Details

Time bar (total: 12.7s)

sample133.0ms

Algorithm
intervals
Results
12.0ms256×body80valid
10.0ms266×body80nan

simplify70.0ms

Counts
1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
0.0b
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
0.0b
(/ (- 1.0 x) (+ 1.0 x))

rewrite215.0ms

Algorithm
rewrite-expression-head
Rules
64×*-un-lft-identity
45×add-sqr-sqrt
41×times-frac
26×sqrt-prod
24×add-cube-cbrt
11×distribute-lft-out
9×distribute-lft-out-- difference-of-squares
5×add-exp-log add-cbrt-cube associate-/l*
4×pow1 associate-/r* associate-/r/
3×add-log-exp
2×rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/
1×cbrt-undiv flip3-- frac-2neg sqrt-pow1 pow1/2 sqrt-div div-sub div-exp clear-num flip--
Counts
3 → 91
Calls
3 calls:
40.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
1.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
163.0ms
(/ (- 1.0 x) (+ 1.0 x))

series228.0ms

Counts
3 → 9
Calls
3 calls:
171.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
5.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
52.0ms
(/ (- 1.0 x) (+ 1.0 x))

simplify2.0s

Counts
100 → 100

prune345.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(atan (sqrt (cbrt (pow (/ (- 1.0 x) (+ 1.0 x)) 3))))
0.0b
(/ (- 1.0 x) (+ 1.0 x))
0.0b
(cbrt (pow (/ (- 1.0 x) (+ 1.0 x)) 3))
0.0b
(pow (/ (- 1.0 x) (+ 1.0 x)) 3)

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
151×*-un-lft-identity
100×times-frac
99×add-sqr-sqrt
58×cbrt-prod
57×add-cube-cbrt
52×unpow-prod-down cube-prod
26×distribute-lft-out
21×distribute-lft-out-- difference-of-squares
10×associate-/r/
9×add-exp-log add-cbrt-cube
5×pow1 flip3-+ flip-+ div-inv associate-/l*
4×associate-/r* add-log-exp
3×pow-unpow
2×cbrt-undiv cube-div cube-mult unpow3 div-exp pow-exp associate-/l/ rem-cube-cbrt sqr-pow
1×pow-to-exp cbrt-div flip3-- pow-pow frac-2neg pow1/3 div-sub clear-num flip-- rem-cbrt-cube
Counts
4 → 193
Calls
4 calls:
1.0ms
(atan (sqrt (cbrt (pow (/ (- 1.0 x) (+ 1.0 x)) 3))))
28.0ms
(/ (- 1.0 x) (+ 1.0 x))
21.0ms
(cbrt (pow (/ (- 1.0 x) (+ 1.0 x)) 3))
43.0ms
(pow (/ (- 1.0 x) (+ 1.0 x)) 3)

series183.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(atan (sqrt (cbrt (pow (/ (- 1.0 x) (+ 1.0 x)) 3))))
43.0ms
(/ (- 1.0 x) (+ 1.0 x))
58.0ms
(cbrt (pow (/ (- 1.0 x) (+ 1.0 x)) 3))
76.0ms
(pow (/ (- 1.0 x) (+ 1.0 x)) 3)

simplify1.2s

Counts
205 → 205

prune560.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x)))
0.0b
(* (+ 1.0 x) (+ 1.0 x))
0.0b
(cbrt (pow (/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x))) 3))
0.0b
(pow (/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x))) 3)

rewrite206.0ms

Algorithm
rewrite-expression-head
Rules
40×associate-/r/
38×cbrt-prod
36×flip3-+ flip-+
34×*-un-lft-identity
32×unpow-prod-down cube-prod
24×frac-times
22×add-sqr-sqrt
20×add-cube-cbrt times-frac
17×add-exp-log add-cbrt-cube
12×pow1 associate-*r/ associate-*l/
6×swap-sqr distribute-lft-out difference-of-squares
5×div-inv
4×cbrt-undiv div-exp associate-*r* associate-*l* associate-/l* add-log-exp
3×pow-unpow pow-exp prod-exp cbrt-unprod rem-cube-cbrt
2×cube-div cube-mult unpow3 associate-/l/ sqr-pow
1×pow2 distribute-rgt-in pow-to-exp cbrt-div flip3-- pow-pow frac-2neg distribute-lft-in pow-plus pow1/3 div-sub pow-prod-down clear-num associate-/r* pow-sqr *-commutative pow-prod-up flip-- rem-cbrt-cube unswap-sqr
Counts
4 → 176
Calls
4 calls:
48.0ms
(/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x)))
48.0ms
(* (+ 1.0 x) (+ 1.0 x))
35.0ms
(cbrt (pow (/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x))) 3))
57.0ms
(pow (/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x))) 3)

series279.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x)))
17.0ms
(* (+ 1.0 x) (+ 1.0 x))
83.0ms
(cbrt (pow (/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x))) 3))
111.0ms
(pow (/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x))) 3)

simplify1.9s

Counts
188 → 188

prune567.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b
(atan (sqrt (* (/ (- (* 1.0 1.0) (* x x)) (* (+ (pow 1.0 3) (pow x 3)) (+ (pow 1.0 3) (pow x 3)))) (* (+ (* x (- x 1.0)) (* 1.0 1.0)) (+ (* x (- x 1.0)) (* 1.0 1.0))))))
0.0b
(* x (- x 1.0))
0.0b
(* x (- x 1.0))
0.0b
(* (+ (* x (- x 1.0)) (* 1.0 1.0)) (+ (* x (- x 1.0)) (* 1.0 1.0)))

rewrite161.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
16×*-un-lft-identity
15×pow1
13×associate-*r*
12×add-cube-cbrt
10×add-exp-log add-cbrt-cube
9×associate-*l*
6×flip3-+ associate-*r/ flip-+
5×distribute-rgt-in distribute-lft-in
4×frac-times sub-neg add-log-exp
3×swap-sqr pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×flip3-- associate-*l/ flip-- distribute-lft-out-- difference-of-squares
1×pow2 pow-plus pow-sqr pow-prod-up
Counts
4 → 94
Calls
4 calls:
1.0ms
(atan (sqrt (* (/ (- (* 1.0 1.0) (* x x)) (* (+ (pow 1.0 3) (pow x 3)) (+ (pow 1.0 3) (pow x 3)))) (* (+ (* x (- x 1.0)) (* 1.0 1.0)) (+ (* x (- x 1.0)) (* 1.0 1.0))))))
28.0ms
(* x (- x 1.0))
26.0ms
(* x (- x 1.0))
102.0ms
(* (+ (* x (- x 1.0)) (* 1.0 1.0)) (+ (* x (- x 1.0)) (* 1.0 1.0)))

series202.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(atan (sqrt (* (/ (- (* 1.0 1.0) (* x x)) (* (+ (pow 1.0 3) (pow x 3)) (+ (pow 1.0 3) (pow x 3)))) (* (+ (* x (- x 1.0)) (* 1.0 1.0)) (+ (* x (- x 1.0)) (* 1.0 1.0))))))
66.0ms
(* x (- x 1.0))
73.0ms
(* x (- x 1.0))
45.0ms
(* (+ (* x (- x 1.0)) (* 1.0 1.0)) (+ (* x (- x 1.0)) (* 1.0 1.0)))

simplify1.2s

Counts
106 → 106

prune493.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes33.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify681.0ms

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.1s8000×body80valid
452.0ms8096×body80nan