Details

Time bar (total: 37.1s)

sample184.0ms

Algorithm
intervals
Results
28.0ms293×body80nan
24.0ms256×body80valid

simplify43.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
42.0ms
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))

prune705.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

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)))

rewrite113.0ms

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
61.0ms
(sqrt (/ (- 1 x) (+ 1 x)))
40.0ms
(/ (- 1 x) (+ 1 x))
3.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))

series228.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
150.0ms
(/ (- 1 x) (+ 1 x))
69.0ms
(sqrt (/ (- 1 x) (+ 1 x)))
8.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))

simplify3.9s

Counts
106 → 118
Calls
106 calls:
Slowest
649.0ms
(/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (+ 1 x) (+ 1 x)) (+ 1 x)))
284.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
278.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
200.0ms
(sqrt (/ (- 1 x) (+ (pow 1 3) (pow x 3))))
165.0ms
(- (* 2 (/ 1 x)) (+ (* 2 (/ 1 (pow x 2))) 1))

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite69.0ms

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
23.0ms
(/ (sqrt (- 1 x)) (sqrt (+ 1 x)))
18.0ms
(sqrt (- 1 x))
15.0ms
(atan (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))
10.0ms
(sqrt (+ 1 x))

series108.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
52.0ms
(/ (sqrt (- 1 x)) (sqrt (+ 1 x)))
29.0ms
(sqrt (- 1 x))
24.0ms
(sqrt (+ 1 x))
3.0ms
(atan (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))

simplify4.6s

Counts
179 → 164
Calls
179 calls:
Slowest
309.0ms
(- (+ (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)))))
228.0ms
(- 1 (+ (* 1/2 x) (* 1/8 (pow x 2))))
200.0ms
(/ (* (* (sqrt (- 1 x)) (sqrt (- 1 x))) (sqrt (- 1 x))) (* (* (sqrt (+ 1 x)) (sqrt (+ 1 x))) (sqrt (+ 1 x))))
143.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))

prune1.8s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
68×add-sqr-sqrt
61×*-un-lft-identity
50×times-frac
49×sqrt-prod
37×add-cube-cbrt
27×associate-*r*
17×add-exp-log
11×add-cbrt-cube
10×sqrt-div unswap-sqr
9×pow1 associate-*l*
7×associate-/r* distribute-lft-out
4×expm1-log1p-u div-exp prod-exp associate-/r/ insert-posit16 log1p-expm1-u add-log-exp difference-of-squares
3×flip3-- pow-flip flip-- associate-/l*
2×frac-times cbrt-undiv rec-exp sqrt-pow1 flip3-+ pow1/2 1-exp associate-*l/ cbrt-unprod flip-+ div-inv distribute-lft-out--
1×rem-sqrt-square clear-num frac-2neg pow-prod-down associate-*r/ un-div-inv *-commutative inv-pow
Counts
4 → 155
Calls
4 calls:
Slowest
37.0ms
(* (sqrt (- 1 x)) (/ 1 (sqrt (+ 1 x))))
15.0ms
(/ 1 (sqrt (+ 1 x)))
9.0ms
(sqrt (- 1 x))
2.0ms
(atan (* (sqrt (- 1 x)) (/ 1 (sqrt (+ 1 x)))))

series128.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
54.0ms
(* (sqrt (- 1 x)) (/ 1 (sqrt (+ 1 x))))
46.0ms
(/ 1 (sqrt (+ 1 x)))
25.0ms
(sqrt (- 1 x))
2.0ms
(atan (* (sqrt (- 1 x)) (/ 1 (sqrt (+ 1 x)))))

simplify6.0s

Counts
151 → 167
Calls
151 calls:
Slowest
478.0ms
(* (* (* (sqrt (- 1 x)) (sqrt (- 1 x))) (sqrt (- 1 x))) (/ (* (* 1 1) 1) (* (* (sqrt (+ 1 x)) (sqrt (+ 1 x))) (sqrt (+ 1 x)))))
352.0ms
(* (sqrt (- (pow 1 3) (pow x 3))) (/ 1 (sqrt (+ 1 x))))
299.0ms
(- 1 (+ (* 1/2 x) (* 1/8 (pow x 2))))
285.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
285.0ms
(* (sqrt (- (pow 1 3) (pow x 3))) 1)

prune1.8s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
244×sqrt-prod
229×*-un-lft-identity
189×times-frac
173×add-sqr-sqrt
138×exp-prod
107×add-cube-cbrt
70×log-pow
44×difference-of-squares
28×distribute-lft-out
22×distribute-lft-out--
9×associate-/l*
8×sqrt-div
7×associate-/r*
6×add-cbrt-cube add-exp-log associate-/r/
5×pow1 add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×log-prod flip3-+ flip-+ div-inv
2×associate-/l/
1×cbrt-undiv sqrt-undiv clear-num frac-2neg flip3-- div-exp rem-log-exp flip-- rem-exp-log
Counts
4 → 273
Calls
4 calls:
Slowest
36.0ms
(exp (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))
24.0ms
(log (exp (/ (sqrt (- 1 x)) (sqrt (+ 1 x)))))
15.0ms
(/ (sqrt (- 1 x)) (sqrt (+ 1 x)))
3.0ms
(atan (log (exp (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))))

series243.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
98.0ms
(exp (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))
77.0ms
(log (exp (/ (sqrt (- 1 x)) (sqrt (+ 1 x)))))
65.0ms
(/ (sqrt (- 1 x)) (sqrt (+ 1 x)))
4.0ms
(atan (log (exp (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))))

simplify9.6s

Counts
303 → 285
Calls
303 calls:
Slowest
307.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
291.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
287.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
264.0ms
(- (+ (exp (sqrt -1)) (/ (exp (sqrt -1)) (* x (sqrt -1)))) (+ (* 1/2 (/ (exp (sqrt -1)) (* (pow x 2) (sqrt -1)))) (* 1/2 (/ (exp (sqrt -1)) (pow x 2)))))
263.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))

prune3.9s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes28.0ms

Accuracy

0% (0.0b remaining)

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

bsearch3.0ms

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.1s8001×body80nan
830.0ms8000×body80valid