Details

Time bar (total: 24.8s)

sample150.0ms

Algorithm
intervals
Results
35.0ms256×body80valid
31.0ms239×body80nan

simplify84.0ms

Calls
1 calls:
Slowest
40.0ms
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 3 expressions with local error:

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

series55.0ms

Calls
3 calls:
Slowest
26.0ms
(/ (- 1 x) (+ 1 x))
25.0ms
(sqrt (/ (- 1 x) (+ 1 x)))
4.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))

simplify2.2s

Calls
57 calls:
Slowest
263.0ms
(/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (+ 1 x) (+ 1 x)) (+ 1 x)))
235.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (+ (/ 1 (* (pow x 2) (sqrt -1))) (* 1/2 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))))
190.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (+ (/ 1 (* (pow x 2) (sqrt -1))) (* 1/2 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))))
152.0ms
(- (* 2 (/ 1 x)) (+ (* 2 (/ 1 (pow x 2))) 1))
120.0ms
(- (* 2 (/ 1 x)) (+ (* 2 (/ 1 (pow x 2))) 1))

prune722.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
12×add-sqr-sqrt associate-/r/
10×sqrt-prod div-inv
8×distribute-rgt-out--
7×add-cube-cbrt
6×associate-/r* flip3-+ flip-+ add-log-exp
5×pow1 add-exp-log
4×add-cbrt-cube sqrt-div insert-posit16 distribute-lft-out--
2×clear-num frac-2neg flip3-- frac-sub flip-- sub-div difference-of-squares
1×rem-sqrt-square rec-exp sub-neg pow1/2 diff-log pow-flip inv-pow
Calls
4 calls:
Slowest
14.0ms
(sqrt (- (/ 1 (+ 1 x)) (/ x (+ 1 x))))
6.0ms
(- (/ 1 (+ 1 x)) (/ x (+ 1 x)))
5.0ms
(/ 1 (+ 1 x))
1.0ms
(/ x (+ 1 x))

series93.0ms

Calls
4 calls:
Slowest
41.0ms
(sqrt (- (/ 1 (+ 1 x)) (/ x (+ 1 x))))
25.0ms
(- (/ 1 (+ 1 x)) (/ x (+ 1 x)))
16.0ms
(/ x (+ 1 x))
10.0ms
(/ 1 (+ 1 x))

simplify4.0s

Calls
55 calls:
Slowest
602.0ms
(- (* 1 (+ 1 x)) (* (+ 1 x) x))
588.0ms
(sqrt (- (* 1 (+ 1 x)) (* (+ 1 x) x)))
496.0ms
(sqrt (- (* (/ 1 (+ 1 x)) (/ 1 (+ 1 x))) (* (/ x (+ 1 x)) (/ x (+ 1 x)))))
371.0ms
(sqrt (- (pow (/ 1 (+ 1 x)) 3) (pow (/ x (+ 1 x)) 3)))
206.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (+ (/ 1 (* (pow x 2) (sqrt -1))) (* 1/2 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))))

prune791.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
23×add-sqr-sqrt *-un-lft-identity add-cube-cbrt sqrt-prod
18×flip3-+ sqrt-div flip-+
12×frac-times
9×pow1
8×add-cbrt-cube add-exp-log associate-/r/
6×associate-*l/ associate-*r/ associate-/l*
4×associate-/r* insert-posit16 add-log-exp
3×associate-*r* associate-*l*
2×associate-/l/
1×pow2 distribute-rgt-in cbrt-undiv rem-sqrt-square sqrt-undiv clear-num frac-2neg distribute-lft-in pow-plus flip3-- pow1/2 div-exp pow-prod-down prod-exp *-commutative pow-prod-up cbrt-unprod div-inv flip--
Calls
4 calls:
Slowest
11.0ms
(/ (sqrt (- 1 (* x x))) (sqrt (* (+ 1 x) (+ 1 x))))
4.0ms
(* (+ 1 x) (+ 1 x))
3.0ms
(atan (/ (sqrt (- 1 (* x x))) (sqrt (* (+ 1 x) (+ 1 x)))))
2.0ms
(sqrt (* (+ 1 x) (+ 1 x)))

series56.0ms

Calls
4 calls:
Slowest
27.0ms
(/ (sqrt (- 1 (* x x))) (sqrt (* (+ 1 x) (+ 1 x))))
15.0ms
(sqrt (* (+ 1 x) (+ 1 x)))
9.0ms
(* (+ 1 x) (+ 1 x))
5.0ms
(atan (/ (sqrt (- 1 (* x x))) (sqrt (* (+ 1 x) (+ 1 x)))))

simplify13.1s

Calls
117 calls:
Slowest
450.0ms
(sqrt (* (- (* 1 1) (* x x)) (+ 1 x)))
438.0ms
(* (+ (pow 1 3) (pow x 3)) (- (* 1 1) (* x x)))
426.0ms
(* (- (* 1 1) (* x x)) (+ 1 x))
421.0ms
(- (log (sqrt (- 1 (* x x)))) (log (sqrt (* (+ 1 x) (+ 1 x)))))
377.0ms
(* (- (* 1 1) (* x x)) (+ (pow 1 3) (pow x 3)))

prune1.3s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes22.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample1.9s

Algorithm
intervals
Results
924.0ms8000×body80valid
785.0ms7904×body80nan