Details

Time bar (total: 21.6s)

sample51.0ms

Algorithm
intervals
Results
17.0ms51×body1280valid
11.0ms45×body640valid
9.0ms136×body80valid
3.0ms16×body320valid
1.0ms8×body160valid

simplify20.0ms

Calls
1 calls:
Slowest
20.0ms
(- (cbrt (+ x 1)) (cbrt x))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize10.0ms

Local error

Found 3 expressions with local error:

2.3b
(- (cbrt (+ x 1)) (cbrt x))
0.6b
(cbrt x)
0.3b
(cbrt (+ x 1))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
64×cbrt-prod
56×*-un-lft-identity
42×prod-diff
41×add-sqr-sqrt
33×add-cube-cbrt
9×distribute-lft-out
7×fma-neg
5×add-log-exp
4×difference-of-squares
3×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u distribute-lft-out--
2×cbrt-div pow1/3
1×sub-neg flip3-+ flip3-- diff-log flip-+ flip--
Calls
3 calls:
Slowest
39.0ms
(- (cbrt (+ x 1)) (cbrt x))
3.0ms
(cbrt (+ x 1))
1.0ms
(cbrt x)

series437.0ms

Calls
3 calls:
Slowest
280.0ms
(cbrt x)
98.0ms
(- (cbrt (+ x 1)) (cbrt x))
59.0ms
(cbrt (+ x 1))

simplify7.1s

Calls
122 calls:
Slowest
363.0ms
(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
300.0ms
(- (+ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (* 1/3 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) x))) (+ (* (pow (* x -1) 1/3) (cbrt -1)) (* 1/9 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (pow x 2)))))
272.0ms
(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (* 5/81 (pow (/ 1 (pow x 8)) 1/3))) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
227.0ms
(- (+ (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))))
215.0ms
(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))

prune971.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.7b

localize36.0ms

Local error

Found 4 expressions with local error:

2.3b
(- (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt x) (cbrt x)))
0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×add-log-exp
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×pow1/3
1×sub-neg flip3-- fma-neg diff-log prod-diff flip-- difference-of-squares
Calls
4 calls:
Slowest
21.0ms
(- (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt x) (cbrt x)))
1.0ms
(cbrt x)
1.0ms
(cbrt x)
1.0ms
(cbrt x)

series909.0ms

Calls
4 calls:
Slowest
322.0ms
(cbrt x)
267.0ms
(cbrt x)
214.0ms
(cbrt x)
106.0ms
(- (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt x) (cbrt x)))

simplify1.5s

Calls
27 calls:
Slowest
282.0ms
(- (+ (* 2/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 2/3)))
246.0ms
(- (+ (* 4/81 (pow (/ 1 (pow x 7)) 1/3)) (* 2/3 (pow (/ 1 x) 1/3))) (* 1/9 (pow (/ 1 (pow x 4)) 1/3)))
177.0ms
(/ (exp (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (exp (* (cbrt x) (cbrt x))))
159.0ms
(- (+ (* 2/3 (pow (/ 1 x) 1/3)) (pow (/ -1 x) -2/3)) (+ (* (pow (pow x 2) 1/3) (pow (cbrt -1) 2)) (* 1/9 (pow (/ 1 (pow x 4)) 1/3))))
158.0ms
(* (pow (* x -1) 1/3) (cbrt -1))

prune754.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize39.0ms

Local error

Found 4 expressions with local error:

2.3b
(- (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt x) (cbrt x)))
0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×add-log-exp
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×pow1/3
1×sub-neg flip3-- fma-neg diff-log prod-diff flip-- difference-of-squares
Calls
4 calls:
Slowest
32.0ms
(- (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt x) (cbrt x)))
1.0ms
(cbrt x)
1.0ms
(cbrt x)
1.0ms
(cbrt x)

series1.5s

Calls
4 calls:
Slowest
710.0ms
(cbrt x)
323.0ms
(cbrt x)
300.0ms
(cbrt x)
128.0ms
(- (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt x) (cbrt x)))

simplify1.5s

Calls
27 calls:
Slowest
308.0ms
(- (+ (* 4/81 (pow (/ 1 (pow x 7)) 1/3)) (* 2/3 (pow (/ 1 x) 1/3))) (* 1/9 (pow (/ 1 (pow x 4)) 1/3)))
275.0ms
(- (+ (* 2/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 2/3)))
190.0ms
(- (+ (* 2/3 (pow (/ 1 x) 1/3)) (pow (/ -1 x) -2/3)) (+ (* (pow (pow x 2) 1/3) (pow (cbrt -1) 2)) (* 1/9 (pow (/ 1 (pow x 4)) 1/3))))
167.0ms
(/ (exp (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (exp (* (cbrt x) (cbrt x))))
131.0ms
(* (pow (* x -1) 1/3) (cbrt -1))

prune689.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize49.0ms

Local error

Found 4 expressions with local error:

29.1b
(fma (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))) (- (cbrt x)))
0.6b
(cbrt x)
0.3b
(cbrt (cbrt (+ x 1)))
0.3b
(cbrt (+ x 1))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-prod
12×*-un-lft-identity
8×add-sqr-sqrt add-cube-cbrt
6×cbrt-div
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
2×flip3-+ flip-+ distribute-lft-out
1×fma-udef
Calls
4 calls:
Slowest
5.0ms
(cbrt (cbrt (+ x 1)))
5.0ms
(cbrt (+ x 1))
1.0ms
(cbrt x)
1.0ms
(fma (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))) (- (cbrt x)))

series475.0ms

Calls
4 calls:
Slowest
236.0ms
(cbrt x)
144.0ms
(fma (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))) (- (cbrt x)))
50.0ms
(cbrt (+ x 1))
44.0ms
(cbrt (cbrt (+ x 1)))

simplify2.8s

Calls
30 calls:
Slowest
338.0ms
(- (+ (* 1/3 (* (pow (/ 1 (pow x 7)) 1/9) (exp (* 1/9 (- (log -1) (log (/ -1 x))))))) (* (pow (pow x 2) 1/9) (exp (* 1/9 (- (log -1) (log (/ -1 x))))))) (+ (* (pow (* x -1) 1/3) (cbrt -1)) (* 1/9 (* (pow (/ 1 (pow x 16)) 1/9) (exp (* 1/9 (- (log -1) (log (/ -1 x)))))))))
327.0ms
(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow x 1/3)) (+ (pow (/ 1 x) -1/3) (* 1/9 (pow (/ 1 (pow x 5)) 1/3))))
307.0ms
(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
262.0ms
(- (+ (pow (/ 1 x) -1/9) (* 1/9 (pow (/ 1 (pow x 8)) 1/9))) (* 4/81 (pow (/ 1 (pow x 17)) 1/9)))
253.0ms
(- (+ (exp (* 1/9 (- (log -1) (log (/ -1 x))))) (* 1/9 (/ (exp (* 1/9 (- (log -1) (log (/ -1 x))))) x))) (* 4/81 (/ (exp (* 1/9 (- (log -1) (log (/ -1 x))))) (pow x 2))))

prune989.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

regimes80.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.6b against oracle of 0.5b and baseline of 29.6b

bsearch240.0ms

end0.0ms

sample1.4s

Algorithm
intervals
Results
483.0ms1650×body1280valid
355.0ms1285×body640valid
261.0ms4109×body80valid
138.0ms612×body320valid
38.0ms344×body160valid