Details

Time bar (total: 2.9m)

sample67.0ms

Algorithm
intervals
Results
15.0ms278×body80nan
15.0ms54×body1280valid
14.0ms143×body80valid
8.0ms35×body640valid
3.0ms20×body320valid
0.0ms4×body160valid

simplify18.0ms

Calls
1 calls:
Slowest
17.0ms
(- (sqrt (+ x 1)) (sqrt x))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.5b

localize19.0ms

Local error

Found 2 expressions with local error:

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

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
19×*-un-lft-identity
18×prod-diff
17×add-cube-cbrt
16×sqrt-prod
6×fma-neg
4×add-log-exp
2×expm1-log1p-u pow1 add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u difference-of-squares
1×rem-sqrt-square sub-neg flip3-+ flip3-- pow1/2 diff-log flip-+ flip-- distribute-lft-out--
Calls
2 calls:
Slowest
14.0ms
(- (sqrt (+ x 1)) (sqrt x))
1.0ms
(sqrt (+ x 1))

series35.0ms

Calls
2 calls:
Slowest
22.0ms
(- (sqrt (+ x 1)) (sqrt x))
13.0ms
(sqrt (+ x 1))

simplify2.0s

Calls
59 calls:
Slowest
188.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
86.0ms
(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (- (* (sqrt (sqrt x)) (sqrt (sqrt x)))))
76.0ms
(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (- (* (sqrt (sqrt x)) (sqrt (sqrt x)))))
70.0ms
(fma 1 (sqrt (+ x 1)) (- (* (sqrt x) 1)))
65.0ms
(/ (exp (sqrt (+ x 1))) (exp (sqrt x)))

prune625.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 27.0b

localize22.0ms

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))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
16×cbrt-div
12×cbrt-prod
11×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×expm1-log1p-u frac-times add-cbrt-cube insert-posit16 log1p-expm1-u
3×prod-diff
2×pow-prod-down associate-*l/ associate-*r/ pow-prod-up
1×pow2 sub-neg pow-plus flip3-- fma-neg diff-log prod-exp *-commutative cbrt-unprod flip--
Calls
4 calls:
Slowest
22.0ms
(- (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1)))) (sqrt x))
13.0ms
(* (cbrt (+ x 1)) (cbrt (+ x 1)))
5.0ms
(cbrt (+ x 1))
1.0ms
(cbrt (+ x 1))

series148.0ms

Calls
4 calls:
Slowest
45.0ms
(cbrt (+ x 1))
39.0ms
(cbrt (+ x 1))
38.0ms
(* (cbrt (+ x 1)) (cbrt (+ x 1)))
27.0ms
(- (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1)))) (sqrt x))

simplify3.2s

Calls
62 calls:
Slowest
303.0ms
(- (+ (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))))
286.0ms
(- (+ (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))))
166.0ms
(- (+ (* 2/3 (pow (/ 1 x) 1/3)) (pow (/ 1 x) -2/3)) (* 1/9 (pow (/ 1 (pow x 4)) 1/3)))
162.0ms
(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
151.0ms
(- (+ (* 1/3 x) 1) (* 1/9 (pow x 2)))

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 26.7b

localize25.0ms

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)))

rewrite335.0ms

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×expm1-log1p-u pow-plus pow1/3 pow3 sqrt-prod insert-posit16 log1p-expm1-u
3×pow2 *-commutative
2×rem-square-sqrt
1×sub-neg flip3-- fma-neg diff-log prod-diff flip-- difference-of-squares
Calls
4 calls:
Slowest
131.0ms
(- (* (* (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)))
87.0ms
(* (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1)))) (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1)))))
6.0ms
(* (cbrt (+ x 1)) (cbrt (+ x 1)))
4.0ms
(* (sqrt x) (sqrt x))

series86.0ms

Calls
4 calls:
Slowest
49.0ms
(* (cbrt (+ x 1)) (cbrt (+ x 1)))
14.0ms
(* (* (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)))
11.0ms
(* (sqrt x) (sqrt x))

simplify2.5m

Calls
1501 calls:
Slowest
782.0ms
(* (* (* (* (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))))))
505.0ms
(* (* (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))))))
383.0ms
(* (* (sqrt (cbrt (+ (* x x) (- (* 1 1) (* x 1))))) (sqrt (cbrt (+ (* x x) (- (* 1 1) (* x 1)))))) (* (sqrt (* (cbrt (- x 1)) (cbrt (+ (* x x) (- (* 1 1) (* x 1)))))) (sqrt (cbrt (+ (* x x) (- (* 1 1) (* x 1)))))))
355.0ms
(* (* (sqrt (cbrt (- x 1))) (sqrt (cbrt (+ (* x x) (- (* 1 1) (* x 1)))))) (* (sqrt (* (cbrt (- x 1)) (cbrt (- x 1)))) (sqrt (cbrt (+ (* x x) (- (* 1 1) (* x 1)))))))
338.0ms
(* (sqrt (* (cbrt (- x 1)) (cbrt (+ (* x x) (- (* 1 1) (* x 1)))))) (* (sqrt (cbrt (+ (* x x) (- (* 1 1) (* x 1))))) (sqrt (cbrt (- x 1)))))

prune13.5s

Pruning

8 alts after pruning (8 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))

rewrite9.0ms

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×expm1-log1p-u frac-times add-cbrt-cube insert-posit16 log1p-expm1-u 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))

series118.0ms

Calls
4 calls:
Slowest
32.0ms
(* (cbrt (+ x 1)) (cbrt (+ x 1)))
30.0ms
(cbrt (+ x 1))
28.0ms
(cbrt (+ x 1))
28.0ms
(cbrt (+ x 1))

simplify2.3s

Calls
59 calls:
Slowest
209.0ms
(- (+ (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))))
205.0ms
(- (+ (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))))
205.0ms
(- (+ (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))))
91.0ms
(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
90.0ms
(- (+ (* 1/3 x) 1) (* 1/9 (pow x 2)))

prune742.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

regimes55.0ms

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
639.0ms1732×body1280valid
285.0ms8167×body80nan
226.0ms1241×body640valid
167.0ms4125×body80valid
64.0ms623×body320valid
19.0ms279×body160valid