Details

Time bar (total: 3.5m)

sample40.0ms

Algorithm
intervals
Results
14.0ms59×body1280valid
8.0ms42×body640valid
6.0ms126×body80valid
2.0ms17×body320valid
1.0ms12×body160valid

simplify13.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
13.0ms
(- (cbrt (+ x 1)) (cbrt x))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize11.0ms

Local error

Found 3 expressions with local error:

3.5b
(- (cbrt (+ x 1)) (cbrt x))
0.6b
(cbrt x)
0.3b
(cbrt (+ x 1))

rewrite71.0ms

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--
Counts
3 → 102
Calls
3 calls:
Slowest
62.0ms
(- (cbrt (+ x 1)) (cbrt x))
5.0ms
(cbrt (+ x 1))
1.0ms
(cbrt x)

series451.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
269.0ms
(cbrt x)
141.0ms
(- (cbrt (+ x 1)) (cbrt x))
40.0ms
(cbrt (+ x 1))

simplify8.0s

Counts
122 → 111
Calls
122 calls:
Slowest
641.0ms
(- (+ (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))))
389.0ms
(- (+ (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)))))
373.0ms
(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
334.0ms
(- (+ (* 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)))
231.0ms
(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))

prune939.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.0b

localize62.0ms

Local error

Found 4 expressions with local error:

2.7b
(- (pow (cbrt (+ x 1)) 3) (pow (cbrt x) 3))
0.7b
(pow (cbrt x) 3)
0.6b
(cbrt x)
0.6b
(cbrt x)

rewrite132.0ms

Algorithm
rewrite-expression-head
Rules
360×prod-diff
324×cbrt-prod
312×*-un-lft-identity
295×unpow-prod-down cube-prod
266×add-sqr-sqrt
206×add-cube-cbrt
52×sqr-pow
42×distribute-lft-out
40×cube-mult unpow3
36×difference-of-squares
20×fma-neg
13×distribute-lft-out--
6×add-log-exp
5×pow1 add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u
3×pow-unpow pow1/3
2×pow-pow
1×pow-to-exp difference-cubes sub-neg flip3-- diff-log pow-exp flip-- rem-cube-cbrt
Counts
4 → 506
Calls
4 calls:
Slowest
103.0ms
(- (pow (cbrt (+ x 1)) 3) (pow (cbrt x) 3))
4.0ms
(pow (cbrt x) 3)
1.0ms
(cbrt x)
1.0ms
(cbrt x)

series961.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
317.0ms
(pow (cbrt x) 3)
291.0ms
(cbrt x)
250.0ms
(cbrt x)
103.0ms
(- (pow (cbrt (+ x 1)) 3) (pow (cbrt x) 3))

simplify3.1m

Counts
873 → 518
Calls
873 calls:
Slowest
1.0s
(fma (- (pow (cbrt (cbrt x)) 3)) (pow (* (cbrt (cbrt x)) (cbrt (cbrt x))) 3) (* (pow (cbrt (cbrt x)) 3) (pow (* (cbrt (cbrt x)) (cbrt (cbrt x))) 3)))
779.0ms
(fma (pow (sqrt (cbrt (+ x 1))) 3) (pow (sqrt (cbrt (+ x 1))) 3) (- (* (* (cbrt x) (cbrt x)) (cbrt x))))
777.0ms
(fma (pow 1 3) (pow (cbrt (+ x 1)) 3) (- (* (pow (cbrt x) (/ 3 2)) (pow (cbrt x) (/ 3 2)))))
754.0ms
(fma (- (pow (cbrt (cbrt x)) 3)) (pow (* (cbrt (cbrt x)) (cbrt (cbrt x))) 3) (* (pow (cbrt (cbrt x)) 3) (pow (* (cbrt (cbrt x)) (cbrt (cbrt x))) 3)))
747.0ms
(fma (- (pow (cbrt (cbrt x)) 3)) (pow (* (cbrt (cbrt x)) (cbrt (cbrt x))) 3) (* (pow (cbrt (cbrt x)) 3) (pow (* (cbrt (cbrt x)) (cbrt (cbrt x))) 3)))

prune5.6s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize39.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)
0.5b
(* (cbrt x) (cbrt x))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×pow1/3
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 85
Calls
4 calls:
Slowest
7.0ms
(* (cbrt x) (cbrt x))
1.0ms
(cbrt x)
1.0ms
(cbrt x)
1.0ms
(cbrt x)

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
328.0ms
(cbrt x)
312.0ms
(* (cbrt x) (cbrt x))
294.0ms
(cbrt x)
260.0ms
(cbrt x)

simplify917.0ms

Counts
63 → 97
Calls
63 calls:
Slowest
138.0ms
(* (pow (* x -1) 1/3) (cbrt -1))
138.0ms
(* (pow (* x -1) 1/3) (cbrt -1))
122.0ms
(* (pow (* x -1) 1/3) (cbrt -1))
117.0ms
(* (pow (pow x 2) 1/3) (pow (cbrt -1) 2))
88.0ms
(* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (* (cbrt (cbrt x)) (cbrt (cbrt x))))

prune1.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.3b

localize53.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube pow1/3 add-exp-log insert-posit16 log1p-expm1-u add-log-exp
Counts
4 → 56
Calls
4 calls:
Slowest
1.0ms
(cbrt x)
1.0ms
(cbrt x)
1.0ms
(cbrt x)
1.0ms
(cbrt x)

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
304.0ms
(cbrt x)
303.0ms
(cbrt x)
279.0ms
(cbrt x)
269.0ms
(cbrt x)

simplify717.0ms

Counts
24 → 68
Calls
24 calls:
Slowest
140.0ms
(* (pow (* x -1) 1/3) (cbrt -1))
136.0ms
(* (pow (* x -1) 1/3) (cbrt -1))
130.0ms
(* (pow (* x -1) 1/3) (cbrt -1))
130.0ms
(* (pow (* x -1) 1/3) (cbrt -1))
31.0ms
(pow (/ 1 x) -1/3)

prune876.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 0.3b

regimes223.0ms

Accuracy

0% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 0.6b

bsearch3.0ms

end0.0ms

sample1.5s

Algorithm
intervals
Results
556.0ms1715×body1280valid
306.0ms4095×body80valid
270.0ms1263×body640valid
135.0ms596×body320valid
73.0ms331×body160valid