Details

Time bar (total: 15.4s)

sample429.0ms

Algorithm
intervals
Results
234.0ms94×body10240exit
132.0ms75×body1280valid
25.0ms38×body640valid
10.0ms31×body320valid
10.0ms94×body80valid
4.0ms18×body160valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
087
187
done87

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b
(expm1 (sin (expm1 a)))
0.2b
(sin (expm1 a))
37.0b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
5×log1p-expm1-u
4×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
2×expm1-udef
1×expm1-log1p sin-diff
Counts
4 → 39
Calls
4 calls:
0.0ms
(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0ms
(expm1 (sin (expm1 a)))
2.0ms
(sin (expm1 a))
0.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series159.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(atan2 (expm1 (sin (expm1 a))) (atan a))
89.0ms
(expm1 (sin (expm1 a)))
64.0ms
(sin (expm1 a))
3.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify121.0ms

Counts
51 → 51
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
0108302
1242264
2720264
32933264
45001264
done5001264

prune204.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 31.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(sin (expm1 a))
0.7b
(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
1.0b
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
37.0b
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×unpow-prod-down cube-prod
5×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow
2×cube-mult unpow3 sqr-pow
1×pow-to-exp pow-pow pow1/3 pow-exp sin-diff rem-cbrt-cube expm1-udef rem-cube-cbrt
Counts
4 → 67
Calls
4 calls:
2.0ms
(sin (expm1 a))
2.0ms
(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
3.0ms
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
0.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

series101.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(sin (expm1 a))
3.0ms
(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
37.0ms
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
3.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

simplify143.0ms

Counts
79 → 79
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0156650
1538592
23301586
35002586
done5002586

prune273.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 31.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(sin (expm1 a))
0.7b
(cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3)))
1.0b
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
37.0b
(fmod (cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3))) a)

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
63×cbrt-prod
21×unpow-prod-down cube-prod
15×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
5×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u cube-mult unpow3 log1p-expm1-u add-log-exp sqr-pow
3×pow-unpow
1×pow-to-exp pow-pow pow1/3 pow-exp sin-diff expm1-udef rem-cube-cbrt
Counts
4 → 87
Calls
4 calls:
2.0ms
(sin (expm1 a))
7.0ms
(cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3)))
3.0ms
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
0.0ms
(fmod (cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3))) a)

series101.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(sin (expm1 a))
3.0ms
(cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3)))
32.0ms
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
3.0ms
(fmod (cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3))) a)

simplify35.0ms

Counts
99 → 99
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
02451050
1770944
25001928
done5001928

prune323.0ms

Pruning

21 alts after pruning (19 fresh and 2 done)

Merged error: 31.1b

localize22.0ms

Local error

Found 4 expressions with local error:

1.0b
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
37.0b
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
37.0b
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
37.0b
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
5×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×unpow-prod-down pow-unpow cube-prod
1×cube-mult pow-to-exp pow-pow unpow3 pow-exp rem-cube-cbrt sqr-pow
Counts
4 → 52
Calls
4 calls:
3.0ms
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
0.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
0.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
0.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

series42.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
3.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
3.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
3.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

simplify125.0ms

Counts
64 → 64
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
092608
1341520
22697516
35002516
done5002516

prune257.0ms

Pruning

26 alts after pruning (24 fresh and 2 done)

Merged error: 30.9b

regimes332.0ms

Accuracy

0% (1.8b remaining)

Error of 33.7b against oracle of 32.0b and baseline of 33.7b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02032
12032
done2032

end0.0ms

sample12.6s

Algorithm
intervals
Results
6.7s2701×body10240exit
3.9s2323×body1280valid
1.2s1702×body640valid
265.0ms808×body320valid
265.0ms2761×body80valid
84.0ms403×body160valid
9.0ms2×body5120valid
2.0ms1×body2560valid