Details

Time bar (total: 18.5s)

sample305.0ms

Algorithm
intervals
Results
60.0ms748×body80nan
16.0ms255×body80valid
0.0ms1×body160valid

simplify69.0ms

Calls
1 calls:
Slowest
68.0ms
(* (sqrt (- x 1)) (sqrt x))

prune41.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize59.0ms

Local error

Found 2 expressions with local error:

0.4b
(* (sqrt (- x 1)) (sqrt x))
0.0b
(sqrt (- x 1))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt
6×*-un-lft-identity associate-*l* add-cube-cbrt sqrt-prod
4×pow1 add-cbrt-cube sqrt-div add-exp-log
3×pow1/2 associate-*r*
2×flip3-- pow-prod-down associate-*l/ insert-posit16 flip-- add-log-exp
1×rem-sqrt-square sqrt-unprod prod-exp *-commutative cbrt-unprod
Calls
2 calls:
Slowest
17.0ms
(* (sqrt (- x 1)) (sqrt x))
1.0ms
(sqrt (- x 1))

series574.0ms

Calls
2 calls:
Slowest
528.0ms
(* (sqrt (- x 1)) (sqrt x))
45.0ms
(sqrt (- x 1))

simplify960.0ms

Calls
27 calls:
Slowest
286.0ms
(* (* (* (sqrt (- x 1)) (sqrt (- x 1))) (sqrt (- x 1))) (* (* (sqrt x) (sqrt x)) (sqrt x)))
122.0ms
(+ (* 1/2 (/ x (sqrt -1))) (+ (* 1/8 (/ (pow x 2) (sqrt -1))) (sqrt -1)))
85.0ms
(* (sqrt (- (* x x) (* 1 1))) (sqrt x))
71.0ms
(+ (log (sqrt (- x 1))) (log (sqrt x)))
69.0ms
(- x (+ (* 1/8 (/ 1 x)) 1/2))

prune360.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 1 expressions with local error:

0.0b
(- x (- 1/2 (/ -1/8 x)))

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
2×sub-neg associate--r+
1×add-sqr-sqrt pow1 *-un-lft-identity flip3-- add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 flip-- associate--r- add-log-exp
Calls
1 calls:
Slowest
1.0ms
(- x (- 1/2 (/ -1/8 x)))

series32.0ms

Calls
1 calls:
Slowest
32.0ms
(- x (- 1/2 (/ -1/8 x)))

simplify265.0ms

Calls
6 calls:
Slowest
90.0ms
(- x (+ (* 1/8 (/ 1 x)) 1/2))
84.0ms
(- x (+ (* 1/8 (/ 1 x)) 1/2))
59.0ms
(- x (+ (* 1/8 (/ 1 x)) 1/2))
13.0ms
(- (/ -1/8 x))
12.0ms
(- (/ -1/8 x))

prune81.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 3 expressions with local error:

30.4b
(sqrt (- (* x x) 1))
18.5b
(/ (* (sqrt (- (* x x) 1)) (sqrt x)) (sqrt (+ x 1)))
0.2b
(* (sqrt (- (* x x) 1)) (sqrt x))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
14×sqrt-prod
12×add-sqr-sqrt
11×*-un-lft-identity add-cube-cbrt
10×add-cbrt-cube add-exp-log
8×sqrt-div
7×associate-*l*
6×associate-/r* times-frac
5×pow1
4×associate-*l/
3×flip3-- pow1/2 associate-*r* insert-posit16 flip-- add-log-exp
2×cbrt-undiv sqrt-unprod difference-of-sqr-1 div-exp pow-prod-down prod-exp associate-/r/ cbrt-unprod associate-/l/
1×rem-sqrt-square sqrt-undiv clear-num frac-2neg flip3-+ *-commutative flip-+ div-inv associate-/l*
Calls
3 calls:
Slowest
10.0ms
(/ (* (sqrt (- (* x x) 1)) (sqrt x)) (sqrt (+ x 1)))
8.0ms
(* (sqrt (- (* x x) 1)) (sqrt x))
3.0ms
(sqrt (- (* x x) 1))

series237.0ms

Calls
3 calls:
Slowest
133.0ms
(/ (* (sqrt (- (* x x) 1)) (sqrt x)) (sqrt (+ x 1)))
58.0ms
(* (sqrt (- (* x x) 1)) (sqrt x))
47.0ms
(sqrt (- (* x x) 1))

simplify4.7s

Calls
60 calls:
Slowest
237.0ms
(/ (* (* (* (sqrt (- (* x x) 1)) (sqrt x)) (* (sqrt (- (* x x) 1)) (sqrt x))) (* (sqrt (- (* x x) 1)) (sqrt x))) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
228.0ms
(/ (* (- (* x x) 1) x) (+ x 1))
196.0ms
(- x (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
191.0ms
(- (+ (log (sqrt (- (* x x) 1))) (log (sqrt x))) (log (sqrt (+ x 1))))
190.0ms
(* (- (* x x) 1) x)

prune661.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

30.4b
(/ (* (sqrt x) (sqrt (+ (* (* x x) x) -1))) (sqrt (+ (* x x) (+ (* 1 1) (* x 1)))))
30.4b
(sqrt (+ (* x x) (+ (* 1 1) (* x 1))))
23.2b
(sqrt (+ (* (* x x) x) -1))
0.2b
(* (sqrt x) (sqrt (+ (* (* x x) x) -1)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt sqrt-prod
13×*-un-lft-identity add-cube-cbrt
11×add-cbrt-cube add-exp-log
10×sqrt-div
6×pow1 associate-/r* times-frac associate-*r*
5×flip3-+ flip-+
4×pow1/2 associate-*r/ insert-posit16 add-log-exp
3×associate-*l*
2×cbrt-undiv rem-sqrt-square sqrt-unprod div-exp pow-prod-down prod-exp associate-/r/ cbrt-unprod associate-/l/
1×sqrt-undiv clear-num frac-2neg *-commutative div-inv associate-/l*
Calls
4 calls:
Slowest
20.0ms
(* (sqrt x) (sqrt (+ (* (* x x) x) -1)))
18.0ms
(/ (* (sqrt x) (sqrt (+ (* (* x x) x) -1))) (sqrt (+ (* x x) (+ (* 1 1) (* x 1)))))
11.0ms
(sqrt (+ (* x x) (+ (* 1 1) (* x 1))))
8.0ms
(sqrt (+ (* (* x x) x) -1))

series370.0ms

Calls
4 calls:
Slowest
151.0ms
(/ (* (sqrt x) (sqrt (+ (* (* x x) x) -1))) (sqrt (+ (* x x) (+ (* 1 1) (* x 1)))))
111.0ms
(* (sqrt x) (sqrt (+ (* (* x x) x) -1)))
81.0ms
(sqrt (+ (* (* x x) x) -1))
27.0ms
(sqrt (+ (* x x) (+ (* 1 1) (* x 1))))

simplify4.8s

Calls
67 calls:
Slowest
437.0ms
(sqrt (+ (pow (* x x) 3) (pow (+ (* 1 1) (* x 1)) 3)))
323.0ms
(sqrt (+ (* (* (* x x) x) (* (* x x) x)) (- (* -1 -1) (* (* (* x x) x) -1))))
311.0ms
(sqrt (+ (* (* x x) (* x x)) (- (* (+ (* 1 1) (* x 1)) (+ (* 1 1) (* x 1))) (* (* x x) (+ (* 1 1) (* x 1))))))
244.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ (* (* x x) x) -1)) (sqrt (+ (* (* x x) x) -1))) (sqrt (+ (* (* x x) x) -1))))
240.0ms
(/ (* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ (* (* x x) x) -1)) (sqrt (+ (* (* x x) x) -1))) (sqrt (+ (* (* x x) x) -1)))) (* (* (sqrt (+ (* x x) (+ (* 1 1) (* x 1)))) (sqrt (+ (* x x) (+ (* 1 1) (* x 1))))) (sqrt (+ (* x x) (+ (* 1 1) (* x 1))))))

prune1.0s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes22.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch1.0ms

end0.0ms

sample3.7s

Algorithm
intervals
Results
2.3s23560×body80nan
1.1s7995×body80valid
1.0ms5×body160valid