Details

Time bar (total: 13.0s)

sample129.0ms

Algorithm
intervals
Results
59.0ms47×body2560valid
39.0ms88×body1280valid
14.0ms61×body640valid
6.0ms38×body320valid
1.0ms11×body160valid
1.0ms11×body80valid

simplify7.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
1117
2147
3167
done167

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
2.4b
(- 1.0 (cos x))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt *-un-lft-identity
19×add-cube-cbrt
15×times-frac
9×prod-diff
5×associate-/l* distribute-lft-out-- difference-of-squares
4×add-exp-log add-cbrt-cube add-log-exp
3×fma-neg associate-/r*
2×pow1 expm1-log1p-u flip3-- flip-- log1p-expm1-u associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp clear-num div-inv
Counts
2 → 68
Calls
2 calls:
25.0ms
(/ (- 1.0 (cos x)) (sin x))
8.0ms
(- 1.0 (cos x))

series56.0ms

Counts
2 → 6
Calls
2 calls:
37.0ms
(/ (- 1.0 (cos x)) (sin x))
20.0ms
(- 1.0 (cos x))

simplify1.3s

Counts
74 → 74
Iterations

Useful iterations: done (1.3s)

IterNodesCost
0134964
1295831
2743731
32333692
done5000683

prune166.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
0.3b
(exp (/ (- 1.0 (cos x)) (sin x)))
1.8b
(log (exp (/ (- 1.0 (cos x)) (sin x))))
2.4b
(- 1.0 (cos x))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
62×add-sqr-sqrt *-un-lft-identity
45×times-frac
40×add-cube-cbrt
38×exp-prod
20×log-pow
11×distribute-lft-out-- difference-of-squares
9×prod-diff
7×add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1 associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×log-prod fma-neg div-sub associate-/r* div-inv
2×flip3-- exp-diff flip-- associate-/l/
1×cbrt-undiv sub-neg log-div frac-2neg diff-log div-exp rem-log-exp clear-num rem-exp-log
Counts
4 → 132
Calls
4 calls:
23.0ms
(/ (- 1.0 (cos x)) (sin x))
22.0ms
(exp (/ (- 1.0 (cos x)) (sin x)))
25.0ms
(log (exp (/ (- 1.0 (cos x)) (sin x))))
8.0ms
(- 1.0 (cos x))

series139.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(/ (- 1.0 (cos x)) (sin x))
47.0ms
(exp (/ (- 1.0 (cos x)) (sin x)))
36.0ms
(log (exp (/ (- 1.0 (cos x)) (sin x))))
20.0ms
(- 1.0 (cos x))

simplify1.4s

Counts
144 → 144
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01951743
13701509
28561372
325631333
done50001322

prune331.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (cos x) 3)
0.5b
(+ 1.0 (cos x))
1.8b
(log (exp (/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))) (sin x))))
2.3b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite254.0ms

Algorithm
rewrite-expression-head
Rules
491×add-sqr-sqrt
462×times-frac
353×*-un-lft-identity
251×add-cube-cbrt
242×log-pow
241×exp-prod
198×unpow-prod-down cube-prod
160×difference-of-squares
144×prod-diff
106×sqr-pow
50×distribute-lft-out--
26×cube-mult unpow3
12×fma-neg
10×difference-cubes
8×add-log-exp
6×pow1
5×add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u div-inv
3×pow-unpow log-prod fma-def
2×div-sub
1×+-commutative pow-to-exp sub-neg log-div flip3-- pow-pow flip3-+ exp-diff diff-log rem-log-exp pow-exp sum-log flip-- flip-+ distribute-lft-out rem-cube-cbrt
Counts
4 → 490
Calls
4 calls:
4.0ms
(pow (cos x) 3)
8.0ms
(+ 1.0 (cos x))
157.0ms
(log (exp (/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))) (sin x))))
36.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series258.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(pow (cos x) 3)
10.0ms
(+ 1.0 (cos x))
164.0ms
(log (exp (/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))) (sin x))))
56.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify1.5s

Counts
502 → 502
Iterations

Useful iterations: done (1.5s)

IterNodesCost
077114584
1137910091
230758968
done50008966

prune983.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(exp (- 1.0 (cos x)))
0.2b
(/ (log (exp (- 1.0 (cos x)))) (sin x))
2.4b
(- 1.0 (cos x))
2.5b
(log (exp (- 1.0 (cos x))))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt *-un-lft-identity
44×add-cube-cbrt
30×exp-prod log-pow
27×times-frac prod-diff
22×exp-sum
14×log-prod
9×pow1 associate-/l* add-log-exp
7×distribute-lft-out-- difference-of-squares
6×add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u
3×sub-neg exp-diff fma-neg associate-/r*
2×log-div diff-log rem-exp-log
1×cbrt-undiv flip3-- frac-2neg div-sub div-exp rem-log-exp clear-num flip-- div-inv
Counts
4 → 141
Calls
4 calls:
18.0ms
(exp (- 1.0 (cos x)))
58.0ms
(/ (log (exp (- 1.0 (cos x)))) (sin x))
8.0ms
(- 1.0 (cos x))
18.0ms
(log (exp (- 1.0 (cos x))))

series120.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(exp (- 1.0 (cos x)))
37.0ms
(/ (log (exp (- 1.0 (cos x)))) (sin x))
23.0ms
(- 1.0 (cos x))
20.0ms
(log (exp (- 1.0 (cos x))))

simplify1.5s

Counts
153 → 153
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02162252
13771668
28731415
326141289
done50011261

prune253.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes63.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.4b

bsearch78.0ms

Steps
ItersRangePoint
11
6.1632953816490534e-12
2923699147.8271213
0.02338074252416356
10
-21283307590.397102
-3.152803306627408e-07
-0.02278801870830147

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
02439
12831
done2831

end0.0ms

sample4.2s

Algorithm
intervals
Results
2.1s1602×body2560valid
1.2s2734×body1280valid
427.0ms1857×body640valid
163.0ms949×body320valid
52.0ms492×body160valid
23.0ms366×body80valid