Details

Time bar (total: 25.9s)

sample127.0ms

Algorithm
intervals
Results
18.0ms256×body80valid
15.0ms241×body80nan

simplify58.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
57.0ms
(* 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)))

rewrite30.0ms

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

series115.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
70.0ms
(sqrt (/ (- 1 x) (+ 1 x)))
41.0ms
(/ (- 1 x) (+ 1 x))
4.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))

simplify7.2s

Counts
172 → 118
Calls
172 calls:
Slowest
689.0ms
(* (+ 1 x) (+ (* 1 1) (+ (* x x) (* 1 x))))
464.0ms
(/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (+ 1 x) (+ 1 x)) (+ 1 x)))
298.0ms
(* (* (/ (- 1 x) (+ 1 x)) (/ (- 1 x) (+ 1 x))) (/ (- 1 x) (+ 1 x)))
266.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
257.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))

prune1.2s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

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
22.0ms
(/ (- 1 x) (+ 1 x))
1.0ms
(sqrt (expm1 (log1p (/ (- 1 x) (+ 1 x)))))
1.0ms
(atan (sqrt (expm1 (log1p (/ (- 1 x) (+ 1 x))))))
0.0ms
(expm1 (log1p (/ (- 1 x) (+ 1 x))))

series253.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
134.0ms
(sqrt (expm1 (log1p (/ (- 1 x) (+ 1 x)))))
88.0ms
(expm1 (log1p (/ (- 1 x) (+ 1 x))))
28.0ms
(/ (- 1 x) (+ 1 x))
2.0ms
(atan (sqrt (expm1 (log1p (/ (- 1 x) (+ 1 x))))))

simplify7.4s

Counts
130 → 104
Calls
130 calls:
Slowest
781.0ms
(- (+ (/ (exp (+ (log 2) (log (/ 1 x)))) (pow x 2)) (exp (+ (log 2) (log (/ 1 x))))) (+ (/ (exp (+ (log 2) (log (/ 1 x)))) x) 1))
616.0ms
(* (* (expm1 (log1p (/ (- 1 x) (+ 1 x)))) (expm1 (log1p (/ (- 1 x) (+ 1 x))))) (expm1 (log1p (/ (- 1 x) (+ 1 x)))))
550.0ms
(* (+ 1 x) (+ (* 1 1) (+ (* x x) (* 1 x))))
405.0ms
(- (+ (exp (+ (log -2) (log (/ -1 x)))) (/ (exp (+ (log -2) (log (/ -1 x)))) (pow x 2))) (+ (/ (exp (+ (log -2) (log (/ -1 x)))) x) 1))
396.0ms
(/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (+ 1 x) (+ 1 x)) (+ 1 x)))

prune1.1s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize35.0ms

Local error

Found 2 expressions with local error:

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

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
88×sqrt-prod
82×*-un-lft-identity
63×times-frac
62×add-sqr-sqrt
38×add-cube-cbrt
16×difference-of-squares
10×distribute-lft-out
9×associate-/l*
8×distribute-lft-out--
7×associate-/r*
4×add-cbrt-cube sqrt-div add-exp-log
2×expm1-log1p-u pow1 associate-/r/ insert-posit16 log1p-expm1-u add-log-exp associate-/l/
1×cbrt-undiv sqrt-undiv clear-num frac-2neg flip3-+ flip3-- div-exp flip-+ div-inv flip--
Counts
2 → 109
Calls
2 calls:
Slowest
20.0ms
(/ (sqrt (- 1 x)) (sqrt (+ 1 x)))
7.0ms
(atan (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))

series52.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
49.0ms
(/ (sqrt (- 1 x)) (sqrt (+ 1 x)))
2.0ms
(atan (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))

simplify4.9s

Counts
179 → 115
Calls
179 calls:
Slowest
311.0ms
(* (* (/ (sqrt (- 1 x)) (sqrt (+ 1 x))) (/ (sqrt (- 1 x)) (sqrt (+ 1 x)))) (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))
278.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
235.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
178.0ms
(/ (* (* (sqrt (- 1 x)) (sqrt (- 1 x))) (sqrt (- 1 x))) (* (* (sqrt (+ 1 x)) (sqrt (+ 1 x))) (sqrt (+ 1 x))))
147.0ms
(/ (sqrt (- 1 x)) (sqrt (+ (pow 1 3) (pow x 3))))

prune1.2s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes43.0ms

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
1.0s8000×body80valid
779.0ms8062×body80nan