Details

Time bar (total: 4.9s)

analyze599.0ms (12.2%)

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 14 to 11 computations (21.4% saved)

sample102.0ms (2.1%)

Algorithm
1×intervals
Results
33.0ms74×body1024valid
19.0ms58×body1024invalid
14.0ms40×body512valid
9.0ms129×body128valid
7.0ms34×body512invalid
2.0ms12×body256valid
2.0ms13×body256invalid
1.0ms19×body128invalid
1.0ms1×body2048valid
Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify128.0ms (2.6%)

Algorithm
1×egg-herbie
Rules
575×fma-def_binary64
533×associate-/l*_binary64
430×unswap-sqr_binary64
374×times-frac_binary64
354×fma-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01118
12818
26518
39917
415417
526917
653217
791617
8333217
9326017
10400617
11426517
12469217
13484017
14489117
15491717

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
0.0b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶0.0b
(*.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
Compiler

Compiled 50 to 33 computations (34% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))
✓0.0b
(*.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
✓0.0b
(/.f64 1/2 (exp.f64 im))

rewrite8.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
15×add-sqr-sqrt_binary64
13×*-un-lft-identity_binary64
13×add-cube-cbrt_binary64
9×times-frac_binary64
7×add-cbrt-cube_binary64
Counts
3 → 61
Calls

3 calls:

3.0ms
(*.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
3.0ms
(/.f64 1/2 (exp.f64 im))
0.0ms
(fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))

series80.0ms (1.6%)

Counts
3 → 40
Calls

3 calls:

54.0ms
(*.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
16.0ms
(fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))
10.0ms
(/.f64 1/2 (exp.f64 im))

simplify114.0ms (2.3%)

Algorithm
1×egg-herbie
Rules
845×fma-neg_binary64
494×associate-*l*_binary64
433×fma-def_binary64
422×associate-*r*_binary64
335×times-frac_binary64
Counts
101 → 163
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01631806
13781669
211421633
338061629
450001629
551481629

prune90.0ms (1.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1621163
Fresh000
Picked011
Done000
Total1622164
Error
0.0b
Counts
164 → 2
Alt Table
StatusErrorProgram
▶0.9b
(+.f64 (*.f64 1/2 (*.f64 (cos.f64 re) (pow.f64 im 2))) (+.f64 (*.f64 1/24 (*.f64 (cos.f64 re) (pow.f64 im 4))) (+.f64 (cos.f64 re) (*.f64 1/720 (*.f64 (cos.f64 re) (pow.f64 im 6))))))
✓0.0b
(*.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
Compiler

Compiled 2018 to 1118 computations (44.6% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(*.f64 1/720 (*.f64 (cos.f64 re) (pow.f64 im 6)))
✓0.1b
(*.f64 (cos.f64 re) (pow.f64 im 4))
✓0.1b
(*.f64 1/24 (*.f64 (cos.f64 re) (pow.f64 im 4)))
✓0.1b
(*.f64 (cos.f64 re) (pow.f64 im 2))

rewrite21.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
34×add-exp-log_binary64
23×add-sqr-sqrt_binary64
20×prod-exp_binary64
18×add-cbrt-cube_binary64
17×associate-*r*_binary64
Counts
4 → 98
Calls

4 calls:

4.0ms
(*.f64 1/720 (*.f64 (cos.f64 re) (pow.f64 im 6)))
4.0ms
(*.f64 1/24 (*.f64 (cos.f64 re) (pow.f64 im 4)))
4.0ms
(*.f64 (cos.f64 re) (pow.f64 im 2))
4.0ms
(*.f64 (cos.f64 re) (pow.f64 im 4))

series203.0ms (4.1%)

Counts
4 → 16
Calls

4 calls:

60.0ms
(*.f64 1/720 (*.f64 (cos.f64 re) (pow.f64 im 6)))
53.0ms
(*.f64 (cos.f64 re) (pow.f64 im 2))
51.0ms
(*.f64 1/24 (*.f64 (cos.f64 re) (pow.f64 im 4)))
39.0ms
(*.f64 (cos.f64 re) (pow.f64 im 4))

simplify107.0ms (2.2%)

Algorithm
1×egg-herbie
Rules
877×fma-neg_binary64
396×fma-def_binary64
322×cancel-sign-sub-inv_binary64
280×distribute-rgt-neg-in_binary64
277×associate-*r*_binary64
Counts
114 → 210
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02031848
14791578
215701508
331551502
447361502
549731502

prune180.0ms (3.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New2100210
Fresh000
Picked011
Done011
Total2102212
Error
0.0b
Counts
212 → 2
Alt Table
StatusErrorProgram
✓0.9b
(+.f64 (*.f64 1/2 (*.f64 (cos.f64 re) (pow.f64 im 2))) (+.f64 (*.f64 1/24 (*.f64 (cos.f64 re) (pow.f64 im 4))) (+.f64 (cos.f64 re) (*.f64 1/720 (*.f64 (cos.f64 re) (pow.f64 im 6))))))
✓0.0b
(*.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
Compiler

Compiled 6179 to 3889 computations (37.1% saved)

regimes164.0ms (3.3%)

Accuracy

Total 0.0b remaining (36.9%)

Threshold costs 0.0b (36.9%)

Compiler

Compiled 2566 to 1781 computations (30.6% saved)

simplify4.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
1×*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0917
11017
21017

end1.0ms (0%)

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample3.1s (62.8%)

Algorithm
1×intervals
Results
947.0ms1963×body1024valid
730.0ms2027×body1024invalid
325.0ms4532×body128valid
230.0ms1004×body512valid
188.0ms927×body512invalid
74.0ms499×body256valid
73.0ms742×body128invalid
59.0ms431×body256invalid
2.0ms2×body2048valid
Compiler

Compiled 73 to 52 computations (28.8% saved)

Profiling

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