Details

Time bar (total: 28.0s)

sample123.0ms

Algorithm
intervals
Results
23.0ms256×body80valid
15.0ms240×body80nan

simplify62.0ms

Counts
1 → 1
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

localize20.0ms

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))))

rewrite37.0ms

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
16.0ms
(/ (- 1 x) (+ 1 x))
9.0ms
(sqrt (/ (- 1 x) (+ 1 x)))
1.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))

series79.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
45.0ms
(sqrt (/ (- 1 x) (+ 1 x)))
31.0ms
(/ (- 1 x) (+ 1 x))
4.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))

simplify3.4s

Counts
106 → 112
Calls
106 calls:
Slowest
388.0ms
(/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (+ 1 x) (+ 1 x)) (+ 1 x)))
281.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
196.0ms
(sqrt (/ (- 1 x) (+ (pow 1 3) (pow x 3))))
163.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
109.0ms
(- (* 2 (/ 1 x)) (+ (* 2 (/ 1 (pow x 2))) 1))

prune1.0s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize60.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (/ (- 1 x) (+ (pow 1 3) (pow x 3))) (+ (- (* x x) x) 1))
0.0b
(sqrt (* (/ (- 1 x) (+ (pow 1 3) (pow x 3))) (+ (- (* x x) x) 1)))
0.0b
(atan (sqrt (* (/ (- 1 x) (+ (pow 1 3) (pow x 3))) (+ (- (* x x) x) 1))))

rewrite205.0ms

Algorithm
rewrite-expression-head
Rules
119×*-un-lft-identity
66×associate-*l*
61×times-frac
56×add-sqr-sqrt
37×distribute-lft-out
24×unpow-prod-down cube-prod
21×add-cube-cbrt
20×difference-of-squares
10×distribute-lft-out--
8×pow1 add-cbrt-cube add-exp-log
6×cube-mult sum-cubes
5×flip3-+ sqrt-div flip-+
4×frac-times associate-*r* associate-*r/
3×insert-posit16 add-log-exp
2×sqrt-pow1 pow-prod-down associate-*l/ prod-exp associate-/r/ cbrt-unprod unswap-sqr
1×distribute-rgt-in cbrt-undiv distribute-lft-in pow1/2 div-exp *-commutative sqrt-prod div-inv
Counts
3 → 118
Calls
3 calls:
Slowest
133.0ms
(* (/ (- 1 x) (+ (pow 1 3) (pow x 3))) (+ (- (* x x) x) 1))
65.0ms
(sqrt (* (/ (- 1 x) (+ (pow 1 3) (pow x 3))) (+ (- (* x x) x) 1)))
1.0ms
(atan (sqrt (* (/ (- 1 x) (+ (pow 1 3) (pow x 3))) (+ (- (* x x) x) 1))))

series201.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
125.0ms
(sqrt (* (/ (- 1 x) (+ (pow 1 3) (pow x 3))) (+ (- (* x x) x) 1)))
67.0ms
(* (/ (- 1 x) (+ (pow 1 3) (pow x 3))) (+ (- (* x x) x) 1))
9.0ms
(atan (sqrt (* (/ (- 1 x) (+ (pow 1 3) (pow x 3))) (+ (- (* x x) x) 1))))

simplify12.6s

Counts
104 → 127
Calls
104 calls:
Slowest
624.0ms
(* (/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (+ (pow 1 3) (pow x 3)) (+ (pow 1 3) (pow x 3))) (+ (pow 1 3) (pow x 3)))) (* (* (+ (- (* x x) x) 1) (+ (- (* x x) x) 1)) (+ (- (* x x) x) 1)))
530.0ms
(* (- 1 x) (+ (pow (- (* x x) x) 3) (pow 1 3)))
515.0ms
(sqrt (* (- 1 x) (+ (pow (- (* x x) x) 3) (pow 1 3))))
445.0ms
(* (* (* (/ (- 1 x) (+ (pow 1 3) (pow x 3))) (/ (- 1 x) (+ (pow 1 3) (pow x 3)))) (/ (- 1 x) (+ (pow 1 3) (pow x 3)))) (* (* (+ (- (* x x) x) 1) (+ (- (* x x) x) 1)) (+ (- (* x x) x) 1)))
329.0ms
(* (/ (- 1 x) (+ (pow 1 3) (pow x 3))) (+ (- (* x x) x) 1))

prune1.6s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

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
18.0ms
(/ (sqrt (- 1 x)) (sqrt (+ 1 x)))
10.0ms
(atan (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))
5.0ms
(sqrt (- 1 x))
4.0ms
(sqrt (+ 1 x))

series146.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
66.0ms
(/ (sqrt (- 1 x)) (sqrt (+ 1 x)))
42.0ms
(sqrt (- 1 x))
34.0ms
(sqrt (+ 1 x))
4.0ms
(atan (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))

simplify4.2s

Counts
178 → 153
Calls
178 calls:
Slowest
225.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
216.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
179.0ms
(- 1 (+ (* 1/2 x) (* 1/8 (pow x 2))))
165.0ms
(/ (* (* (sqrt (- 1 x)) (sqrt (- 1 x))) (sqrt (- 1 x))) (* (* (sqrt (+ 1 x)) (sqrt (+ 1 x))) (sqrt (+ 1 x))))
102.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))

prune2.1s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes40.0ms

Accuracy

0% (0.0b remaining)

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

bsearch3.0ms

end0.0ms

sample2.1s

Algorithm
intervals
Results
967.0ms8000×body80valid
811.0ms8060×body80nan