Details

Time bar (total: 35.8s)

sample205.0ms

Algorithm
intervals
Results
85.0ms283×body80nan
37.0ms256×body80valid

simplify73.0ms

Calls
1 calls:
Slowest
72.0ms
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize516.0ms

Local error

Found 3 expressions with local error:

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

rewrite18.0ms

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×expm1-log1p-u pow1 associate-/r* insert-posit16 log1p-expm1-u 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
7.0ms
(sqrt (/ (- 1 x) (+ 1 x)))
7.0ms
(/ (- 1 x) (+ 1 x))
1.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))

series85.0ms

Calls
3 calls:
Slowest
59.0ms
(sqrt (/ (- 1 x) (+ 1 x)))
20.0ms
(/ (- 1 x) (+ 1 x))
7.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))

simplify2.4s

Calls
57 calls:
Slowest
397.0ms
(/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (+ 1 x) (+ 1 x)) (+ 1 x)))
213.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (+ (/ 1 (* (pow x 2) (sqrt -1))) (* 1/2 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))))
173.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (+ (/ 1 (* (pow x 2) (sqrt -1))) (* 1/2 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))))
163.0ms
(- (* 2 (/ 1 x)) (+ (* 2 (/ 1 (pow x 2))) 1))
109.0ms
(- (* 2 (/ 1 x)) (+ (* 2 (/ 1 (pow x 2))) 1))

prune789.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
23×*-un-lft-identity add-cube-cbrt
21×sqrt-prod
18×times-frac
12×associate-/r*
8×sqrt-div
7×add-exp-log
6×add-cbrt-cube
5×pow1
4×expm1-log1p-u flip3-+ associate-/r/ flip-+ insert-posit16 log1p-expm1-u add-log-exp
3×pow1/2 associate-/l*
2×rem-sqrt-square clear-num frac-2neg div-inv pow-flip associate-/l/
1×cbrt-undiv rec-exp flip3-- div-sub div-exp flip-- inv-pow
Calls
4 calls:
Slowest
4.0ms
(/ (- 1 x) (sqrt (+ 1 x)))
2.0ms
(/ 1 (sqrt (+ 1 x)))
1.0ms
(sqrt (+ 1 x))
1.0ms
(sqrt (+ 1 x))

series70.0ms

Calls
4 calls:
Slowest
30.0ms
(/ (- 1 x) (sqrt (+ 1 x)))
17.0ms
(sqrt (+ 1 x))
12.0ms
(/ 1 (sqrt (+ 1 x)))
11.0ms
(sqrt (+ 1 x))

simplify2.4s

Calls
85 calls:
Slowest
287.0ms
(/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (sqrt (+ 1 x)) (sqrt (+ 1 x))) (sqrt (+ 1 x))))
133.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
133.0ms
(- (+ (* 7/8 (pow x 2)) 1) (* 3/2 x))
120.0ms
(sqrt (+ (* 1 1) (- (* x x) (* 1 x))))
96.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))

prune1.3s

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

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
57×add-cbrt-cube add-exp-log
30×associate-*r*
27×add-sqr-sqrt times-frac
26×*-un-lft-identity add-cube-cbrt
23×pow1
22×prod-exp cbrt-unprod
17×cbrt-undiv div-exp
16×frac-times associate-*l* associate-*l/
14×cbrt-div
10×associate-*r/
7×sqrt-div
6×pow-plus associate-/r/ pow-prod-up
4×expm1-log1p-u pow-prod-down sqrt-prod insert-posit16 log1p-expm1-u add-log-exp
3×pow2 flip3-+ flip-+ div-inv
2×cbrt-prod pow3 *-commutative
1×rem-sqrt-square pow1/2 pow1/3 rem-cbrt-cube
Calls
4 calls:
Slowest
32.0ms
(* (* (/ (- 1 x) (+ x 1)) (/ (- 1 x) (+ x 1))) (/ (- 1 x) (+ x 1)))
32.0ms
(cbrt (* (* (/ (- 1 x) (+ x 1)) (/ (- 1 x) (+ x 1))) (/ (- 1 x) (+ x 1))))
19.0ms
(* (/ (- 1 x) (+ x 1)) (/ (- 1 x) (+ x 1)))
6.0ms
(sqrt (cbrt (* (* (/ (- 1 x) (+ x 1)) (/ (- 1 x) (+ x 1))) (/ (- 1 x) (+ x 1)))))

series91.0ms

Calls
4 calls:
Slowest
42.0ms
(sqrt (cbrt (* (* (/ (- 1 x) (+ x 1)) (/ (- 1 x) (+ x 1))) (/ (- 1 x) (+ x 1)))))
22.0ms
(* (* (/ (- 1 x) (+ x 1)) (/ (- 1 x) (+ x 1))) (/ (- 1 x) (+ x 1)))
16.0ms
(* (/ (- 1 x) (+ x 1)) (/ (- 1 x) (+ x 1)))
10.0ms
(cbrt (* (* (/ (- 1 x) (+ x 1)) (/ (- 1 x) (+ x 1))) (/ (- 1 x) (+ x 1))))

simplify23.3s

Calls
136 calls:
Slowest
843.0ms
(cbrt (* (* (- 1 x) (- 1 x)) (/ (- 1 x) (+ x 1))))
821.0ms
(* (* (* (/ (- 1 x) (+ x 1)) (/ (- 1 x) (+ x 1))) (/ (- 1 x) (+ x 1))) (* (* (/ (- 1 x) (+ x 1)) (/ (- 1 x) (+ x 1))) (/ (- 1 x) (+ x 1))))
768.0ms
(sqrt (cbrt (* (* (- 1 x) (- 1 x)) (/ (- 1 x) (+ x 1)))))
729.0ms
(* (* (- 1 x) (- 1 x)) (/ (- 1 x) (+ x 1)))
667.0ms
(* (* (* (* (/ (- 1 x) (+ x 1)) (/ (- 1 x) (+ x 1))) (/ (- 1 x) (+ x 1))) (/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (+ x 1) (+ x 1)) (+ x 1)))) (/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (+ x 1) (+ x 1)) (+ x 1))))

prune2.2s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes29.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample2.0s

Algorithm
intervals
Results
974.0ms8000×body80valid
836.0ms8022×body80nan