Details

Time bar (total: 2.7m)

sample66.0ms

Algorithm
intervals
Results
22.0ms54×body1280valid
15.0ms278×body80nan
9.0ms143×body80valid
7.0ms35×body640valid
3.0ms20×body320valid
0.0ms4×body160valid

simplify10.0ms

Calls
1 calls:
Slowest
10.0ms
(- (sqrt (+ x 1)) (sqrt x))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.5b

localize17.0ms

Local error

Found 2 expressions with local error:

1.2b
(- (sqrt (+ x 1)) (sqrt x))
0.0b
(sqrt (+ x 1))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
5×*-un-lft-identity
4×sqrt-prod add-log-exp
3×add-cube-cbrt
2×pow1 add-cbrt-cube sqrt-div add-exp-log insert-posit16 difference-of-squares
1×rem-sqrt-square sub-neg flip3-+ flip3-- pow1/2 diff-log flip-+ flip-- distribute-lft-out--
Calls
2 calls:
Slowest
11.0ms
(- (sqrt (+ x 1)) (sqrt x))
1.0ms
(sqrt (+ x 1))

series51.0ms

Calls
2 calls:
Slowest
27.0ms
(- (sqrt (+ x 1)) (sqrt x))
25.0ms
(sqrt (+ x 1))

simplify373.0ms

Calls
18 calls:
Slowest
115.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
50.0ms
(sqrt (- (* x x) (* 1 1)))
41.0ms
(/ (exp (sqrt (+ x 1))) (exp (sqrt x)))
24.0ms
(- (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))
24.0ms
(- (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))

prune323.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 27.0b

localize30.0ms

Local error

Found 4 expressions with local error:

12.6b
(- (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1)))) (sqrt x))
0.3b
(* (cbrt (+ x 1)) (cbrt (+ x 1)))
0.3b
(cbrt (+ x 1))
0.3b
(cbrt (+ x 1))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
16×cbrt-div
12×cbrt-prod
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×pow1
8×flip3-+ flip-+
6×pow1/3 associate-*r* associate-*l* add-exp-log add-log-exp
4×frac-times add-cbrt-cube insert-posit16
2×pow-prod-down associate-*l/ associate-*r/ pow-prod-up
1×pow2 sub-neg pow-plus flip3-- diff-log prod-exp *-commutative cbrt-unprod flip--
Calls
4 calls:
Slowest
27.0ms
(- (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1)))) (sqrt x))
6.0ms
(* (cbrt (+ x 1)) (cbrt (+ x 1)))
1.0ms
(cbrt (+ x 1))
1.0ms
(cbrt (+ x 1))

series144.0ms

Calls
4 calls:
Slowest
47.0ms
(* (cbrt (+ x 1)) (cbrt (+ x 1)))
37.0ms
(cbrt (+ x 1))
32.0ms
(cbrt (+ x 1))
29.0ms
(- (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1)))) (sqrt x))

simplify2.4s

Calls
55 calls:
Slowest
285.0ms
(- (+ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (* 1/3 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) x))) (* 1/9 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (pow x 2))))
260.0ms
(- (+ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (* 1/3 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) x))) (* 1/9 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (pow x 2))))
165.0ms
(- (+ (* 2/3 (pow (/ 1 x) 1/3)) (pow (/ -1 x) -2/3)) (* 1/9 (pow (/ 1 (pow x 4)) 1/3)))
126.0ms
(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
114.0ms
(- (+ (* 2/3 (pow (/ 1 x) 1/3)) (pow (/ 1 x) -2/3)) (* 1/9 (pow (/ 1 (pow x 4)) 1/3)))

prune1.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 26.7b

localize17.0ms

Local error

Found 4 expressions with local error:

12.3b
(- (* (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1)))) (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))))) (* (sqrt x) (sqrt x)))
0.5b
(* (sqrt x) (sqrt x))
0.3b
(* (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1)))) (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1)))))
0.3b
(* (cbrt (+ x 1)) (cbrt (+ x 1)))

rewrite376.0ms

Algorithm
rewrite-expression-head
Rules
2928×cbrt-div
2268×sqrt-div
2192×frac-times
1464×flip3-+ flip-+
784×associate-*l/
460×associate-*r/
41×pow1
23×pow-prod-down
20×add-exp-log
18×add-cbrt-cube
12×pow1/2
10×add-sqr-sqrt *-un-lft-identity associate-*r* associate-*l* prod-exp pow-prod-up add-cube-cbrt cbrt-unprod
6×cbrt-prod sqrt-unprod add-log-exp
4×pow-plus pow1/3 pow3 sqrt-prod insert-posit16
3×pow2 *-commutative
2×rem-square-sqrt
1×sub-neg flip3-- diff-log flip-- difference-of-squares
Calls
4 calls:
Slowest
119.0ms
(- (* (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1)))) (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))))) (* (sqrt x) (sqrt x)))
107.0ms
(* (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1)))) (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1)))))
12.0ms
(* (cbrt (+ x 1)) (cbrt (+ x 1)))
4.0ms
(* (sqrt x) (sqrt x))

series103.0ms

Calls
4 calls:
Slowest
60.0ms
(* (cbrt (+ x 1)) (cbrt (+ x 1)))
17.0ms
(* (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1)))) (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1)))))
13.0ms
(- (* (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1)))) (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))))) (* (sqrt x) (sqrt x)))
13.0ms
(* (sqrt x) (sqrt x))

simplify2.3m

Calls
1498 calls:
Slowest
678.0ms
(* (* (* (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (* (* (sqrt (cbrt (+ x 1))) (sqrt (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))))) (* (* (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (* (* (sqrt (cbrt (+ x 1))) (sqrt (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))))))
574.0ms
(* (* (sqrt (* (cbrt (+ (* x x) (- (* 1 1) (* x 1)))) (cbrt (- x 1)))) (sqrt (cbrt (+ (* x x) (- (* 1 1) (* x 1)))))) (* (sqrt (cbrt (+ (* x x) (- (* 1 1) (* x 1))))) (sqrt (cbrt (- x 1)))))
366.0ms
(* (* (sqrt (* (cbrt (+ x 1)) (cbrt (- (* x x) (* 1 1))))) (sqrt (cbrt (+ x 1)))) (* (sqrt (* (cbrt (+ (pow x 3) (pow 1 3))) (cbrt (+ (pow x 3) (pow 1 3))))) (sqrt (cbrt (+ (pow x 3) (pow 1 3))))))
357.0ms
(* (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ (pow x 3) (pow 1 3))))) (sqrt (cbrt (+ (pow x 3) (pow 1 3))))) (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (- (* x x) (* 1 1))))))
320.0ms
(* (* (sqrt (cbrt (- x 1))) (sqrt (cbrt (- x 1)))) (* (sqrt (cbrt (+ (* x x) (- (* 1 1) (* x 1))))) (sqrt (cbrt (+ (* x x) (- (* 1 1) (* x 1)))))))

prune13.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize3.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (cbrt (+ x 1)) (cbrt (+ x 1)))
0.3b
(cbrt (+ x 1))
0.3b
(cbrt (+ x 1))
0.3b
(cbrt (+ x 1))

rewrite8.0ms

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
6.0ms
(* (cbrt (+ x 1)) (cbrt (+ x 1)))
1.0ms
(cbrt (+ x 1))
1.0ms
(cbrt (+ x 1))
1.0ms
(cbrt (+ x 1))

series119.0ms

Calls
4 calls:
Slowest
31.0ms
(cbrt (+ x 1))
30.0ms
(* (cbrt (+ x 1)) (cbrt (+ x 1)))
29.0ms
(cbrt (+ x 1))
29.0ms
(cbrt (+ x 1))

simplify1.9s

Calls
59 calls:
Slowest
181.0ms
(- (+ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (* 1/3 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) x))) (* 1/9 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (pow x 2))))
178.0ms
(- (+ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (* 1/3 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) x))) (* 1/9 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (pow x 2))))
178.0ms
(- (+ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (* 1/3 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) x))) (* 1/9 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (pow x 2))))
81.0ms
(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
80.0ms
(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))

prune674.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

regimes51.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch3.0ms

end0.0ms

sample1.5s

Algorithm
intervals
Results
541.0ms8167×body80nan
353.0ms1732×body1280valid
249.0ms1241×body640valid
167.0ms4125×body80valid
61.0ms623×body320valid
40.0ms279×body160valid