Details

Time bar (total: 44.8s)

sample142.0ms

Algorithm
intervals
Results
29.0ms256×body80valid
21.0ms249×body80nan

simplify45.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
44.0ms
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))

prune19.0ms

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

rewrite32.0ms

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
19.0ms
(/ (- 1 x) (+ 1 x))
10.0ms
(sqrt (/ (- 1 x) (+ 1 x)))
1.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))

series128.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
73.0ms
(sqrt (/ (- 1 x) (+ 1 x)))
47.0ms
(/ (- 1 x) (+ 1 x))
8.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))

simplify3.7s

Counts
106 → 112
Calls
106 calls:
Slowest
404.0ms
(/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (+ 1 x) (+ 1 x)) (+ 1 x)))
317.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
263.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
210.0ms
(sqrt (/ (- 1 x) (+ (pow 1 3) (pow x 3))))
121.0ms
(- (* 2 (/ 1 x)) (+ (* 2 (/ 1 (pow x 2))) 1))

prune985.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
199×sqrt-prod
179×add-sqr-sqrt
153×*-un-lft-identity
133×times-frac
64×add-cube-cbrt
51×associate-*r*
30×associate-*l* difference-of-squares
24×unswap-sqr
18×distribute-lft-out
15×distribute-lft-out--
14×sqrt-div
10×pow1
8×add-cbrt-cube add-exp-log
7×associate-/r*
6×associate-/r/ associate-/l*
5×flip3-+ flip-+
4×sqrt-pow1 pow1/2 insert-posit16 add-log-exp
3×pow-prod-down div-inv
2×rem-sqrt-square associate-/l/
1×frac-times cbrt-undiv clear-num frac-2neg flip3-- sqrt-unprod div-sub div-exp associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod flip--
Counts
4 → 230
Calls
4 calls:
Slowest
56.0ms
(* (sqrt (/ 1 (sqrt (+ 1 x)))) (sqrt (/ (- 1 x) (sqrt (+ 1 x)))))
26.0ms
(/ (- 1 x) (sqrt (+ 1 x)))
4.0ms
(sqrt (+ 1 x))
4.0ms
(sqrt (+ 1 x))

series209.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
62.0ms
(/ (- 1 x) (sqrt (+ 1 x)))
61.0ms
(* (sqrt (/ 1 (sqrt (+ 1 x)))) (sqrt (/ (- 1 x) (sqrt (+ 1 x)))))
45.0ms
(sqrt (+ 1 x))
41.0ms
(sqrt (+ 1 x))

simplify9.4s

Counts
269 → 242
Calls
269 calls:
Slowest
298.0ms
(/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (sqrt (+ 1 x)) (sqrt (+ 1 x))) (sqrt (+ 1 x))))
290.0ms
(* (* (* (sqrt (/ 1 (sqrt (+ 1 x)))) (sqrt (/ 1 (sqrt (+ 1 x))))) (sqrt (/ 1 (sqrt (+ 1 x))))) (* (* (sqrt (/ (- 1 x) (sqrt (+ 1 x)))) (sqrt (/ (- 1 x) (sqrt (+ 1 x))))) (sqrt (/ (- 1 x) (sqrt (+ 1 x))))))
282.0ms
(* (/ 1 (sqrt (+ 1 x))) (/ (- 1 x) (sqrt (+ 1 x))))
256.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
252.0ms
(* (/ 1 (sqrt (+ 1 x))) (/ (- 1 x) (sqrt (+ 1 x))))

prune3.0s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite50.0ms

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
23.0ms
(/ (sqrt (- 1 x)) (sqrt (+ 1 x)))
10.0ms
(sqrt (- 1 x))
7.0ms
(atan (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))
4.0ms
(sqrt (+ 1 x))

series135.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
51.0ms
(/ (sqrt (- 1 x)) (sqrt (+ 1 x)))
41.0ms
(sqrt (+ 1 x))
39.0ms
(sqrt (- 1 x))
4.0ms
(atan (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))

simplify4.7s

Counts
178 → 153
Calls
178 calls:
Slowest
284.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
264.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
202.0ms
(/ (* (* (sqrt (- 1 x)) (sqrt (- 1 x))) (sqrt (- 1 x))) (* (* (sqrt (+ 1 x)) (sqrt (+ 1 x))) (sqrt (+ 1 x))))
196.0ms
(- 1 (+ (* 1/2 x) (* 1/8 (pow x 2))))
143.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))

prune1.5s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
365×*-un-lft-identity
270×cbrt-prod
222×times-frac
213×add-sqr-sqrt
93×add-cube-cbrt
64×difference-of-squares
62×distribute-lft-out
57×swap-sqr
44×distribute-lft-out--
33×associate-*r* associate-*l*
14×associate-/r/
11×pow1
9×pow1/3 unswap-sqr
7×cbrt-div flip3-+ flip-+ div-inv
6×add-exp-log
4×add-cbrt-cube insert-posit16 add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 frac-times pow-plus associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod
Counts
4 → 274
Calls
4 calls:
Slowest
56.0ms
(* (cbrt (/ (- 1 x) (+ 1 x))) (cbrt (/ (- 1 x) (+ 1 x))))
19.0ms
(cbrt (/ (- 1 x) (+ 1 x)))
10.0ms
(cbrt (/ (- 1 x) (+ 1 x)))
10.0ms
(cbrt (/ (- 1 x) (+ 1 x)))

series364.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
111.0ms
(cbrt (/ (- 1 x) (+ 1 x)))
93.0ms
(cbrt (/ (- 1 x) (+ 1 x)))
89.0ms
(cbrt (/ (- 1 x) (+ 1 x)))
71.0ms
(* (cbrt (/ (- 1 x) (+ 1 x))) (cbrt (/ (- 1 x) (+ 1 x))))

simplify14.0s

Counts
319 → 286
Calls
319 calls:
Slowest
892.0ms
(- (+ (* 2/9 (* (/ 1 (pow x 2)) (pow -1 1/3))) (pow -1 1/3)) (* 2/3 (* (/ 1 x) (pow -1 1/3))))
590.0ms
(- (+ (* 2/9 (* (/ 1 (pow x 2)) (pow -1 1/3))) (pow -1 1/3)) (* 2/3 (* (/ 1 x) (pow -1 1/3))))
538.0ms
(- (+ (* 2/9 (* (/ 1 (pow x 2)) (pow -1 1/3))) (pow -1 1/3)) (* 2/3 (* (/ 1 x) (pow -1 1/3))))
522.0ms
(- (+ (* 2/9 (* (/ 1 (pow x 2)) (pow -1 1/3))) (pow -1 1/3)) (* 2/3 (* (/ 1 x) (pow -1 1/3))))
515.0ms
(- (+ (* 2/9 (* (/ 1 (pow x 2)) (pow -1 1/3))) (pow -1 1/3)) (* 2/3 (* (/ 1 x) (pow -1 1/3))))

prune3.9s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes74.0ms

Accuracy

0% (0.0b remaining)

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

bsearch3.0ms

end0.0ms

sample2.0s

Algorithm
intervals
Results
978.0ms8000×body80valid
795.0ms7941×body80nan