Details

Time bar (total: 29.8s)

sample146.0ms

Algorithm
intervals
Results
72.0ms144×body1280valid
24.0ms19×body2560valid
23.0ms57×body640valid
6.0ms25×body320valid
2.0ms9×body160valid
0.0ms2×body80valid

simplify9.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
197
2107
done107

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.0b

localize19.0ms

Local error

Found 2 expressions with local error:

1.3b
(- (cos (+ x eps)) (cos x))
3.5b
(cos (+ x eps))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×add-cube-cbrt prod-diff
4×add-log-exp
3×fma-neg
2×pow1 add-exp-log expm1-log1p-u cos-sum add-cbrt-cube log1p-expm1-u
1×associate--l- sub-neg flip3-- diff-log flip-- diff-cos distribute-lft-out-- difference-of-squares
Counts
2 → 40
Calls
2 calls:
54.0ms
(- (cos (+ x eps)) (cos x))
16.0ms
(cos (+ x eps))

series100.0ms

Counts
2 → 6
Calls
2 calls:
81.0ms
(- (cos (+ x eps)) (cos x))
18.0ms
(cos (+ x eps))

simplify4.9s

Counts
46 → 46
Iterations

Useful iterations: 4 (2.9s)

IterNodesCost
091664
1194540
2439453
31358389
44783375
done5000375

prune169.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b
(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
0.2b
(/ (fma 2 x eps) 2)
0.3b
(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
3.3b
(sin (/ (fma 2 x eps) 2))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
13×add-exp-log add-cbrt-cube
11×pow1
9×times-frac
6×associate-*l*
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×associate-/r* associate-/l*
2×*-commutative sin-mult
1×cbrt-undiv frac-2neg associate-*r/ div-exp clear-num div-inv unswap-sqr
Counts
4 → 80
Calls
4 calls:
54.0ms
(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
5.0ms
(/ (fma 2 x eps) 2)
19.0ms
(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
6.0ms
(sin (/ (fma 2 x eps) 2))

series266.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
39.0ms
(/ (fma 2 x eps) 2)
76.0ms
(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
66.0ms
(sin (/ (fma 2 x eps) 2))

simplify6.3s

Counts
92 → 92
Iterations

Useful iterations: 4 (5.0s)

IterNodesCost
01491295
13001258
28001099
322301095
44896949
done5000949

prune436.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(log1p (* (sin (fma 1/2 eps x)) (sin (/ eps 2))))
0.2b
(expm1 (log1p (* (sin (fma 1/2 eps x)) (sin (/ eps 2)))))
0.3b
(* (sin (fma 1/2 eps x)) (sin (/ eps 2)))
3.3b
(sin (fma 1/2 eps x))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
5×expm1-log1p-u
4×log1p-expm1-u add-log-exp
3×associate-*r* associate-*l*
1×log1p-udef expm1-log1p sin-sum log1p-expm1 pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef sin-mult expm1-udef unswap-sqr
Counts
4 → 53
Calls
4 calls:
0.0ms
(log1p (* (sin (fma 1/2 eps x)) (sin (/ eps 2))))
0.0ms
(expm1 (log1p (* (sin (fma 1/2 eps x)) (sin (/ eps 2)))))
27.0ms
(* (sin (fma 1/2 eps x)) (sin (/ eps 2)))
3.0ms
(sin (fma 1/2 eps x))

series401.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(log1p (* (sin (fma 1/2 eps x)) (sin (/ eps 2))))
157.0ms
(expm1 (log1p (* (sin (fma 1/2 eps x)) (sin (/ eps 2)))))
73.0ms
(* (sin (fma 1/2 eps x)) (sin (/ eps 2)))
27.0ms
(sin (fma 1/2 eps x))

simplify4.7s

Counts
65 → 65
Iterations

Useful iterations: 4 (780.0ms)

IterNodesCost
095844
1172809
2411711
3789707
41557704
53731704
done5000704

prune405.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize62.0ms

Local error

Found 4 expressions with local error:

0.1b
(log1p (* (+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x))) (sin (/ eps 2))))
0.1b
(* (cos (* 1/2 eps)) (sin x))
0.2b
(expm1 (log1p (* (+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x))) (sin (/ eps 2)))))
0.3b
(* (+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x))) (sin (/ eps 2)))

rewrite168.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×associate-*r* associate-*l*
5×expm1-log1p-u
4×log1p-expm1-u add-log-exp
2×pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod unswap-sqr
1×log1p-udef expm1-log1p flip3-+ log1p-expm1 flip-+ expm1-udef
Counts
4 → 64
Calls
4 calls:
0.0ms
(log1p (* (+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x))) (sin (/ eps 2))))
20.0ms
(* (cos (* 1/2 eps)) (sin x))
0.0ms
(expm1 (log1p (* (+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x))) (sin (/ eps 2)))))
146.0ms
(* (+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x))) (sin (/ eps 2)))

series801.0ms

Counts
4 → 12
Calls
4 calls:
258.0ms
(log1p (* (+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x))) (sin (/ eps 2))))
51.0ms
(* (cos (* 1/2 eps)) (sin x))
272.0ms
(expm1 (log1p (* (+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x))) (sin (/ eps 2)))))
221.0ms
(* (+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x))) (sin (/ eps 2)))

simplify2.9s

Counts
76 → 76
Iterations

Useful iterations: done (2.9s)

IterNodesCost
01331587
12991475
29161297
329891290
done50021286

prune522.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes210.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01321
11721
done1721

end0.0ms

sample7.1s

Algorithm
intervals
Results
3.4s4523×body1280valid
1.9s1821×body640valid
949.0ms611×body2560valid
337.0ms670×body320valid
54.0ms292×body160valid
8.0ms83×body80valid