.0ms
(pow.f64 (exp.f64 im) -3)

series173.0ms (3.8%)

Counts
4 → 12
Calls

4 calls:

76.0ms
(pow.f64 (exp.f64 im) -3)
44.0ms
(pow.f64 (exp.f64 im) 3)
30.0ms
(+.f64 (pow.f64 (exp.f64 im) 2) -1)
23.0ms
(pow.f64 (exp.f64 im) 2)

simplify92.0ms (2%)

Algorithm
1×egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 0 (78.0ms)

IterNodesCost
04883788
14883788

prune140.0ms (3.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New95095
Fresh011
Picked011
Done011
Total95398

Merged error: 0b

Counts
98 → 3
Compiler

Compiled 2789 to 1739 computations (37.6% saved)

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b
(+.f64 (*.f64 im im) (+.f64 2 (*.f64 1/12 (pow.f64 im 4))))
0.0b
(*.f64 (*.f64 1/2 (cos.f64 re)) (+.f64 (*.f64 im im) (+.f64 2 (*.f64 1/12 (pow.f64 im 4)))))
0.1b
(*.f64 1/12 (pow.f64 im 4))

rewrite28.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
13×add-exp-log_binary64_449
12×add-sqr-sqrt_binary64_435
10×add-cbrt-cube_binary64_447 associate-*r*_binary64_356
8×pow1_binary64_472 add-log-exp_binary64_450
7×add-cube-cbrt_binary64_446 *-un-lft-identity_binary64_414
6×prod-exp_binary64_460
4×associate-*l*_binary64_357 unpow-prod-down_binary64_490 cbrt-unprod_binary64_444
3×pow-prod-down_binary64_482 unswap-sqr_binary64_382 sum-log_binary64_502
2×flip3-+_binary64_417 *-commutative_binary64_347 sqr-pow_binary64_386 flip-+_binary64_388 associate-*r/_binary64_358
1×distribute-lft-in_binary64_365 distribute-rgt-in_binary64_366 +-commutative_binary64_346 pow-exp_binary64_479 associate-+r+_binary64_348 pow-to-exp_binary64_480
Counts
3 → 60
Calls

3 calls:

11.0ms
(*.f64 (*.f64 1/2 (cos.f64 re)) (+.f64 (*.f64 im im) (+.f64 2 (*.f64 1/12 (pow.f64 im 4)))))
7.0ms
(+.f64 (*.f64 im im) (+.f64 2 (*.f64 1/12 (pow.f64 im 4))))
6.0ms
(*.f64 1/12 (pow.f64 im 4))

series287.0ms (6.4%)

Counts
3 → 9
Calls

3 calls:

189.0ms
(*.f64 (*.f64 1/2 (cos.f64 re)) (+.f64 (*.f64 im im) (+.f64 2 (*.f64 1/12 (pow.f64 im 4)))))
52.0ms
(*.f64 1/12 (pow.f64 im 4))
47.0ms
(+.f64 (*.f64 im im) (+.f64 2 (*.f64 1/12 (pow.f64 im 4))))

simplify56.0ms (1.2%)

Algorithm
1×egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
049511255
149511255

prune77.0ms (1.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New69069
Fresh000
Picked011
Done022
Total69372

Merged error: 0b

Counts
72 → 3
Compiler

Compiled 1507 to 1001 computations (33.6% saved)

regimes85.0ms (1.9%)

Compiler

Compiled 560 to 470 computations (16.1% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02118
12118

end0.0ms (0%)

sample2.7s (59.6%)

Algorithm
1×intervals
Results
854.0ms1994×body1024valid
550.0ms2065×body1024invalid
281.0ms4534×body128valid
204.0ms972×body512valid
178.0ms1009×body512invalid
65.0ms493×body256valid
65.0ms522×body256invalid
53.0ms777×body128invalid
6.0ms7×body2048valid
Compiler

Compiled 108 to 92 computations (14.8% saved)

Profiling

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