Details

Time bar (total: 16.5s)

sample121.0ms

Algorithm
intervals
Results
45.0ms306×body160nan
37.0ms601×body80nan
20.0ms256×body80valid

simplify162.0ms

Calls
1 calls:
Slowest
162.0ms
(log (+ x (sqrt (- (* x x) 1))))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize25.0ms

Local error

Found 3 expressions with local error:

29.9b
(sqrt (- (* x x) 1))
0.0b
(+ x (sqrt (- (* x x) 1)))
0.0b
(log (+ x (sqrt (- (* x x) 1))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
5×*-un-lft-identity add-cube-cbrt
4×pow1 add-exp-log sqrt-prod
3×log-prod add-cbrt-cube insert-posit16 add-log-exp
2×log-div flip3-+ sqrt-div flip-+
1×+-commutative rem-sqrt-square flip3-- pow1/2 difference-of-sqr-1 rem-log-exp log-pow flip--
Calls
3 calls:
Slowest
5.0ms
(sqrt (- (* x x) 1))
4.0ms
(+ x (sqrt (- (* x x) 1)))
4.0ms
(log (+ x (sqrt (- (* x x) 1))))

series123.0ms

Calls
3 calls:
Slowest
78.0ms
(log (+ x (sqrt (- (* x x) 1))))
24.0ms
(+ x (sqrt (- (* x x) 1)))
20.0ms
(sqrt (- (* x x) 1))

simplify2.8s

Calls
22 calls:
Slowest
333.0ms
(+ (log -1/2) (+ (log (/ -1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
281.0ms
(- (log 2) (+ (log (/ 1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
247.0ms
(- (+ (log (sqrt -1)) (/ x (sqrt -1))) (* 1/6 (/ (pow x 3) (pow (sqrt -1) 3))))
223.0ms
(log (+ (pow x 3) (pow (sqrt (- (* x x) 1)) 3)))
209.0ms
(log (- (* x x) (* (sqrt (- (* x x) 1)) (sqrt (- (* x x) 1)))))

prune260.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.5b
(* (sqrt (+ x 1)) (sqrt (- x 1)))
0.0b
(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
0.0b
(log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
12×sqrt-div
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow1 associate-*r* associate-*l* add-exp-log sqrt-prod
5×flip3-+ add-cbrt-cube flip-+
4×frac-times
3×log-prod flip3-- insert-posit16 flip-- add-log-exp
2×log-div pow1/2 pow-prod-down associate-*l/ associate-*r/
1×+-commutative sqrt-unprod rem-log-exp prod-exp log-pow *-commutative cbrt-unprod
Calls
3 calls:
Slowest
6.0ms
(* (sqrt (+ x 1)) (sqrt (- x 1)))
2.0ms
(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
1.0ms
(log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))

series117.0ms

Calls
3 calls:
Slowest
58.0ms
(log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))
33.0ms
(* (sqrt (+ x 1)) (sqrt (- x 1)))
26.0ms
(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))

simplify2.8s

Calls
43 calls:
Slowest
412.0ms
(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
327.0ms
(log (+ (pow x 3) (pow (* (sqrt (+ x 1)) (sqrt (- x 1))) 3)))
265.0ms
(- (+ (* 1/2 (/ (pow x 2) (sqrt -1))) (sqrt -1)) (* 1/8 (/ (pow x 4) (pow (sqrt -1) 3))))
256.0ms
(- (+ (log (sqrt -1)) (/ x (sqrt -1))) (* 1/6 (/ (pow x 3) (pow (sqrt -1) 3))))
192.0ms
(- (log 2) (+ (log (/ 1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))

prune508.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (- x 1)) (cbrt (- x 1)))
0.5b
(cbrt (- x 1))
0.5b
(cbrt (- x 1))
0.5b
(cbrt (- x 1))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
15×cbrt-prod
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×pow1 flip3-- flip--
7×pow1/3
6×associate-*r* associate-*l* add-exp-log
4×frac-times add-cbrt-cube insert-posit16 add-log-exp
2×pow-prod-down associate-*l/ associate-*r/ pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
7.0ms
(* (cbrt (- x 1)) (cbrt (- x 1)))
1.0ms
(cbrt (- x 1))
1.0ms
(cbrt (- x 1))
1.0ms
(cbrt (- x 1))

series192.0ms

Calls
4 calls:
Slowest
59.0ms
(* (cbrt (- x 1)) (cbrt (- x 1)))
49.0ms
(cbrt (- x 1))
48.0ms
(cbrt (- x 1))
35.0ms
(cbrt (- x 1))

simplify3.9s

Calls
59 calls:
Slowest
412.0ms
(- (* (pow (* x -1) 1/3) (cbrt -1)) (+ (* 1/9 (* (pow (/ -1 (pow x 5)) 1/3) (cbrt -1))) (* 1/3 (* (pow (/ -1 (pow x 2)) 1/3) (cbrt -1)))))
400.0ms
(- (* (pow (* x -1) 1/3) (cbrt -1)) (+ (* 1/9 (* (pow (/ -1 (pow x 5)) 1/3) (cbrt -1))) (* 1/3 (* (pow (/ -1 (pow x 2)) 1/3) (cbrt -1)))))
339.0ms
(- (* (pow (* x -1) 1/3) (cbrt -1)) (+ (* 1/9 (* (pow (/ -1 (pow x 5)) 1/3) (cbrt -1))) (* 1/3 (* (pow (/ -1 (pow x 2)) 1/3) (cbrt -1)))))
305.0ms
(- (pow -1 1/3) (+ (* 1/3 (* x (pow -1 1/3))) (* 1/9 (* (pow x 2) (pow -1 1/3)))))
295.0ms
(- (pow -1 1/3) (+ (* 1/3 (* x (pow -1 1/3))) (* 1/9 (* (pow x 2) (pow -1 1/3)))))

prune1.2s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes18.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 0.1b

bsearch2.0ms

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.7s7755×body160nan
1.3s16298×body80nan
813.0ms8000×body80valid