Details

Time bar (total: 29.9s)

sample674.0ms

Algorithm
intervals
Results
37.0ms256×body80valid
26.0ms257×body80nan

simplify62.0ms

Calls
1 calls:
Slowest
61.0ms
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

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))))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×times-frac
18×*-un-lft-identity add-cube-cbrt
15×sqrt-prod
5×add-cbrt-cube add-exp-log
4×associate-/r/
3×pow1 associate-/r* insert-posit16 associate-/l* add-log-exp
2×rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/
1×cbrt-undiv clear-num frac-2neg flip3-- pow1/2 sqrt-div div-sub div-exp flip--
Calls
3 calls:
Slowest
5.0ms
(/ (- 1 x) (+ 1 x))
2.0ms
(sqrt (/ (- 1 x) (+ 1 x)))
1.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))

series93.0ms

Calls
3 calls:
Slowest
56.0ms
(sqrt (/ (- 1 x) (+ 1 x)))
31.0ms
(/ (- 1 x) (+ 1 x))
6.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))

simplify2.5s

Calls
57 calls:
Slowest
321.0ms
(/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (+ 1 x) (+ 1 x)) (+ 1 x)))
292.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
281.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
153.0ms
(- (* 2 (/ 1 x)) (+ (* 2 (/ 1 (pow x 2))) 1))
151.0ms
(- (* 2 (/ 1 x)) (+ (* 2 (/ 1 (pow x 2))) 1))

prune653.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
48×sqrt-prod
36×add-sqr-sqrt times-frac
34×*-un-lft-identity add-cube-cbrt
8×sqrt-div
6×associate-/r* add-cbrt-cube add-exp-log associate-/l*
4×pow1 insert-posit16 add-log-exp
2×rem-sqrt-square flip3-+ flip3-- pow1/2 associate-/r/ flip-+ flip-- associate-/l/
1×cbrt-undiv sqrt-undiv clear-num frac-2neg div-exp div-inv
Calls
4 calls:
Slowest
10.0ms
(/ (sqrt (- 1 x)) (sqrt (+ 1 x)))
7.0ms
(atan (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))
1.0ms
(sqrt (- 1 x))
1.0ms
(sqrt (+ 1 x))

series122.0ms

Calls
4 calls:
Slowest
53.0ms
(/ (sqrt (- 1 x)) (sqrt (+ 1 x)))
37.0ms
(sqrt (+ 1 x))
28.0ms
(sqrt (- 1 x))
4.0ms
(atan (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))

simplify3.2s

Calls
114 calls:
Slowest
312.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
223.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
173.0ms
(/ (* (* (sqrt (- 1 x)) (sqrt (- 1 x))) (sqrt (- 1 x))) (* (* (sqrt (+ 1 x)) (sqrt (+ 1 x))) (sqrt (+ 1 x))))
168.0ms
(- 1 (+ (* 1/2 x) (* 1/8 (pow x 2))))
110.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))

prune1.1s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (sqrt (- 1 x)) (sqrt (- 1 x)))
0.0b
(/ (cbrt (* (* (sqrt (- 1 x)) (sqrt (- 1 x))) (sqrt (- 1 x)))) (sqrt (+ 1 x)))
0.0b
(cbrt (* (* (sqrt (- 1 x)) (sqrt (- 1 x))) (sqrt (- 1 x))))
0.0b
(* (* (sqrt (- 1 x)) (sqrt (- 1 x))) (sqrt (- 1 x)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
176×sqrt-div
88×frac-times
87×flip3-- flip--
52×cbrt-div
44×associate-*l/
27×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
26×associate-*r/ associate-/l/
24×times-frac sqrt-prod
23×pow1
13×add-exp-log
12×add-cbrt-cube associate-*r*
10×pow1/2
9×pow-prod-up
8×cbrt-prod
7×associate-*l* pow-prod-down
6×associate-/r* pow-plus
4×prod-exp cbrt-unprod insert-posit16 associate-/l* add-log-exp
3×pow2 sqrt-unprod
2×pow3 associate-/r/ *-commutative
1×cbrt-undiv clear-num rem-square-sqrt frac-2neg flip3-+ pow1/3 div-exp rem-cbrt-cube flip-+ div-inv
Calls
4 calls:
Slowest
34.0ms
(* (* (sqrt (- 1 x)) (sqrt (- 1 x))) (sqrt (- 1 x)))
21.0ms
(cbrt (* (* (sqrt (- 1 x)) (sqrt (- 1 x))) (sqrt (- 1 x))))
10.0ms
(/ (cbrt (* (* (sqrt (- 1 x)) (sqrt (- 1 x))) (sqrt (- 1 x)))) (sqrt (+ 1 x)))
7.0ms
(* (sqrt (- 1 x)) (sqrt (- 1 x)))

series174.0ms

Calls
4 calls:
Slowest
72.0ms
(/ (cbrt (* (* (sqrt (- 1 x)) (sqrt (- 1 x))) (sqrt (- 1 x)))) (sqrt (+ 1 x)))
55.0ms
(* (* (sqrt (- 1 x)) (sqrt (- 1 x))) (sqrt (- 1 x)))
27.0ms
(cbrt (* (* (sqrt (- 1 x)) (sqrt (- 1 x))) (sqrt (- 1 x))))
21.0ms
(* (sqrt (- 1 x)) (sqrt (- 1 x)))

simplify16.0s

Calls
229 calls:
Slowest
361.0ms
(* (* (* (sqrt (- 1 x)) (sqrt (- 1 x))) (sqrt (- 1 x))) (* (* (sqrt (- 1 x)) (sqrt (- 1 x))) (sqrt (- 1 x))))
266.0ms
(* (* (* (* (sqrt (- 1 x)) (sqrt (- 1 x))) (* (sqrt (- 1 x)) (sqrt (- 1 x)))) (* (sqrt (- 1 x)) (sqrt (- 1 x)))) (* (* (sqrt (- 1 x)) (sqrt (- 1 x))) (sqrt (- 1 x))))
246.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
239.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
214.0ms
(* (* (sqrt (- (pow 1 3) (pow x 3))) (sqrt (- (pow 1 3) (pow x 3)))) (sqrt (- 1 x)))

prune2.6s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes116.0ms

Accuracy

0% (0.0b remaining)

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

bsearch5.0ms

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.4s8000×body80valid
765.0ms8010×body80nan