Details

Time bar (total: 12.6s)

sample119.0ms

Algorithm
intervals
Results
20.0ms256×body80valid
16.0ms270×body80nan

simplify26.0ms

Counts
1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite81.0ms

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:
1.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
18.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
57.0ms
(/ (- 1.0 x) (+ 1.0 x))

series364.0ms

Counts
3 → 9
Calls
3 calls:
8.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
264.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
92.0ms
(/ (- 1.0 x) (+ 1.0 x))

simplify2.2s

Counts
100 → 100

prune369.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
18×flip3-+ flip-+
16×add-sqr-sqrt sqrt-prod associate-/r/
12×pow1 frac-times add-cube-cbrt
11×add-exp-log add-cbrt-cube
9×times-frac
6×associate-*r/ swap-sqr associate-*l/ distribute-lft-out
4×associate-*r* associate-*l* associate-/l* add-log-exp
3×difference-of-squares
2×cbrt-undiv rem-sqrt-square div-exp prod-exp cbrt-unprod div-inv associate-/l/
1×pow2 distribute-rgt-in flip3-- frac-2neg distribute-lft-in sqrt-pow1 pow-plus pow1/2 sqrt-div div-sub pow-prod-down clear-num associate-/r* pow-sqr *-commutative pow-prod-up flip-- unswap-sqr
Counts
4 → 109
Calls
4 calls:
1.0ms
(atan (sqrt (/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x)))))
25.0ms
(sqrt (/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x))))
61.0ms
(/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x)))
38.0ms
(* (+ 1.0 x) (+ 1.0 x))

series261.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(atan (sqrt (/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x)))))
139.0ms
(sqrt (/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x))))
90.0ms
(/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x)))
24.0ms
(* (+ 1.0 x) (+ 1.0 x))

simplify1.4s

Counts
121 → 121

prune464.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (sqrt (/ (- (* 1.0 1.0) (* x x)) (* (- (* 1.0 1.0) (* x x)) (- (* 1.0 1.0) (* x x))))) (fabs (- 1.0 x)))
0.0b
(/ (- (* 1.0 1.0) (* x x)) (* (- (* 1.0 1.0) (* x x)) (- (* 1.0 1.0) (* x x))))
0.0b
(sqrt (/ (- (* 1.0 1.0) (* x x)) (* (- (* 1.0 1.0) (* x x)) (- (* 1.0 1.0) (* x x)))))
0.0b
(* (- (* 1.0 1.0) (* x x)) (- (* 1.0 1.0) (* x x)))

rewrite454.0ms

Algorithm
rewrite-expression-head
Rules
34×sqrt-prod
32×pow1
26×add-sqr-sqrt
25×flip3-- flip--
24×associate-/r/
23×associate-*l*
16×frac-times add-cube-cbrt *-un-lft-identity
14×times-frac
13×add-exp-log add-cbrt-cube
9×associate-*l/
8×associate-*r/ difference-of-squares pow-div
7×associate-*r*
5×sqrt-pow1
4×swap-sqr associate-/l* add-log-exp unswap-sqr
3×pow2 pow-plus prod-exp pow-sqr pow-prod-up cbrt-unprod div-inv
2×cbrt-undiv distribute-rgt-in sub-neg rem-sqrt-square distribute-lft-in sqrt-div div-exp pow-prod-down *-commutative associate-/l/
1×frac-2neg pow1/2 div-sub clear-num associate-/r*
Counts
4 → 147
Calls
4 calls:
213.0ms
(* (sqrt (/ (- (* 1.0 1.0) (* x x)) (* (- (* 1.0 1.0) (* x x)) (- (* 1.0 1.0) (* x x))))) (fabs (- 1.0 x)))
87.0ms
(/ (- (* 1.0 1.0) (* x x)) (* (- (* 1.0 1.0) (* x x)) (- (* 1.0 1.0) (* x x))))
57.0ms
(sqrt (/ (- (* 1.0 1.0) (* x x)) (* (- (* 1.0 1.0) (* x x)) (- (* 1.0 1.0) (* x x)))))
85.0ms
(* (- (* 1.0 1.0) (* x x)) (- (* 1.0 1.0) (* x x)))

series433.0ms

Counts
4 → 12
Calls
4 calls:
151.0ms
(* (sqrt (/ (- (* 1.0 1.0) (* x x)) (* (- (* 1.0 1.0) (* x x)) (- (* 1.0 1.0) (* x x))))) (fabs (- 1.0 x)))
85.0ms
(/ (- (* 1.0 1.0) (* x x)) (* (- (* 1.0 1.0) (* x x)) (- (* 1.0 1.0) (* x x))))
137.0ms
(sqrt (/ (- (* 1.0 1.0) (* x x)) (* (- (* 1.0 1.0) (* x x)) (- (* 1.0 1.0) (* x x)))))
60.0ms
(* (- (* 1.0 1.0) (* x x)) (- (* 1.0 1.0) (* x x)))

simplify2.2s

Counts
159 → 159

prune744.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes30.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.3s

end0.0ms

sample2.0s

Algorithm
intervals
Results
890.0ms7844×body80nan
669.0ms8000×body80valid