Details

Time bar (total: 17.7s)

sample433.0ms

Algorithm
intervals
Results
230.0ms87×body10240exit
113.0ms67×body1280valid
43.0ms56×body640valid
16.0ms29×body320valid
16.0ms92×body80valid
4.0ms12×body160valid

simplify2.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
087

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(sin (expm1 a))
0.0b
(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b
(expm1 (sin (expm1 a)))
37.9b
(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:
1.0ms
(sin (expm1 a))
0.0ms
(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0ms
(expm1 (sin (expm1 a)))
0.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series65.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(sin (expm1 a))
2.0ms
(atan2 (expm1 (sin (expm1 a))) (atan a))
1.0ms
(expm1 (sin (expm1 a)))
2.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify118.0ms

Algorithm
egg-herbie
Counts
40 → 40
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
039248
144212
254212
368212
4114212
5228212
6919212
73184212
85001212

prune154.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 31.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (sin (expm1 a)))
0.4b
(cbrt (sin (expm1 a)))
0.7b
(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
37.9b
(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
22×cbrt-prod add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity
11×pow1
8×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×add-cbrt-cube add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 69
Calls
4 calls:
1.0ms
(cbrt (sin (expm1 a)))
1.0ms
(cbrt (sin (expm1 a)))
7.0ms
(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
0.0ms
(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

series507.0ms

Counts
4 → 12
Calls
4 calls:
162.0ms
(cbrt (sin (expm1 a)))
162.0ms
(cbrt (sin (expm1 a)))
180.0ms
(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
3.0ms
(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify78.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 3 (72.0ms)

IterNodesCost
099673
1366578
22587543
35002526

prune343.0ms

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 31.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (sin (expm1 a)))
0.5b
(* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a)))))
0.7b
(* (cbrt (sin (expm1 a))) (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))))
37.9b
(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
34×pow1
20×pow1/3
18×add-exp-log cbrt-prod
14×pow-prod-down pow-prod-up
13×add-sqr-sqrt
11×add-cube-cbrt
10×*-un-lft-identity associate-*r*
9×prod-exp cbrt-unprod
7×associate-*l* add-cbrt-cube
6×pow-plus
4×pow-sqr add-log-exp
3×unswap-sqr
2×pow2 *-commutative
1×swap-sqr pow3
Counts
4 → 85
Calls
4 calls:
1.0ms
(cbrt (sin (expm1 a)))
20.0ms
(* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a)))))
56.0ms
(* (cbrt (sin (expm1 a))) (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))))
0.0ms
(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

series505.0ms

Counts
4 → 12
Calls
4 calls:
163.0ms
(cbrt (sin (expm1 a)))
160.0ms
(* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a)))))
178.0ms
(* (cbrt (sin (expm1 a))) (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))))
3.0ms
(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify44.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
02231399
18601068
25002827

prune395.0ms

Pruning

31 alts after pruning (31 fresh and 0 done)

Merged error: 31.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.8b
(cbrt (* (cbrt (sin (expm1 a))) (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a)))))))
0.8b
(cbrt (* (cbrt (sin (expm1 a))) (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a)))))))
0.8b
(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
37.9b
(fmod (atan2 (expm1 (* (* (* (cbrt (* (cbrt (sin (expm1 a))) (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))))) (cbrt (* (cbrt (sin (expm1 a))) (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a)))))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite103.0ms

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
3×cbrt-prod pow1/3
Counts
4 → 34
Calls
4 calls:
50.0ms
(cbrt (* (cbrt (sin (expm1 a))) (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a)))))))
48.0ms
(cbrt (* (cbrt (sin (expm1 a))) (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a)))))))
3.0ms
(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
0.0ms
(fmod (atan2 (expm1 (* (* (* (cbrt (* (cbrt (sin (expm1 a))) (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))))) (cbrt (* (cbrt (sin (expm1 a))) (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a)))))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

series545.0ms

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

simplify109.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 5 (97.0ms)

IterNodesCost
0661160
1108952
2202748
3537742
41768742
55001692

prune226.0ms

Pruning

37 alts after pruning (37 fresh and 0 done)

Merged error: 30.7b

regimes461.0ms

Accuracy

0% (2.0b remaining)

Error of 33.3b against oracle of 31.3b and baseline of 33.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02559
12559

end0.0ms

sample13.4s

Algorithm
intervals
Results
6.9s2599×body10240exit
4.0s2274×body1280valid
1.3s1659×body640valid
496.0ms2829×body80valid
334.0ms822×body320valid
124.0ms411×body160valid
19.0ms4×body5120valid
2.0ms1×body2560valid