Details

Time bar (total: 23.1s)

sample393.0ms

Algorithm
intervals
Results
219.0ms88×body10240exit
104.0ms67×body1280valid
36.0ms48×body640valid
10.0ms102×body80valid
9.0ms27×body320valid
3.0ms12×body160valid

simplify2.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0810
done810

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize12.0ms

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
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)))
1.0ms
(sin (expm1 a))
0.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series150.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(atan2 (expm1 (sin (expm1 a))) (atan a))
84.0ms
(expm1 (sin (expm1 a)))
61.0ms
(sin (expm1 a))
3.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.4s

Counts
51 → 51
Iterations

Useful iterations: 3 (68.0ms)

IterNodesCost
070438
1110422
2206375
3429374
41100374
53065374
done5001374

prune208.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 29.9b

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)
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×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:
1.0ms
(sin (expm1 a))
1.0ms
(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
1.0ms
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
0.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

series98.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(sin (expm1 a))
2.0ms
(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
36.0ms
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
2.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

simplify1.8s

Counts
79 → 79
Iterations

Useful iterations: 3 (312.0ms)

IterNodesCost
0921068
1158876
2369778
31851777
done5000777

prune261.0ms

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)

rewrite12.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 99
Calls
4 calls:
1.0ms
(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)

series193.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3))
151.0ms
(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
36.0ms
(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)

simplify2.0s

Counts
111 → 111
Iterations

Useful iterations: 3 (471.0ms)

IterNodesCost
01282472
12362174
25691349
324211095
done50001095

prune418.0ms

Pruning

27 alts after pruning (26 fresh and 1 done)

Merged error: 29.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b
(pow (cbrt (cbrt (sin (expm1 a)))) 4)
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)

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
21×cbrt-prod
15×unpow-prod-down
14×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×pow1 add-exp-log pow-unpow cube-prod
5×add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-pow sqr-pow
2×cube-mult pow-to-exp pow1/3 unpow3 pow-exp
1×rem-cbrt-cube rem-cube-cbrt
Counts
4 → 83
Calls
4 calls:
3.0ms
(pow (cbrt (cbrt (sin (expm1 a)))) 4)
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)

series199.0ms

Counts
4 → 12
Calls
4 calls:
159.0ms
(pow (cbrt (cbrt (sin (expm1 a)))) 4)
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))
33.0ms
(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)

simplify1.8s

Counts
95 → 95
Iterations

Useful iterations: 3 (542.0ms)

IterNodesCost
01413118
12712836
26272024
327211613
done50001613

prune374.0ms

Pruning

34 alts after pruning (33 fresh and 1 done)

Merged error: 29.1b

regimes439.0ms

Accuracy

0% (2.1b remaining)

Error of 33.5b against oracle of 31.4b and baseline of 33.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02153
12453
done2453

end0.0ms

sample12.3s

Algorithm
intervals
Results
6.4s2556×body10240exit
3.8s2256×body1280valid
1.1s1639×body640valid
278.0ms839×body320valid
275.0ms2820×body80valid
104.0ms440×body160valid
14.0ms3×body5120valid
6.0ms3×body2560valid