Details

Time bar (total: 23.6s)

sample392.0ms

Algorithm
intervals
Results
220.0ms88×body10240exit
105.0ms67×body1280valid
32.0ms48×body640valid
11.0ms102×body80valid
9.0ms27×body320valid
3.0ms12×body160valid

simplify2.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0810
done810

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize18.0ms

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))
35.6b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
Counts
4 → 28
Calls
4 calls:
0.0ms
(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0ms
(expm1 (sin (expm1 a)))
1.0ms
(sin (expm1 a))
0.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series62.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(atan2 (expm1 (sin (expm1 a))) (atan a))
1.0ms
(expm1 (sin (expm1 a)))
56.0ms
(sin (expm1 a))
3.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify3.4s

Counts
40 → 40
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
035339
139339
244293
355293
470293
5101293
6176293
7397293
81211293
94879293
done5000293

prune180.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 29.9b

localize18.0ms

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)
35.6b
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

rewrite5.0ms

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×add-log-exp
3×pow-unpow
2×cube-mult unpow3 sqr-pow
1×pow-to-exp pow-pow pow1/3 pow-exp rem-cbrt-cube rem-cube-cbrt
Counts
4 → 58
Calls
4 calls:
1.0ms
(sin (expm1 a))
1.0ms
(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
2.0ms
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
0.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

series95.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(sin (expm1 a))
2.0ms
(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
33.0ms
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
2.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

simplify1.6s

Counts
70 → 70
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
067966
1113791
2289693
31675693
done5000693

prune240.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 29.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3))
0.7b
(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
1.0b
(pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)
35.5b
(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
28×cbrt-prod
26×add-sqr-sqrt
18×add-cube-cbrt *-un-lft-identity
12×pow1
7×add-exp-log pow1/3
6×unpow-prod-down cube-prod swap-sqr associate-*r* associate-*l*
5×add-cbrt-cube
4×add-log-exp unswap-sqr
3×pow-unpow
2×cube-mult unpow3 pow-prod-down pow-sqr pow-prod-up sqr-pow
1×pow2 pow-to-exp pow-pow pow-plus pow-exp prod-exp *-commutative rem-cbrt-cube cbrt-unprod rem-cube-cbrt
Counts
4 → 91
Calls
4 calls:
2.0ms
(cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3))
7.0ms
(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
1.0ms
(pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)
0.0ms
(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

series221.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3))
180.0ms
(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
33.0ms
(pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)
3.0ms
(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

simplify1.6s

Counts
103 → 103
Iterations

Useful iterations: 3 (370.0ms)

IterNodesCost
01042302
11822021
24691245
321471014
done50011014

prune411.0ms

Pruning

27 alts after pruning (26 fresh and 1 done)

Merged error: 29.5b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (* (pow (cbrt (cbrt (sin (expm1 a)))) 4) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a)))))
0.7b
(cbrt (pow (atan2 (expm1 (* (* (* (pow (cbrt (cbrt (sin (expm1 a)))) 4) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (sin (expm1 a))))) (atan a)) 3))
1.0b
(pow (atan2 (expm1 (* (* (* (pow (cbrt (cbrt (sin (expm1 a)))) 4) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (sin (expm1 a))))) (atan a)) 3)
35.5b
(fmod (cbrt (pow (atan2 (expm1 (* (* (* (pow (cbrt (cbrt (sin (expm1 a)))) 4) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
21×cbrt-prod
15×add-exp-log
13×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
11×pow1
9×associate-*r*
7×prod-exp add-cbrt-cube
6×unpow-prod-down cube-prod
4×pow-plus pow-prod-up add-log-exp
3×pow-unpow cbrt-unprod
2×cube-mult pow-to-exp unpow3 pow-exp sqr-pow
1×pow-pow pow1/3 associate-*l* pow-prod-down *-commutative rem-cbrt-cube rem-cube-cbrt
Counts
4 → 80
Calls
4 calls:
24.0ms
(* (* (pow (cbrt (cbrt (sin (expm1 a)))) 4) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a)))))
1.0ms
(cbrt (pow (atan2 (expm1 (* (* (* (pow (cbrt (cbrt (sin (expm1 a)))) 4) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (sin (expm1 a))))) (atan a)) 3))
1.0ms
(pow (atan2 (expm1 (* (* (* (pow (cbrt (cbrt (sin (expm1 a)))) 4) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (sin (expm1 a))))) (atan a)) 3)
0.0ms
(fmod (cbrt (pow (atan2 (expm1 (* (* (* (pow (cbrt (cbrt (sin (expm1 a)))) 4) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

series222.0ms

Counts
4 → 12
Calls
4 calls:
181.0ms
(* (* (pow (cbrt (cbrt (sin (expm1 a)))) 4) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a)))))
3.0ms
(cbrt (pow (atan2 (expm1 (* (* (* (pow (cbrt (cbrt (sin (expm1 a)))) 4) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (sin (expm1 a))))) (atan a)) 3))
34.0ms
(pow (atan2 (expm1 (* (* (* (pow (cbrt (cbrt (sin (expm1 a)))) 4) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (sin (expm1 a))))) (atan a)) 3)
4.0ms
(fmod (cbrt (pow (atan2 (expm1 (* (* (* (pow (cbrt (cbrt (sin (expm1 a)))) 4) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

simplify2.0s

Counts
92 → 92
Iterations

Useful iterations: 3 (737.0ms)

IterNodesCost
01213199
12612300
27901494
334581492
done50011492

prune359.0ms

Pruning

30 alts after pruning (29 fresh and 1 done)

Merged error: 29.3b

regimes405.0ms

Accuracy

0% (1.8b remaining)

Error of 33.4b against oracle of 31.6b and baseline of 33.4b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01113
done1113

end0.0ms

sample12.3s

Algorithm
intervals
Results
6.5s2556×body10240exit
3.8s2256×body1280valid
1.1s1639×body640valid
295.0ms839×body320valid
280.0ms2820×body80valid
101.0ms440×body160valid
13.0ms3×body5120valid
6.0ms3×body2560valid