Details

Time bar (total: 20.3s)

sample233.0ms

Algorithm
intervals
Results
94.0ms45×body2560valid
82.0ms98×body1280valid
27.0ms59×body640valid
9.0ms29×body320valid
6.0ms16×body160valid
1.0ms9×body80valid

simplify9.0ms

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: 29.8b

localize48.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
2.0b
(- 1.0 (cos x))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt *-un-lft-identity
15×times-frac
12×add-cube-cbrt
5×associate-/l* distribute-lft-out-- difference-of-squares
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r*
2×pow1 flip3-- flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp clear-num div-inv
Counts
2 → 52
Calls
2 calls:
28.0ms
(/ (- 1.0 (cos x)) (sin x))
13.0ms
(- 1.0 (cos x))

series80.0ms

Counts
2 → 6
Calls
2 calls:
50.0ms
(/ (- 1.0 (cos x)) (sin x))
30.0ms
(- 1.0 (cos x))

simplify2.9s

Counts
58 → 58
Iterations

Useful iterations: 3 (849.0ms)

IterNodesCost
0106665
1240645
2805611
34711609
done5002609

prune211.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.3b

localize25.0ms

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)))
1.3b
(log (exp (/ (- 1.0 (cos x)) (sin x))))
2.0b
(- 1.0 (cos x))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
55×add-sqr-sqrt *-un-lft-identity
45×times-frac
38×exp-prod
33×add-cube-cbrt
20×log-pow
11×distribute-lft-out-- difference-of-squares
7×add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1 associate-/l*
3×log-prod 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 → 112
Calls
4 calls:
20.0ms
(/ (- 1.0 (cos x)) (sin x))
40.0ms
(exp (/ (- 1.0 (cos x)) (sin x)))
45.0ms
(log (exp (/ (- 1.0 (cos x)) (sin x))))
13.0ms
(- 1.0 (cos x))

series206.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(/ (- 1.0 (cos x)) (sin x))
67.0ms
(exp (/ (- 1.0 (cos x)) (sin x)))
49.0ms
(log (exp (/ (- 1.0 (cos x)) (sin x))))
40.0ms
(- 1.0 (cos x))

simplify637.0ms

Counts
124 → 124
Iterations

Useful iterations: done (633.0ms)

IterNodesCost
01631406
13181293
29521222
done50001218

prune474.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (cos x) 3)
0.5b
(+ 1.0 (cos x))
1.3b
(log (exp (/ (- (pow 1.0 3) (pow (cos x) 3)) (* (sin x) (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0))))))
1.8b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite237.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt
32×*-un-lft-identity log-pow difference-of-squares
31×exp-prod
27×unpow-prod-down cube-prod
25×times-frac
17×sqr-pow
10×add-cube-cbrt distribute-lft-out--
8×add-log-exp
6×pow1
5×add-exp-log add-cbrt-cube
3×pow-unpow log-prod
2×difference-cubes flip3-+ associate-*r/ associate-/r/ flip-+
1×+-commutative cube-mult pow-to-exp sub-neg log-div flip3-- pow-pow exp-diff diff-log unpow3 div-sub rem-log-exp pow-exp sum-log flip-- div-inv distribute-lft-out rem-cube-cbrt
Counts
4 → 113
Calls
4 calls:
6.0ms
(pow (cos x) 3)
12.0ms
(+ 1.0 (cos x))
165.0ms
(log (exp (/ (- (pow 1.0 3) (pow (cos x) 3)) (* (sin x) (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0))))))
47.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series383.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(pow (cos x) 3)
20.0ms
(+ 1.0 (cos x))
233.0ms
(log (exp (/ (- (pow 1.0 3) (pow (cos x) 3)) (* (sin x) (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0))))))
80.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify1.8s

Counts
125 → 125
Iterations

Useful iterations: 2 (543.0ms)

IterNodesCost
02271942
15511712
225731612
done50011612

prune634.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (cos x) 3)
0.5b
(+ 1.0 (cos x))
0.5b
(+ 1.0 (cos x))
1.9b
(- (/ (pow 1.0 3) (* (sin x) (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)))) (/ (pow (cos x) 3) (* (sin x) (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)))))

rewrite298.0ms

Algorithm
rewrite-expression-head
Rules
23×*-un-lft-identity
10×times-frac add-log-exp
9×add-sqr-sqrt
7×add-cube-cbrt unpow-prod-down cube-prod
6×distribute-lft-out--
5×pow1 add-exp-log add-cbrt-cube
4×flip3-+ associate-*r/ associate-/r/ flip-+
3×pow-unpow distribute-rgt-out--
2×+-commutative sum-log div-inv distribute-lft-out
1×cube-mult pow-to-exp sub-neg flip3-- pow-pow diff-log unpow3 pow-exp frac-sub flip-- sub-div rem-cube-cbrt difference-of-squares sqr-pow
Counts
4 → 71
Calls
4 calls:
4.0ms
(pow (cos x) 3)
6.0ms
(+ 1.0 (cos x))
7.0ms
(+ 1.0 (cos x))
278.0ms
(- (/ (pow 1.0 3) (* (sin x) (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)))) (/ (pow (cos x) 3) (* (sin x) (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)))))

series600.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(pow (cos x) 3)
17.0ms
(+ 1.0 (cos x))
17.0ms
(+ 1.0 (cos x))
529.0ms
(- (/ (pow 1.0 3) (* (sin x) (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)))) (/ (pow (cos x) 3) (* (sin x) (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)))))

simplify1.7s

Counts
83 → 83
Iterations

Useful iterations: 2 (456.0ms)

IterNodesCost
01411720
14471643
224061495
done50001495

prune310.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

regimes284.0ms

Accuracy

98.7% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 30.2b

bsearch149.0ms

Steps
ItersRangePoint
9
0.00015484893005477947
28918.939680702064
0.01743449574326637
10
-2676750800.736259
-2.9526231381329305e-09
-0.020888553749077

simplify12.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
038117
148117
done48117

end0.0ms

sample8.9s

Algorithm
intervals
Results
4.3s1567×body2560valid
2.6s2839×body1280valid
1.3s1853×body640valid
302.0ms943×body320valid
84.0ms440×body160valid
44.0ms357×body80valid
3.0ms1×body5120valid