Details

Time bar (total: 35.1s)

sample173.0ms

Algorithm
intervals
Results
81.0ms293×body80nan
35.0ms256×body80valid

simplify43.0ms

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize826.0ms

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)))

rewrite64.0ms

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
35.0ms
(/ (- 1 x) (+ 1 x))
22.0ms
(sqrt (/ (- 1 x) (+ 1 x)))
1.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))

series107.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
53.0ms
(sqrt (/ (- 1 x) (+ 1 x)))
48.0ms
(/ (- 1 x) (+ 1 x))
6.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))

simplify3.6s

Counts
106 → 112
Calls
106 calls:
Slowest
446.0ms
(/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (+ 1 x) (+ 1 x)) (+ 1 x)))
273.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
225.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
209.0ms
(sqrt (/ (- 1 x) (+ (pow 1 3) (pow x 3))))
117.0ms
(- (* 2 (/ 1 x)) (+ (* 2 (/ 1 (pow x 2))) 1))

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize39.0ms

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))

rewrite42.0ms

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
24.0ms
(/ (sqrt (- 1 x)) (sqrt (+ 1 x)))
7.0ms
(atan (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))
5.0ms
(sqrt (- 1 x))
4.0ms
(sqrt (+ 1 x))

series131.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
69.0ms
(/ (sqrt (- 1 x)) (sqrt (+ 1 x)))
32.0ms
(sqrt (- 1 x))
25.0ms
(sqrt (+ 1 x))
4.0ms
(atan (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))

simplify4.4s

Counts
178 → 153
Calls
178 calls:
Slowest
251.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
236.0ms
(/ (* (* (sqrt (- 1 x)) (sqrt (- 1 x))) (sqrt (- 1 x))) (* (* (sqrt (+ 1 x)) (sqrt (+ 1 x))) (sqrt (+ 1 x))))
215.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
174.0ms
(- 1 (+ (* 1/2 x) (* 1/8 (pow x 2))))
124.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))

prune1.4s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize41.0ms

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))

rewrite87.0ms

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×div-exp prod-exp associate-/r/ insert-posit16 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 → 147
Calls
4 calls:
Slowest
61.0ms
(* (sqrt (- 1 x)) (/ 1 (sqrt (+ 1 x))))
16.0ms
(/ 1 (sqrt (+ 1 x)))
5.0ms
(sqrt (- 1 x))
2.0ms
(atan (* (sqrt (- 1 x)) (/ 1 (sqrt (+ 1 x)))))

series129.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
60.0ms
(* (sqrt (- 1 x)) (/ 1 (sqrt (+ 1 x))))
35.0ms
(/ 1 (sqrt (+ 1 x)))
30.0ms
(sqrt (- 1 x))
4.0ms
(atan (* (sqrt (- 1 x)) (/ 1 (sqrt (+ 1 x)))))

simplify6.0s

Counts
151 → 159
Calls
151 calls:
Slowest
480.0ms
(* (* (* (sqrt (- 1 x)) (sqrt (- 1 x))) (sqrt (- 1 x))) (/ (* (* 1 1) 1) (* (* (sqrt (+ 1 x)) (sqrt (+ 1 x))) (sqrt (+ 1 x)))))
423.0ms
(* (sqrt (- (pow 1 3) (pow x 3))) (/ 1 (sqrt (+ 1 x))))
339.0ms
(* (sqrt (- (pow 1 3) (pow x 3))) 1)
313.0ms
(- (+ (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)))))

prune1.5s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize46.0ms

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))))))

rewrite132.0ms

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×insert-posit16
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 → 265
Calls
4 calls:
Slowest
46.0ms
(exp (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))
44.0ms
(log (exp (/ (sqrt (- 1 x)) (sqrt (+ 1 x)))))
29.0ms
(/ (sqrt (- 1 x)) (sqrt (+ 1 x)))
2.0ms
(atan (log (exp (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))))

series252.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
112.0ms
(exp (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))
81.0ms
(/ (sqrt (- 1 x)) (sqrt (+ 1 x)))
55.0ms
(log (exp (/ (sqrt (- 1 x)) (sqrt (+ 1 x)))))
4.0ms
(atan (log (exp (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))))

simplify9.2s

Counts
303 → 277
Calls
303 calls:
Slowest
278.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
273.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
246.0ms
(- (+ (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)))))
245.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
234.0ms
(- (+ (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)))))

prune3.4s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes19.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.4s8000×body80valid
682.0ms8001×body80nan