Details

Time bar (total: 2.7m)

sample363.0ms

Algorithm
intervals
Results
114.0ms116×body1280valid
66.0ms25×body1280nan
38.0ms32×body10240exit
36.0ms47×body640valid
27.0ms164×body80valid
17.0ms34×body320valid
14.0ms135×body80nan
13.0ms16×body640nan
9.0ms19×body320nan
3.0ms10×body160valid
2.0ms5×body160nan

simplify341.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
341.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.6b

localize38.0ms

Local error

Found 3 expressions with local error:

1.3b
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.2b
(pow (+ x 1) (/ 1 n))
0.8b
(pow x (/ 1 n))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
76×*-un-lft-identity
73×unpow-prod-down
63×add-sqr-sqrt
56×prod-diff
51×add-cube-cbrt
26×pow-unpow
24×sqr-pow
18×times-frac
10×distribute-lft-out
9×difference-of-squares
8×fma-neg
5×pow1 add-exp-log add-log-exp
3×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u distribute-lft-out--
2×pow-to-exp pow-pow pow-exp div-inv
1×sub-neg flip3-- diff-log flip--
Counts
3 → 152
Calls
3 calls:
Slowest
105.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
7.0ms
(pow (+ x 1) (/ 1 n))
3.0ms
(pow x (/ 1 n))

series483.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
286.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
119.0ms
(pow (+ x 1) (/ 1 n))
78.0ms
(pow x (/ 1 n))

simplify40.6s

Counts
188 → 161
Calls
188 calls:
Slowest
703.0ms
(fma (- (sqrt (pow x (/ 1 n)))) (sqrt (pow x (/ 1 n))) (* (sqrt (pow x (/ 1 n))) (sqrt (pow x (/ 1 n)))))
565.0ms
(+ (sqrt (pow (+ x 1) (/ 1 n))) (pow (sqrt x) (/ 1 n)))
529.0ms
(fma (pow 1 (/ 1 n)) (pow (+ x 1) (/ 1 n)) (- (* (pow (sqrt x) (/ 1 n)) (pow (sqrt x) (/ 1 n)))))
519.0ms
(- (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow x (/ 1 n))))
513.0ms
(+ (pow (sqrt (+ x 1)) (/ 1 n)) (sqrt (pow x (/ 1 n))))

prune1.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 17.5b

localize27.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (pow (+ x 1) (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))
1.2b
(pow (+ x 1) (/ (/ 1 n) 2))
1.2b
(pow (+ x 1) (/ (/ 1 n) 2))
0.8b
(pow x (/ (/ 1 n) 2))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
198×times-frac
171×*-un-lft-identity
156×add-sqr-sqrt
144×add-cube-cbrt
129×pow-unpow
77×unpow-prod-down
56×prod-diff
25×sqr-pow
12×div-inv
11×distribute-lft-out
9×difference-of-squares
8×fma-neg
7×pow1 add-exp-log
6×add-log-exp
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u
3×pow-to-exp pow-pow pow-exp distribute-lft-out--
1×sub-neg flip3-- diff-log flip--
Counts
4 → 273
Calls
4 calls:
Slowest
69.0ms
(- (pow (+ x 1) (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))
16.0ms
(pow (+ x 1) (/ (/ 1 n) 2))
12.0ms
(pow (+ x 1) (/ (/ 1 n) 2))
8.0ms
(pow x (/ (/ 1 n) 2))

series561.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
250.0ms
(- (pow (+ x 1) (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))
123.0ms
(pow (+ x 1) (/ (/ 1 n) 2))
116.0ms
(pow (+ x 1) (/ (/ 1 n) 2))
72.0ms
(pow x (/ (/ 1 n) 2))

simplify43.5s

Counts
300 → 285
Calls
300 calls:
Slowest
599.0ms
(* (cbrt (pow (+ x 1) (/ (/ 1 n) 2))) (cbrt (pow (+ x 1) (/ (/ 1 n) 2))))
589.0ms
(fma (- (cbrt (pow x (/ (/ 1 n) 2)))) (* (cbrt (pow x (/ (/ 1 n) 2))) (cbrt (pow x (/ (/ 1 n) 2)))) (* (cbrt (pow x (/ (/ 1 n) 2))) (* (cbrt (pow x (/ (/ 1 n) 2))) (cbrt (pow x (/ (/ 1 n) 2))))))
562.0ms
(+ (sqrt (pow (+ x 1) (/ (/ 1 n) 2))) (sqrt (pow x (/ (/ 1 n) 2))))
497.0ms
(fma (pow (sqrt (+ x 1)) (/ (/ 1 n) 2)) (pow (sqrt (+ x 1)) (/ (/ 1 n) 2)) (- (* (pow x (/ (/ 1 n) 2)) (pow 1 (/ (/ 1 n) 2)))))
494.0ms
(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ (/ 1 n) 2)) (pow (cbrt (+ x 1)) (/ (/ 1 n) 2)) (- (* (pow (cbrt x) (/ (/ 1 n) 2)) (pow (* (cbrt x) (cbrt x)) (/ (/ 1 n) 2)))))

prune3.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 17.5b

localize29.0ms

Local error

Found 4 expressions with local error:

2.8b
(- (pow (+ x 1) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
1.2b
(pow (+ x 1) (/ 1 n))
0.8b
(pow (cbrt x) (/ 1 n))
0.6b
(cbrt x)

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
32×*-un-lft-identity
26×add-sqr-sqrt pow-unpow add-cube-cbrt
18×unpow-prod-down times-frac
8×fma-neg prod-diff
6×cbrt-prod pow1 add-exp-log add-log-exp
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u sqr-pow
3×pow-pow distribute-lft-out
2×pow-to-exp pow1/3 pow-exp div-inv
1×sub-neg flip3-- diff-log flip--
Counts
4 → 110
Calls
4 calls:
Slowest
105.0ms
(- (pow (+ x 1) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
7.0ms
(pow (+ x 1) (/ 1 n))
3.0ms
(pow (cbrt x) (/ 1 n))
1.0ms
(cbrt x)

series977.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
478.0ms
(- (pow (+ x 1) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
249.0ms
(cbrt x)
134.0ms
(pow (cbrt x) (/ 1 n))
115.0ms
(pow (+ x 1) (/ 1 n))

simplify9.8s

Counts
79 → 122
Calls
79 calls:
Slowest
606.0ms
(- (+ (/ 1 (* x n)) (* 1/2 (/ (pow (log (/ 1 x)) 2) (pow n 2)))) (+ (/ (log (pow (/ 1 x) -1/3)) n) (+ (/ (log (/ 1 x)) n) (+ (/ (log (pow (/ 1 x) -2/3)) n) (+ (* 1/2 (/ (pow (log (pow (/ 1 x) -1/3)) 2) (pow n 2))) (+ (/ (* (log (pow (/ 1 x) -1/3)) (log (pow (/ 1 x) -2/3))) (pow n 2)) (* 1/2 (/ (pow (log (pow (/ 1 x) -2/3)) 2) (pow n 2)))))))))
454.0ms
(* (cbrt (pow (+ x 1) (/ 1 n))) (cbrt (pow (+ x 1) (/ 1 n))))
437.0ms
(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))
437.0ms
(- 1 (* (exp (/ (log (pow x 2/3)) n)) (exp (/ (log (pow x 1/3)) n))))
436.0ms
(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 17.2b

localize61.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (pow (+ x 1) (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))
1.2b
(pow (+ x 1) (/ (/ 1 n) 2))
1.2b
(pow (+ x 1) (/ (/ 1 n) 2))
0.8b
(pow x (/ (/ 1 n) 2))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
198×times-frac
171×*-un-lft-identity
156×add-sqr-sqrt
144×add-cube-cbrt
129×pow-unpow
77×unpow-prod-down
56×prod-diff
25×sqr-pow
12×div-inv
11×distribute-lft-out
9×difference-of-squares
8×fma-neg
7×pow1 add-exp-log
6×add-log-exp
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u
3×pow-to-exp pow-pow pow-exp distribute-lft-out--
1×sub-neg flip3-- diff-log flip--
Counts
4 → 273
Calls
4 calls:
Slowest
80.0ms
(- (pow (+ x 1) (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))
7.0ms
(pow (+ x 1) (/ (/ 1 n) 2))
7.0ms
(pow (+ x 1) (/ (/ 1 n) 2))
3.0ms
(pow x (/ (/ 1 n) 2))

series585.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
270.0ms
(- (pow (+ x 1) (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))
134.0ms
(pow (+ x 1) (/ (/ 1 n) 2))
106.0ms
(pow (+ x 1) (/ (/ 1 n) 2))
75.0ms
(pow x (/ (/ 1 n) 2))

simplify43.5s

Counts
300 → 285
Calls
300 calls:
Slowest
629.0ms
(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ (/ 1 n) 2)) (pow (cbrt (+ x 1)) (/ (/ 1 n) 2)) (- (* (pow (sqrt x) (/ (/ 1 n) 2)) (pow (sqrt x) (/ (/ 1 n) 2)))))
629.0ms
(fma (pow (+ x 1) (/ (/ (/ 1 n) 2) 2)) (pow (+ x 1) (/ (/ (/ 1 n) 2) 2)) (- (* (pow x (/ (/ (/ 1 n) 2) 2)) (pow x (/ (/ (/ 1 n) 2) 2)))))
559.0ms
(pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ (/ 1 n) 2))
527.0ms
(fma (pow (sqrt (+ x 1)) (/ (/ 1 n) 2)) (pow (sqrt (+ x 1)) (/ (/ 1 n) 2)) (- (* (pow x (/ (/ 1 n) 2)) 1)))
524.0ms
(pow (+ x 1) (/ (/ (/ 1 n) 2) 2))

prune4.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 17.2b

regimes508.0ms

Accuracy

86.4% (1.6b remaining)

Error of 19.3b against oracle of 17.7b and baseline of 29.5b

bsearch454.0ms

end0.0ms

sample11.0s

Algorithm
intervals
Results
4.0s3198×body1280valid
1.7s1203×body10240exit
1.3s1543×body640valid
837.0ms674×body1280nan
760.0ms4800×body80valid
608.0ms5103×body80nan
509.0ms676×body640nan
493.0ms890×body320valid
203.0ms379×body320nan
174.0ms445×body160valid
50.0ms178×body160nan