Details

Time bar (total: 19.9s)

sample240.0ms

Algorithm
intervals
Results
23.0ms256×body80valid
16.0ms240×body80nan

simplify70.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
69.0ms
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

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))))

rewrite38.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u 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 → 109
Calls
3 calls:
Slowest
17.0ms
(/ (- 1 x) (+ 1 x))
14.0ms
(sqrt (/ (- 1 x) (+ 1 x)))
1.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))

series124.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
64.0ms
(/ (- 1 x) (+ 1 x))
52.0ms
(sqrt (/ (- 1 x) (+ 1 x)))
7.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))

simplify3.8s

Counts
106 → 118
Calls
106 calls:
Slowest
559.0ms
(/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (+ 1 x) (+ 1 x)) (+ 1 x)))
277.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
258.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
161.0ms
(- (* 2 (/ 1 x)) (+ (* 2 (/ 1 (pow x 2))) 1))
136.0ms
(sqrt (/ (- 1 x) (+ (pow 1 3) (pow x 3))))

prune1.0s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b
(expm1 (log1p (/ (- 1 x) (+ 1 x))))
0.0b
(/ (- 1 x) (+ 1 x))
0.0b
(sqrt (expm1 (log1p (/ (- 1 x) (+ 1 x)))))
0.0b
(atan (sqrt (expm1 (log1p (/ (- 1 x) (+ 1 x))))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
46×*-un-lft-identity
33×add-sqr-sqrt
24×times-frac
17×add-cube-cbrt
10×difference-of-squares
7×distribute-lft-out
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×expm1-log1p-u associate-/r* insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-prod
2×associate-/r/ associate-/l/
1×cbrt-undiv rem-sqrt-square expm1-log1p clear-num frac-2neg sqrt-pow1 flip3-+ flip3-- pow1/2 div-sub div-exp flip-+ div-inv flip-- expm1-udef
Counts
4 → 92
Calls
4 calls:
Slowest
31.0ms
(/ (- 1 x) (+ 1 x))
6.0ms
(atan (sqrt (expm1 (log1p (/ (- 1 x) (+ 1 x))))))
2.0ms
(sqrt (expm1 (log1p (/ (- 1 x) (+ 1 x)))))
1.0ms
(expm1 (log1p (/ (- 1 x) (+ 1 x))))

series290.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
171.0ms
(sqrt (expm1 (log1p (/ (- 1 x) (+ 1 x)))))
73.0ms
(expm1 (log1p (/ (- 1 x) (+ 1 x))))
41.0ms
(/ (- 1 x) (+ 1 x))
4.0ms
(atan (sqrt (expm1 (log1p (/ (- 1 x) (+ 1 x))))))

simplify4.0s

Counts
81 → 104
Calls
81 calls:
Slowest
479.0ms
(/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (+ 1 x) (+ 1 x)) (+ 1 x)))
400.0ms
(- (+ (exp (+ (log -2) (log (/ -1 x)))) (/ (exp (+ (log -2) (log (/ -1 x)))) (pow x 2))) (+ (/ (exp (+ (log -2) (log (/ -1 x)))) x) 1))
394.0ms
(- (+ (* 1/2 (* (/ (exp (+ (log -2) (log (/ -1 x)))) (pow x 2)) (sqrt (/ 1 (- (exp (+ (log -2) (log (/ -1 x)))) 1))))) (sqrt (- (exp (+ (log -2) (log (/ -1 x)))) 1))) (+ (* 1/8 (* (/ (pow (exp (+ (log -2) (log (/ -1 x)))) 2) (pow x 2)) (sqrt (/ 1 (pow (- (exp (+ (log -2) (log (/ -1 x)))) 1) 3))))) (* 1/2 (* (/ (exp (+ (log -2) (log (/ -1 x)))) x) (sqrt (/ 1 (- (exp (+ (log -2) (log (/ -1 x)))) 1)))))))
324.0ms
(- (+ (* 1/2 (* (/ (exp (+ (log 2) (log (/ 1 x)))) (pow x 2)) (sqrt (/ 1 (- (exp (+ (log 2) (log (/ 1 x)))) 1))))) (sqrt (- (exp (+ (log 2) (log (/ 1 x)))) 1))) (+ (* 1/2 (* (/ (exp (+ (log 2) (log (/ 1 x)))) x) (sqrt (/ 1 (- (exp (+ (log 2) (log (/ 1 x)))) 1))))) (* 1/8 (* (/ (pow (exp (+ (log 2) (log (/ 1 x)))) 2) (pow x 2)) (sqrt (/ 1 (pow (- (exp (+ (log 2) (log (/ 1 x)))) 1) 3)))))))
321.0ms
(- (+ (/ (exp (+ (log 2) (log (/ 1 x)))) (pow x 2)) (exp (+ (log 2) (log (/ 1 x))))) (+ (/ (exp (+ (log 2) (log (/ 1 x)))) x) 1))

prune1.1s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize38.0ms

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))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
98×sqrt-prod
92×*-un-lft-identity
75×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×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 flip3-+ flip3-- pow1/2 associate-/r/ flip-+ hypot-def flip-- associate-/l/
1×cbrt-undiv sqrt-undiv clear-num frac-2neg div-exp hypot-1-def div-inv
Counts
4 → 152
Calls
4 calls:
Slowest
29.0ms
(/ (sqrt (- 1 x)) (sqrt (+ 1 x)))
15.0ms
(atan (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))
13.0ms
(sqrt (- 1 x))
9.0ms
(sqrt (+ 1 x))

series130.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
63.0ms
(/ (sqrt (- 1 x)) (sqrt (+ 1 x)))
36.0ms
(sqrt (- 1 x))
28.0ms
(sqrt (+ 1 x))
3.0ms
(atan (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))

simplify5.2s

Counts
179 → 164
Calls
179 calls:
Slowest
431.0ms
(/ (sqrt (sqrt (- 1 x))) (sqrt (sqrt (+ 1 x))))
292.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
277.0ms
(- 1 (+ (* 1/2 x) (* 1/8 (pow x 2))))
246.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
224.0ms
(/ (* (* (sqrt (- 1 x)) (sqrt (- 1 x))) (sqrt (- 1 x))) (* (* (sqrt (+ 1 x)) (sqrt (+ 1 x))) (sqrt (+ 1 x))))

prune1.5s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes54.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample2.1s

Algorithm
intervals
Results
964.0ms8060×body80nan
919.0ms8000×body80valid