Details

Time bar (total: 7.5s)

sample25.0ms

Algorithm
intervals
Results
7.0ms65×body640valid
4.0ms129×body80valid
4.0ms43×body320valid
1.0ms19×body160valid

simplify3.0ms

Counts
1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.3b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ 1.0 (+ x 1.0))
3.6b
(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
65×*-un-lft-identity
40×times-frac
31×add-sqr-sqrt
21×distribute-lft-out--
19×add-cube-cbrt
10×distribute-lft-out
4×add-exp-log associate-/r* associate-/r/ add-cbrt-cube add-log-exp difference-of-squares
3×div-inv associate-/l*
2×pow1 flip-- flip-+
1×cbrt-undiv sub-neg flip3-- frac-2neg flip3-+ diff-log div-exp clear-num frac-sub
Counts
2 → 65
Calls
2 calls:
11.0ms
(/ 1.0 (+ x 1.0))
83.0ms
(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

series218.0ms

Counts
2 → 6
Calls
2 calls:
31.0ms
(/ 1.0 (+ x 1.0))
186.0ms
(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

simplify163.0ms

Counts
71 → 71

prune132.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0)))
2.4b
(+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ x 1.0)))
3.5b
(- (pow (/ 1.0 (+ x 1.0)) 3) (pow (/ 1.0 (- x 1.0)) 3))
13.4b
(/ (- (pow (/ 1.0 (+ x 1.0)) 3) (pow (/ 1.0 (- x 1.0)) 3)) (+ (* (/ 1.0 (- x 1.0)) (+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ x 1.0)))) (* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0)))))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
1164×*-un-lft-identity
991×times-frac
746×add-sqr-sqrt
431×distribute-lft-out--
420×unpow-prod-down cube-prod
314×add-cube-cbrt
180×difference-of-squares
159×distribute-lft-out
101×associate-/l*
73×associate-/r/
60×sqr-pow
47×div-inv
33×flip-+
28×frac-add
24×swap-sqr
23×flip--
18×add-exp-log associate-*r* associate-*l* add-cbrt-cube
17×frac-times associate-*r/
12×flip3-+
11×pow1 associate-*l/
8×add-log-exp
5×difference-cubes cbrt-undiv div-exp
4×cube-div prod-exp cbrt-unprod unswap-sqr
3×associate-/r* associate-/l/
2×flip3-- frac-sub
1×+-commutative pow2 sub-neg frac-2neg pow-plus diff-log div-sub pow-prod-down clear-num sum-log pow-sqr *-commutative pow-prod-up
Counts
4 → 672
Calls
4 calls:
324.0ms
(* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0)))
69.0ms
(+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ x 1.0)))
230.0ms
(- (pow (/ 1.0 (+ x 1.0)) 3) (pow (/ 1.0 (- x 1.0)) 3))
704.0ms
(/ (- (pow (/ 1.0 (+ x 1.0)) 3) (pow (/ 1.0 (- x 1.0)) 3)) (+ (* (/ 1.0 (- x 1.0)) (+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ x 1.0)))) (* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0)))))

series1.2s

Counts
4 → 12
Calls
4 calls:
38.0ms
(* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0)))
162.0ms
(+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ x 1.0)))
318.0ms
(- (pow (/ 1.0 (+ x 1.0)) 3) (pow (/ 1.0 (- x 1.0)) 3))
663.0ms
(/ (- (pow (/ 1.0 (+ x 1.0)) 3) (pow (/ 1.0 (- x 1.0)) 3)) (+ (* (/ 1.0 (- x 1.0)) (+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ x 1.0)))) (* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0)))))

simplify196.0ms

Counts
684 → 684

prune1.0s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 2.0 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4))))
0.1b
(/ 1 (pow x 4))
0.1b
(/ (- 2.0) (pow x 6))
0.7b
(/ 1 (pow x 2))

rewrite259.0ms

Algorithm
rewrite-expression-head
Rules
121×times-frac
97×*-un-lft-identity
89×add-sqr-sqrt
87×add-cube-cbrt
57×unpow-prod-down
29×add-exp-log
24×distribute-lft-neg-in distribute-rgt-neg-in
22×associate-/r*
19×sqr-pow
16×associate-/l*
15×div-exp
12×add-cbrt-cube
10×associate-*r*
8×neg-mul-1
7×pow-to-exp pow-exp div-inv distribute-lft-out
6×pow1 rec-exp 1-exp
4×unpow2 add-log-exp
3×cbrt-undiv frac-2neg associate-*r/ associate-*l* clear-num
2×pow-flip inv-pow
1×neg-sub0 distribute-rgt-in distribute-lft-in flip3-+ div-sub distribute-frac-neg pow-prod-down frac-add prod-exp *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 243
Calls
4 calls:
220.0ms
(* 2.0 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4))))
8.0ms
(/ 1 (pow x 4))
12.0ms
(/ (- 2.0) (pow x 6))
9.0ms
(/ 1 (pow x 2))

series198.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(* 2.0 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4))))
30.0ms
(/ 1 (pow x 4))
57.0ms
(/ (- 2.0) (pow x 6))
19.0ms
(/ 1 (pow x 2))

simplify88.0ms

Counts
255 → 255

prune515.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow x (- 2)) (/ 1 (pow x 4)))
0.0b
(* 2.0 (+ (pow x (- 2)) (/ 1 (pow x 4))))
0.1b
(/ 1 (pow x 4))
0.1b
(/ (- 2.0) (pow x 6))

rewrite168.0ms

Algorithm
rewrite-expression-head
Rules
91×times-frac
74×*-un-lft-identity
70×add-sqr-sqrt
68×add-cube-cbrt
45×unpow-prod-down
24×distribute-lft-neg-in distribute-rgt-neg-in
20×add-exp-log
15×sqr-pow
14×associate-/r*
13×associate-/l*
10×add-cbrt-cube
9×div-exp
8×neg-mul-1
6×pow1 add-log-exp
5×associate-*r*
4×pow-to-exp associate-*r/ frac-add pow-exp div-inv distribute-lft-out
3×neg-sub0 rec-exp 1-exp associate-*l*
2×cbrt-undiv pow-neg frac-2neg flip3-+ clear-num flip-+ pow-sub
1×+-commutative distribute-rgt-in pow-flip distribute-lft-in div-sub distribute-frac-neg pow-prod-down prod-exp sum-log *-commutative cbrt-unprod inv-pow unswap-sqr
Counts
4 → 197
Calls
4 calls:
30.0ms
(+ (pow x (- 2)) (/ 1 (pow x 4)))
104.0ms
(* 2.0 (+ (pow x (- 2)) (/ 1 (pow x 4))))
14.0ms
(/ 1 (pow x 4))
11.0ms
(/ (- 2.0) (pow x 6))

series299.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(+ (pow x (- 2)) (/ 1 (pow x 4)))
114.0ms
(* 2.0 (+ (pow x (- 2)) (/ 1 (pow x 4))))
39.0ms
(/ 1 (pow x 4))
54.0ms
(/ (- 2.0) (pow x 6))

simplify74.0ms

Counts
209 → 209

prune447.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes34.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.7b

bsearch117.0ms

Steps
ItersRangePoint
9
0.21963308938311268
137362616.0762091
221.64952326934542
11
-2445851338.3862987
-4.2674702477225e-16
-285.6341066092971

simplify1.0ms

end0.0ms

sample808.0ms

Algorithm
intervals
Results
371.0ms1898×body640valid
134.0ms1273×body320valid
125.0ms4196×body80valid
34.0ms633×body160valid