Details

Time bar (total: 5.5m)

sample293.0ms

Algorithm
intervals
Results
113.0ms106×body1280valid
40.0ms33×body10240exit
31.0ms50×body640valid
23.0ms20×body1280nan
18.0ms25×body640nan
18.0ms142×body80valid
13.0ms28×body320valid
12.0ms121×body80nan
4.0ms13×body160valid
3.0ms7×body320nan
1.0ms4×body160nan

simplify361.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
361.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize16.0ms

Local error

Found 3 expressions with local error:

2.4b
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.0b
(pow (+ x 1) (/ 1 n))
0.2b
(pow x (/ 1 n))

rewrite118.0ms

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
106.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
7.0ms
(pow (+ x 1) (/ 1 n))
3.0ms
(pow x (/ 1 n))

series427.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
263.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
95.0ms
(pow (+ x 1) (/ 1 n))
69.0ms
(pow x (/ 1 n))

simplify55.0s

Counts
237 → 161
Calls
237 calls:
Slowest
699.0ms
(* (cbrt (pow (+ x 1) (/ 1 n))) (cbrt (pow (+ x 1) (/ 1 n))))
638.0ms
(pow (+ x 1) (/ 1 (* (cbrt n) (cbrt n))))
593.0ms
(pow (+ x 1) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt n) (cbrt n))))
583.0ms
(+ (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow x (/ 1 n))))
573.0ms
(fma (- (pow x (/ 1 n))) (pow 1 (/ 1 n)) (* (pow x (/ 1 n)) (pow 1 (/ 1 n))))

prune1.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.8b

localize31.0ms

Local error

Found 4 expressions with local error:

2.4b
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.0b
(pow (+ x 1) (/ 1 n))
0.2b
(pow x (/ 1 n))
0.1b
(expm1 (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
77×*-un-lft-identity
73×unpow-prod-down
64×add-sqr-sqrt
56×prod-diff
52×add-cube-cbrt
26×pow-unpow
24×sqr-pow
18×times-frac
10×distribute-lft-out
9×difference-of-squares
8×fma-neg
6×pow1 add-exp-log add-log-exp
5×log1p-expm1-u
4×expm1-log1p-u add-cbrt-cube insert-posit16
3×distribute-lft-out--
2×pow-to-exp pow-pow pow-exp div-inv
1×expm1-log1p sub-neg flip3-- diff-log flip-- expm1-udef
Counts
4 → 164
Calls
4 calls:
Slowest
80.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
13.0ms
(pow (+ x 1) (/ 1 n))
5.0ms
(pow x (/ 1 n))
1.0ms
(expm1 (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))))

series787.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
347.0ms
(expm1 (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))))
252.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
119.0ms
(pow (+ x 1) (/ 1 n))
68.0ms
(pow x (/ 1 n))

simplify59.9s

Counts
251 → 176
Calls
251 calls:
Slowest
1.0s
(pow (+ x 1) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt n) (cbrt n))))
757.0ms
(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)))))
668.0ms
(pow x (/ 1 (* (cbrt n) (cbrt n))))
614.0ms
(pow (+ x 1) (/ 1 (* (cbrt n) (cbrt n))))
612.0ms
(pow x (/ (* (cbrt 1) (cbrt 1)) (* (cbrt n) (cbrt n))))

prune2.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.8b

localize26.0ms

Local error

Found 4 expressions with local error:

2.4b
(log (exp (expm1 (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))))))
2.4b
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.0b
(pow (+ x 1) (/ 1 n))
0.2b
(pow x (/ 1 n))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
79×*-un-lft-identity
73×unpow-prod-down
66×add-sqr-sqrt
56×prod-diff
54×add-cube-cbrt
26×pow-unpow
24×sqr-pow
18×times-frac
10×distribute-lft-out
9×difference-of-squares
8×fma-neg
7×pow1
6×add-exp-log add-log-exp
4×expm1-log1p-u add-cbrt-cube log-pow insert-posit16 log1p-expm1-u
3×log-prod exp-prod distribute-lft-out--
2×pow-to-exp pow-pow pow-exp div-inv
1×log-div sub-neg flip3-- exp-diff diff-log rem-log-exp flip-- expm1-udef
Counts
4 → 171
Calls
4 calls:
Slowest
61.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
7.0ms
(pow (+ x 1) (/ 1 n))
5.0ms
(pow x (/ 1 n))
3.0ms
(log (exp (expm1 (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))))))

series889.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
408.0ms
(log (exp (expm1 (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))))))
251.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
139.0ms
(pow (+ x 1) (/ 1 n))
92.0ms
(pow x (/ 1 n))

simplify1.0m

Counts
262 → 183
Calls
262 calls:
Slowest
778.0ms
(fma (pow (sqrt (+ x 1)) (/ 1 n)) (pow (sqrt (+ x 1)) (/ 1 n)) (- (* (sqrt (pow x (/ 1 n))) (sqrt (pow x (/ 1 n))))))
759.0ms
(fma (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2)) (- (* (cbrt (pow x (/ 1 n))) (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))))))
672.0ms
(pow x (/ 1 (* (cbrt n) (cbrt n))))
621.0ms
(pow x (/ (* (cbrt 1) (cbrt 1)) (* (cbrt n) (cbrt n))))
581.0ms
(fma (pow 1 (/ 1 n)) (pow (+ x 1) (/ 1 n)) (- (* (pow (sqrt x) (/ 1 n)) (pow (sqrt x) (/ 1 n)))))

prune2.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.8b

localize58.0ms

Local error

Found 4 expressions with local error:

2.4b
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
2.4b
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
2.4b
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.9b
(log (exp (* (cbrt (expm1 (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))))) (cbrt (expm1 (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))))))))

rewrite227.0ms

Algorithm
rewrite-expression-head
Rules
198×unpow-prod-down
170×*-un-lft-identity
168×prod-diff
137×add-sqr-sqrt
101×add-cube-cbrt
66×sqr-pow
27×distribute-lft-out difference-of-squares
24×fma-neg
11×add-log-exp
9×distribute-lft-out--
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×log-prod sub-neg flip3-- diff-log log-pow flip--
1×exp-prod exp-to-pow rem-log-exp
Counts
4 → 290
Calls
4 calls:
Slowest
74.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
73.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
63.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
6.0ms
(log (exp (* (cbrt (expm1 (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))))) (cbrt (expm1 (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))))))))

series2.2s

Counts
4 → 12
Calls
4 calls:
Slowest
1.4s
(log (exp (* (cbrt (expm1 (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))))) (cbrt (expm1 (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))))))))
297.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
269.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
214.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

simplify2.2m

Counts
505 → 302
Calls
505 calls:
Slowest
850.0ms
(fma (pow (sqrt (+ x 1)) (/ 1 n)) (pow (sqrt (+ x 1)) (/ 1 n)) (- (* (pow x (/ 1 n)) (pow 1 (/ 1 n)))))
819.0ms
(fma 1 (pow (+ x 1) (/ 1 n)) (- (* (pow (sqrt x) (/ 1 n)) (pow (sqrt x) (/ 1 n)))))
818.0ms
(fma (pow 1 (/ 1 n)) (pow (+ x 1) (/ 1 n)) (- (* (pow (sqrt x) (/ 1 n)) (pow (sqrt x) (/ 1 n)))))
813.0ms
(fma (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))
590.0ms
(fma (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2)) (- (* (pow x (/ 1 n)) 1)))

prune4.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.8b

regimes227.0ms

Accuracy

86.3% (1.6b remaining)

Error of 19.4b against oracle of 17.8b and baseline of 29.4b

bsearch346.0ms

end0.0ms

sample8.1s

Algorithm
intervals
Results
2.7s3264×body1280valid
1.1s4618×body80valid
947.0ms1142×body10240exit
935.0ms1590×body640valid
572.0ms660×body1280nan
440.0ms4993×body80nan
372.0ms665×body640nan
352.0ms877×body320valid
136.0ms408×body320nan
94.0ms427×body160valid
35.0ms179×body160nan