Details

Time bar (total: 29.7s)

sample324.0ms

Algorithm
intervals
Results
107.0ms256×body80valid
66.0ms251×body80nan

simplify77.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
77.0ms
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize97.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- 1 x) (+ 1 x))
0.0b
(sqrt (/ (- 1 x) (+ 1 x)))
0.0b
(atan (sqrt (/ (- 1 x) (+ 1 x))))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
79×*-un-lft-identity
56×add-sqr-sqrt
49×times-frac
30×sqrt-prod
26×add-cube-cbrt
18×difference-of-squares
13×distribute-lft-out
9×distribute-lft-out--
6×associate-/l*
5×add-cbrt-cube add-exp-log
4×pow1 associate-/r* associate-/r/
3×insert-posit16 add-log-exp
2×rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/
1×cbrt-undiv clear-num frac-2neg sqrt-pow1 flip3-- pow1/2 sqrt-div div-sub div-exp flip--
Counts
3 → 103
Calls
3 calls:
Slowest
34.0ms
(/ (- 1 x) (+ 1 x))
22.0ms
(sqrt (/ (- 1 x) (+ 1 x)))
1.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))

series142.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
69.0ms
(sqrt (/ (- 1 x) (+ 1 x)))
69.0ms
(/ (- 1 x) (+ 1 x))
4.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))

simplify3.7s

Counts
106 → 112
Calls
106 calls:
Slowest
526.0ms
(/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (+ 1 x) (+ 1 x)) (+ 1 x)))
272.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
243.0ms
(sqrt (/ (- 1 x) (+ (pow 1 3) (pow x 3))))
242.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
125.0ms
(- (+ (* 2 (pow x 2)) 1) (* 2 x))

prune1.0s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- 1 x))
0.0b
(/ (sqrt (- 1 x)) (sqrt (+ 1 x)))
0.0b
(sqrt (+ 1 x))
0.0b
(atan (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
98×sqrt-prod
91×*-un-lft-identity
71×add-sqr-sqrt
63×times-frac
42×add-cube-cbrt
18×difference-of-squares
11×distribute-lft-out
9×associate-/l* distribute-lft-out--
8×sqrt-div
7×associate-/r*
6×pow1 add-cbrt-cube add-exp-log
4×insert-posit16 add-log-exp
2×rem-sqrt-square sqrt-pow1 flip3-+ flip3-- pow1/2 associate-/r/ flip-+ flip-- associate-/l/
1×cbrt-undiv sqrt-undiv clear-num frac-2neg div-exp div-inv
Counts
4 → 141
Calls
4 calls:
Slowest
30.0ms
(/ (sqrt (- 1 x)) (sqrt (+ 1 x)))
15.0ms
(atan (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))
10.0ms
(sqrt (- 1 x))
8.0ms
(sqrt (+ 1 x))

series138.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
50.0ms
(/ (sqrt (- 1 x)) (sqrt (+ 1 x)))
49.0ms
(sqrt (- 1 x))
35.0ms
(sqrt (+ 1 x))
4.0ms
(atan (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))

simplify4.4s

Counts
178 → 153
Calls
178 calls:
Slowest
245.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
206.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
190.0ms
(/ (* (* (sqrt (- 1 x)) (sqrt (- 1 x))) (sqrt (- 1 x))) (* (* (sqrt (+ 1 x)) (sqrt (+ 1 x))) (sqrt (+ 1 x))))
160.0ms
(- 1 (+ (* 1/2 x) (* 1/8 (pow x 2))))
151.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))

prune1.6s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize71.0ms

Local error

Found 4 expressions with local error:

0.1b
(* x (* x x))
0.0b
(/ (sqrt (- 1 (* x (* x x)))) (* (sqrt (+ 1 x)) (sqrt (+ (* 1 1) (+ (* x x) (* 1 x))))))
0.0b
(* (sqrt (+ 1 x)) (sqrt (+ (* 1 1) (+ (* x x) (* 1 x)))))
0.0b
(atan (/ (sqrt (- 1 (* x (* x x)))) (* (sqrt (+ 1 x)) (sqrt (+ (* 1 1) (+ (* x x) (* 1 x)))))))

rewrite197.0ms

Algorithm
rewrite-expression-head
Rules
26×sqrt-div
22×add-sqr-sqrt pow1
18×sqrt-prod
16×*-un-lft-identity add-cbrt-cube add-exp-log
13×add-cube-cbrt
12×flip3-+ flip-+
10×associate-*l*
8×frac-times associate-*r* associate-/r/
6×times-frac pow-prod-down associate-/l*
5×prod-exp pow-prod-up cbrt-unprod unswap-sqr
4×associate-*l/ associate-*r/ insert-posit16 add-log-exp
2×cbrt-undiv sqrt-pow1 pow1/2 sqrt-unprod div-exp *-commutative distribute-lft-out associate-/l/
1×pow2 sqrt-undiv clear-num associate-/r* frac-2neg pow-plus flip3-- cube-unmult pow-sqr div-inv flip--
Counts
4 → 113
Calls
4 calls:
Slowest
117.0ms
(* (sqrt (+ 1 x)) (sqrt (+ (* 1 1) (+ (* x x) (* 1 x)))))
53.0ms
(/ (sqrt (- 1 (* x (* x x)))) (* (sqrt (+ 1 x)) (sqrt (+ (* 1 1) (+ (* x x) (* 1 x))))))
15.0ms
(* x (* x x))
11.0ms
(atan (/ (sqrt (- 1 (* x (* x x)))) (* (sqrt (+ 1 x)) (sqrt (+ (* 1 1) (+ (* x x) (* 1 x)))))))

series239.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
110.0ms
(/ (sqrt (- 1 (* x (* x x)))) (* (sqrt (+ 1 x)) (sqrt (+ (* 1 1) (+ (* x x) (* 1 x))))))
74.0ms
(* (sqrt (+ 1 x)) (sqrt (+ (* 1 1) (+ (* x x) (* 1 x)))))
45.0ms
(* x (* x x))
9.0ms
(atan (/ (sqrt (- 1 (* x (* x x)))) (* (sqrt (+ 1 x)) (sqrt (+ (* 1 1) (+ (* x x) (* 1 x)))))))

simplify13.2s

Counts
99 → 125
Calls
99 calls:
Slowest
552.0ms
(* (* (* x x) x) (* (* (* x x) (* x x)) (* x x)))
491.0ms
(* (* (* x x) x) (* (* (* x x) x) (* (* x x) x)))
440.0ms
(* (+ 1 x) (+ (* 1 1) (+ (* x x) (* 1 x))))
396.0ms
(* (+ 1 x) (+ (* 1 1) (+ (* x x) (* 1 x))))
375.0ms
(/ (- 1 (* x (* x x))) (* (+ 1 x) (+ (* 1 1) (+ (* x x) (* 1 x)))))

prune2.2s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes127.0ms

Accuracy

0% (0.0b remaining)

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

bsearch7.0ms

end0.0ms

sample1.9s

Algorithm
intervals
Results
892.0ms8000×body80valid
855.0ms8057×body80nan