Details

Time bar (total: 14.0s)

sample28.0ms

Algorithm
intervals
Results
9.0ms66×body640valid
5.0ms129×body80valid
3.0ms32×body320valid
3.0ms17×body1280valid
1.0ms12×body160valid

simplify7.0ms

Counts
1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.8b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 1.0 (+ x 1.0))
0.0b
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
2.4b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite367.0ms

Algorithm
rewrite-expression-head
Rules
64×*-un-lft-identity
32×times-frac
24×add-sqr-sqrt
13×distribute-lft-out
12×add-cube-cbrt
10×distribute-lft-out-- add-log-exp
5×add-exp-log add-cbrt-cube
4×associate-/r* difference-of-squares
3×pow1 frac-add associate-/l*
2×sub-neg associate-+l+ flip3-- flip3-+ diff-log sum-log associate-/r/ frac-sub flip-- flip-+
1×cbrt-undiv +-commutative associate-+l- frac-2neg div-exp clear-num div-inv
Counts
3 → 77
Calls
3 calls:
11.0ms
(/ 1.0 (+ x 1.0))
63.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
290.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series293.0ms

Counts
3 → 9
Calls
3 calls:
28.0ms
(/ 1.0 (+ x 1.0))
44.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
221.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify39.0ms

Counts
86 → 86

prune179.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (/ 1.0 (+ x 1.0)))
0.4b
(cbrt (/ 1.0 (+ x 1.0)))
0.4b
(cbrt (/ 1.0 (+ x 1.0)))
18.9b
(+ (- (* (* (cbrt (/ 1.0 (+ x 1.0))) (cbrt (/ 1.0 (+ x 1.0)))) (cbrt (/ 1.0 (+ x 1.0)))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite532.0ms

Algorithm
rewrite-expression-head
Rules
54×cbrt-prod
48×*-un-lft-identity
36×times-frac
28×add-sqr-sqrt add-cube-cbrt
15×cbrt-div
10×distribute-lft-out
9×frac-add add-log-exp
7×frac-sub
6×associate-/r/
5×frac-times associate-*l/
4×pow1 add-exp-log flip3-+ add-cbrt-cube flip-+
3×pow1/3 associate-*r/ div-inv
2×associate-+l+ sum-log
1×+-commutative associate-+l- sub-neg flip3-- diff-log flip--
Counts
4 → 106
Calls
4 calls:
5.0ms
(cbrt (/ 1.0 (+ x 1.0)))
5.0ms
(cbrt (/ 1.0 (+ x 1.0)))
7.0ms
(cbrt (/ 1.0 (+ x 1.0)))
510.0ms
(+ (- (* (* (cbrt (/ 1.0 (+ x 1.0))) (cbrt (/ 1.0 (+ x 1.0)))) (cbrt (/ 1.0 (+ x 1.0)))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series726.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(cbrt (/ 1.0 (+ x 1.0)))
154.0ms
(cbrt (/ 1.0 (+ x 1.0)))
159.0ms
(cbrt (/ 1.0 (+ x 1.0)))
258.0ms
(+ (- (* (* (cbrt (/ 1.0 (+ x 1.0))) (cbrt (/ 1.0 (+ x 1.0)))) (cbrt (/ 1.0 (+ x 1.0)))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify56.0ms

Counts
118 → 118

prune399.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
0.4b
(cbrt (/ 1.0 (+ x 1.0)))
9.7b
(/ (+ (* (- (* (* (* (cbrt 1.0) (cbrt (/ 1.0 (+ x 1.0)))) (cbrt 1.0)) x) (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) 2.0)) (- x 1.0)) (* (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) x) 1.0)) (* (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) x) (- x 1.0)))
24.1b
(+ (* (- (* (* (* (cbrt 1.0) (cbrt (/ 1.0 (+ x 1.0)))) (cbrt 1.0)) x) (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) 2.0)) (- x 1.0)) (* (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) x) 1.0))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
2600×associate-*l/
1777×cbrt-div
800×frac-times
699×flip3-+ flip-+
650×associate-*r/
512×frac-add
384×frac-sub
258×associate-/l/
233×flip3-- flip--
42×cbrt-prod *-un-lft-identity
30×add-sqr-sqrt
28×associate-/r/
22×add-cube-cbrt
20×add-exp-log
16×add-cbrt-cube
15×times-frac
11×pow1
9×swap-sqr distribute-lft-out
7×pow1/3 associate-*r* associate-*l* prod-exp cbrt-unprod
6×add-log-exp
4×cbrt-undiv associate-+l+ div-exp unswap-sqr
3×associate-/l*
2×distribute-rgt-in sub-neg distribute-lft-in pow-prod-down pow-sqr pow-prod-up div-inv
1×+-commutative pow2 frac-2neg pow-plus clear-num associate-/r* sum-log *-commutative
Counts
4 → 660
Calls
4 calls:
40.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
6.0ms
(cbrt (/ 1.0 (+ x 1.0)))
787.0ms
(/ (+ (* (- (* (* (* (cbrt 1.0) (cbrt (/ 1.0 (+ x 1.0)))) (cbrt 1.0)) x) (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) 2.0)) (- x 1.0)) (* (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) x) 1.0)) (* (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) x) (- x 1.0)))
278.0ms
(+ (* (- (* (* (* (cbrt 1.0) (cbrt (/ 1.0 (+ x 1.0)))) (cbrt 1.0)) x) (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) 2.0)) (- x 1.0)) (* (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) x) 1.0))

series1.9s

Counts
4 → 12
Calls
4 calls:
111.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
163.0ms
(cbrt (/ 1.0 (+ x 1.0)))
1.2s
(/ (+ (* (- (* (* (* (cbrt 1.0) (cbrt (/ 1.0 (+ x 1.0)))) (cbrt 1.0)) x) (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) 2.0)) (- x 1.0)) (* (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) x) 1.0)) (* (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) x) (- x 1.0)))
409.0ms
(+ (* (- (* (* (* (cbrt 1.0) (cbrt (/ 1.0 (+ x 1.0)))) (cbrt 1.0)) x) (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) 2.0)) (- x 1.0)) (* (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) x) 1.0))

simplify294.0ms

Counts
672 → 672

prune4.8s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 2.0 (+ (/ 1 (pow x 7)) (+ (/ 1 (pow x 5)) (/ 1 (pow x 3)))))
0.1b
(/ 1 (pow x 5))
0.4b
(/ 1 (pow x 7))
0.4b
(/ 1 (pow x 3))

rewrite841.0ms

Algorithm
rewrite-expression-head
Rules
90×*-un-lft-identity
87×times-frac
68×add-sqr-sqrt
66×add-cube-cbrt
36×unpow-prod-down
33×add-exp-log
26×associate-/r*
24×distribute-lft-out
18×div-exp
16×associate-*r* div-inv
12×cube-prod add-cbrt-cube sqr-pow
9×pow-to-exp rec-exp 1-exp pow-exp associate-/l*
6×pow1
5×associate-*r/
4×cube-mult unpow3 frac-add add-log-exp
3×cbrt-undiv pow-flip frac-2neg associate-*l* clear-num inv-pow
2×flip3-+ flip-+
1×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 217
Calls
4 calls:
806.0ms
(* 2.0 (+ (/ 1 (pow x 7)) (+ (/ 1 (pow x 5)) (/ 1 (pow x 3)))))
9.0ms
(/ 1 (pow x 5))
9.0ms
(/ 1 (pow x 7))
9.0ms
(/ 1 (pow x 3))

series218.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(* 2.0 (+ (/ 1 (pow x 7)) (+ (/ 1 (pow x 5)) (/ 1 (pow x 3)))))
52.0ms
(/ 1 (pow x 5))
59.0ms
(/ 1 (pow x 7))
40.0ms
(/ 1 (pow x 3))

simplify86.0ms

Counts
229 → 229

prune368.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes34.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 23.7b

bsearch125.0ms

Steps
ItersRangePoint
9
0.21963308938311268
137362616.0762091
98.00054950125781
11
-2445851338.3862987
-4.2674702477225e-16
-101.77579100982673

simplify1.0ms

end0.0ms

sample1.4s

Algorithm
intervals
Results
401.0ms1861×body640valid
381.0ms480×body160valid
162.0ms4132×body80valid
135.0ms570×body1280valid
131.0ms961×body320valid