Details

Time bar (total: 9.7s)

sample158.0ms

Algorithm
intervals
Results
68.0ms51×body2560valid
46.0ms86×body1280valid
24.0ms65×body640valid
5.0ms27×body320valid
3.0ms18×body160valid
1.0ms9×body80valid

simplify2.0ms

Counts
1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize9.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
1.5b
(- 1.0 (cos x))

rewrite53.0ms

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:
45.0ms
(/ (- 1.0 (cos x)) (sin x))
7.0ms
(- 1.0 (cos x))

series64.0ms

Counts
2 → 6
Calls
2 calls:
39.0ms
(/ (- 1.0 (cos x)) (sin x))
25.0ms
(- 1.0 (cos x))

simplify75.0ms

Counts
58 → 58

prune176.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
0.3b
(pow (cos x) 3)
0.4b
(+ (cos x) 1.0)
1.3b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
157×add-sqr-sqrt
89×*-un-lft-identity
80×difference-of-squares
75×times-frac
63×unpow-prod-down cube-prod
41×sqr-pow
37×add-cube-cbrt
25×associate-/l* distribute-lft-out--
8×add-log-exp
7×add-exp-log add-cbrt-cube
5×pow1 difference-cubes
3×pow-unpow associate-/r*
2×flip3-- flip3-+ associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative cube-mult pow-to-exp sub-neg pow-pow frac-2neg diff-log unpow3 div-sub div-exp pow-exp clear-num sum-log div-inv distribute-lft-out rem-cube-cbrt
Counts
4 → 189
Calls
4 calls:
81.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
3.0ms
(pow (cos x) 3)
7.0ms
(+ (cos x) 1.0)
29.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series241.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
30.0ms
(pow (cos x) 3)
11.0ms
(+ (cos x) 1.0)
56.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify92.0ms

Counts
201 → 201

prune482.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (cos x) 3)
0.4b
(+ (cos x) 1.0)
0.4b
(+ (cos x) 1.0)
1.4b
(- (/ (pow 1.0 3) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))) (/ (pow (cos x) 3) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))))

rewrite274.0ms

Algorithm
rewrite-expression-head
Rules
97×add-sqr-sqrt
70×times-frac
53×*-un-lft-identity
25×unpow-prod-down cube-prod difference-of-squares
17×add-cube-cbrt
16×distribute-lft-out--
11×sqr-pow
10×add-log-exp
5×pow1 add-exp-log add-cbrt-cube
4×flip3-+ 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
Counts
4 → 105
Calls
4 calls:
3.0ms
(pow (cos x) 3)
7.0ms
(+ (cos x) 1.0)
7.0ms
(+ (cos x) 1.0)
251.0ms
(- (/ (pow 1.0 3) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))) (/ (pow (cos x) 3) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))))

series348.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(pow (cos x) 3)
11.0ms
(+ (cos x) 1.0)
12.0ms
(+ (cos x) 1.0)
295.0ms
(- (/ (pow 1.0 3) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))) (/ (pow (cos x) 3) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))))

simplify59.0ms

Counts
117 → 117

prune371.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (cos x) 3)
0.4b
(+ (cos x) 1.0)
1.3b
(- (pow 1.0 3) (pow (cos x) 3))
1.4b
(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
57×add-sqr-sqrt
32×difference-of-squares
31×*-un-lft-identity
27×unpow-prod-down cube-prod
26×log-pow
25×exp-prod
17×sqr-pow
10×distribute-lft-out--
9×add-cube-cbrt
8×add-log-exp
6×pow1
5×add-exp-log log-prod add-cbrt-cube
3×pow-unpow
2×difference-cubes sub-neg exp-sum
1×+-commutative cube-mult pow-to-exp log-div flip3-- pow-pow flip3-+ exp-diff diff-log unpow3 rem-log-exp pow-exp sum-log flip-- flip-+ distribute-lft-out rem-cube-cbrt
Counts
4 → 109
Calls
4 calls:
3.0ms
(pow (cos x) 3)
8.0ms
(+ (cos x) 1.0)
26.0ms
(- (pow 1.0 3) (pow (cos x) 3))
78.0ms
(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

series151.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(pow (cos x) 3)
13.0ms
(+ (cos x) 1.0)
57.0ms
(- (pow 1.0 3) (pow (cos x) 3))
50.0ms
(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

simplify42.0ms

Counts
121 → 121

prune328.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 0.1b

regimes108.0ms

Accuracy

98.7% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 30.0b

bsearch113.0ms

Steps
ItersRangePoint
9
5.155942382976535e-09
0.21963308938311268
0.022836634539273117
11
-2445851338.3862987
-4.2674702477225e-16
-0.026676798341091105

simplify1.0ms

end0.0ms

sample6.2s

Algorithm
intervals
Results
2.6s1589×body2560valid
1.8s2733×body1280valid
1.3s1880×body640valid
182.0ms944×body320valid
106.0ms476×body160valid
30.0ms375×body80valid
9.0ms3×body5120valid