Details

Time bar (total: 1.9m)

sample95.0ms

Algorithm
intervals
Results
48.0ms292×body80valid
11.0ms33×body640valid
9.0ms20×body1280valid
4.0ms17×body320valid
2.0ms15×body160valid

simplify932.0ms

Counts
1 → 1
Iterations
IterNodes
done5000
41263
3241
267
126
012

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 25.8b

localize39.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos (* 2.0 x)) (pow sin 2.0))
5.6b
(/ (/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x)) x)
6.3b
(* (pow cos 2.0) x)
19.5b
(/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x))

rewrite149.0ms

Algorithm
rewrite-expression-head
Rules
359×times-frac
146×add-sqr-sqrt
141×*-un-lft-identity add-cube-cbrt
128×add-exp-log
76×div-exp
70×unpow-prod-down
57×associate-/l*
38×add-cbrt-cube
27×prod-exp
24×sqr-pow
18×pow-to-exp cbrt-undiv pow-exp
13×div-inv
11×associate-/r*
7×associate-*l*
5×cbrt-unprod
4×expm1-log1p-u pow1 log1p-expm1-u add-log-exp
3×clear-num frac-2neg associate-*r* unswap-sqr
2×associate-/l/
1×*-commutative
Counts
4 → 312
Calls
4 calls:
20.0ms
(/ (cos (* 2.0 x)) (pow sin 2.0))
56.0ms
(/ (/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x)) x)
14.0ms
(* (pow cos 2.0) x)
34.0ms
(/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x))

series1.3s

Counts
4 → 12
Calls
4 calls:
263.0ms
(/ (cos (* 2.0 x)) (pow sin 2.0))
457.0ms
(/ (/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x)) x)
286.0ms
(* (pow cos 2.0) x)
312.0ms
(/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x))

simplify481.0ms

Counts
324 → 324
Iterations
IterNodes
done5001
11224
0468

prune2.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (cbrt x) (cbrt x))
5.2b
(/ (/ (cos (* 2.0 x)) (pow sin (/ 2.0 2))) (* (cbrt x) x))
8.6b
(* (/ (/ (/ 1 (pow sin (/ 2.0 2))) (* (cbrt x) (cbrt x))) (pow cos 2.0)) (/ (/ (cos (* 2.0 x)) (pow sin (/ 2.0 2))) (* (cbrt x) x)))
12.0b
(/ (/ (/ 1 (pow sin (/ 2.0 2))) (* (cbrt x) (cbrt x))) (pow cos 2.0))

rewrite546.0ms

Algorithm
rewrite-expression-head
Rules
3589×add-exp-log
2500×div-exp
1272×times-frac
1137×prod-exp
520×pow-to-exp pow-exp
476×add-sqr-sqrt
408×*-un-lft-identity
399×add-cube-cbrt
353×unpow-prod-down
213×associate-*l*
180×rec-exp 1-exp
169×add-cbrt-cube
127×sqr-pow
108×cbrt-undiv
57×cbrt-unprod
54×associate-/l*
37×div-inv
35×associate-*r*
29×unswap-sqr
16×cbrt-prod
13×pow1
8×associate-/r*
6×pow1/3 swap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down
2×clear-num frac-2neg pow-sqr *-commutative pow-prod-up associate-/l/
1×pow2 frac-times pow-plus associate-*l/ associate-*r/
Counts
4 → 1319
Calls
4 calls:
14.0ms
(* (cbrt x) (cbrt x))
26.0ms
(/ (/ (cos (* 2.0 x)) (pow sin (/ 2.0 2))) (* (cbrt x) x))
287.0ms
(* (/ (/ (/ 1 (pow sin (/ 2.0 2))) (* (cbrt x) (cbrt x))) (pow cos 2.0)) (/ (/ (cos (* 2.0 x)) (pow sin (/ 2.0 2))) (* (cbrt x) x)))
43.0ms
(/ (/ (/ 1 (pow sin (/ 2.0 2))) (* (cbrt x) (cbrt x))) (pow cos 2.0))

series1.5s

Counts
4 → 12
Calls
4 calls:
239.0ms
(* (cbrt x) (cbrt x))
417.0ms
(/ (/ (cos (* 2.0 x)) (pow sin (/ 2.0 2))) (* (cbrt x) x))
450.0ms
(* (/ (/ (/ 1 (pow sin (/ 2.0 2))) (* (cbrt x) (cbrt x))) (pow cos 2.0)) (/ (/ (cos (* 2.0 x)) (pow sin (/ 2.0 2))) (* (cbrt x) x)))
404.0ms
(/ (/ (/ 1 (pow sin (/ 2.0 2))) (* (cbrt x) (cbrt x))) (pow cos 2.0))

simplify1.8s

Counts
1331 → 1331
Iterations
IterNodes
done5001
14539
01232

prune5.8s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 1.2b

localize92.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt x)
0.5b
(cbrt x)
0.6b
(* (cbrt (/ 1 (pow sin (/ 2.0 2)))) (cbrt (/ 1 (pow sin (/ 2.0 2)))))
3.4b
(* (/ (/ (cbrt (/ 1 (pow sin (/ 2.0 2)))) (cbrt x)) (pow cos (/ 2.0 2))) (/ (/ (/ (cos (* x 2.0)) (pow sin (/ 2.0 2))) (cbrt x)) x))

rewrite8.1s

Algorithm
rewrite-expression-head
Rules
7278×times-frac
5156×add-sqr-sqrt
2953×cbrt-prod
2230×*-un-lft-identity
2000×add-cube-cbrt
1518×unpow-prod-down
1236×associate-*l*
790×sqr-pow
584×unswap-sqr
494×associate-*r*
209×add-exp-log
138×div-exp
78×div-inv
44×add-cbrt-cube
43×prod-exp
30×cbrt-undiv swap-sqr
19×pow-to-exp pow-exp
13×pow1 cbrt-unprod
8×pow1/3
4×expm1-log1p-u cbrt-div log1p-expm1-u add-log-exp
3×pow-prod-down
2×frac-times associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
1×pow2 pow-plus
Counts
4 → 2461
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
50.0ms
(* (cbrt (/ 1 (pow sin (/ 2.0 2)))) (cbrt (/ 1 (pow sin (/ 2.0 2)))))
7.6s
(* (/ (/ (cbrt (/ 1 (pow sin (/ 2.0 2)))) (cbrt x)) (pow cos (/ 2.0 2))) (/ (/ (/ (cos (* x 2.0)) (pow sin (/ 2.0 2))) (cbrt x)) x))

series2.0s

Counts
4 → 12
Calls
4 calls:
247.0ms
(cbrt x)
244.0ms
(cbrt x)
578.0ms
(* (cbrt (/ 1 (pow sin (/ 2.0 2)))) (cbrt (/ 1 (pow sin (/ 2.0 2)))))
898.0ms
(* (/ (/ (cbrt (/ 1 (pow sin (/ 2.0 2)))) (cbrt x)) (pow cos (/ 2.0 2))) (/ (/ (/ (cos (* x 2.0)) (pow sin (/ 2.0 2))) (cbrt x)) x))

simplify2.3s

Counts
2473 → 2473
Iterations
IterNodes
done5000
03193

prune33.3s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 0.3b

localize119.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (* (cbrt (/ 1 (pow sin (/ 2.0 2)))) (cbrt (/ 1 (pow sin (/ 2.0 2))))))
1.4b
(* (/ (/ (cbrt (cbrt (/ 1 (pow sin (/ 2.0 2))))) (cbrt x)) (pow cos (/ 2.0 2))) (/ (/ (cos (* x 2.0)) (pow sin (/ 2.0 2))) (cbrt x)))
1.6b
(/ (* (/ (/ (cbrt (cbrt (/ 1 (pow sin (/ 2.0 2))))) (cbrt x)) (pow cos (/ 2.0 2))) (/ (/ (cos (* x 2.0)) (pow sin (/ 2.0 2))) (cbrt x))) x)
1.8b
(* (/ (/ (cbrt (* (cbrt (/ 1 (pow sin (/ 2.0 2)))) (cbrt (/ 1 (pow sin (/ 2.0 2)))))) 1) (pow 1 (/ 2.0 2))) (/ (* (/ (/ (cbrt (cbrt (/ 1 (pow sin (/ 2.0 2))))) (cbrt x)) (pow cos (/ 2.0 2))) (/ (/ (cos (* x 2.0)) (pow sin (/ 2.0 2))) (cbrt x))) x))

rewrite4.4s

Algorithm
rewrite-expression-head
Rules
6163×times-frac
4400×add-sqr-sqrt
4267×cbrt-prod
3591×add-exp-log
2654×div-exp
1901×*-un-lft-identity
1726×add-cube-cbrt
1455×unpow-prod-down
1450×associate-*l*
1006×prod-exp
750×sqr-pow
543×unswap-sqr
477×pow-exp
366×pow-to-exp
259×1-exp
226×add-cbrt-cube
163×cbrt-undiv
161×associate-*r*
78×cbrt-unprod
67×div-inv
8×pow1
7×cbrt-div
4×expm1-log1p-u frac-times associate-*l/ associate-*r/ log1p-expm1-u add-log-exp
3×associate-/r* associate-/l/
2×pow-prod-down *-commutative
1×clear-num frac-2neg pow1/3 associate-/l*
Counts
4 → 2822
Calls
4 calls:
14.0ms
(cbrt (* (cbrt (/ 1 (pow sin (/ 2.0 2)))) (cbrt (/ 1 (pow sin (/ 2.0 2))))))
3.0s
(* (/ (/ (cbrt (cbrt (/ 1 (pow sin (/ 2.0 2))))) (cbrt x)) (pow cos (/ 2.0 2))) (/ (/ (cos (* x 2.0)) (pow sin (/ 2.0 2))) (cbrt x)))
140.0ms
(/ (* (/ (/ (cbrt (cbrt (/ 1 (pow sin (/ 2.0 2))))) (cbrt x)) (pow cos (/ 2.0 2))) (/ (/ (cos (* x 2.0)) (pow sin (/ 2.0 2))) (cbrt x))) x)
433.0ms
(* (/ (/ (cbrt (* (cbrt (/ 1 (pow sin (/ 2.0 2)))) (cbrt (/ 1 (pow sin (/ 2.0 2)))))) 1) (pow 1 (/ 2.0 2))) (/ (* (/ (/ (cbrt (cbrt (/ 1 (pow sin (/ 2.0 2))))) (cbrt x)) (pow cos (/ 2.0 2))) (/ (/ (cos (* x 2.0)) (pow sin (/ 2.0 2))) (cbrt x))) x))

series2.0s

Counts
4 → 12
Calls
4 calls:
425.0ms
(cbrt (* (cbrt (/ 1 (pow sin (/ 2.0 2)))) (cbrt (/ 1 (pow sin (/ 2.0 2))))))
532.0ms
(* (/ (/ (cbrt (cbrt (/ 1 (pow sin (/ 2.0 2))))) (cbrt x)) (pow cos (/ 2.0 2))) (/ (/ (cos (* x 2.0)) (pow sin (/ 2.0 2))) (cbrt x)))
556.0ms
(/ (* (/ (/ (cbrt (cbrt (/ 1 (pow sin (/ 2.0 2))))) (cbrt x)) (pow cos (/ 2.0 2))) (/ (/ (cos (* x 2.0)) (pow sin (/ 2.0 2))) (cbrt x))) x)
513.0ms
(* (/ (/ (cbrt (* (cbrt (/ 1 (pow sin (/ 2.0 2)))) (cbrt (/ 1 (pow sin (/ 2.0 2)))))) 1) (pow 1 (/ 2.0 2))) (/ (* (/ (/ (cbrt (cbrt (/ 1 (pow sin (/ 2.0 2))))) (cbrt x)) (pow cos (/ 2.0 2))) (/ (/ (cos (* x 2.0)) (pow sin (/ 2.0 2))) (cbrt x))) x))

simplify1.3s

Counts
2834 → 2834
Iterations
IterNodes
done5000
02909

prune39.5s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 0.3b

regimes1.9s

Accuracy

0% (1.4b remaining)

Error of 1.9b against oracle of 0.5b and baseline of 1.9b

bsearch0.0ms

simplify6.0ms

Iterations
IterNodes
done42
142
036

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.1s1005×body640valid
1.0s9056×body80valid
612.0ms780×body1280valid
159.0ms537×body320valid
66.0ms330×body160valid