Details

Time bar (total: 5.3m)

sample379.0ms

Algorithm
intervals
Results
111.0ms104×body1280valid
80.0ms54×body640valid
54.0ms52×body10240exit
24.0ms28×body640nan
23.0ms155×body80valid
22.0ms17×body1280nan
22.0ms178×body80nan
10.0ms18×body320valid
6.0ms12×body320nan
5.0ms15×body160valid
2.0ms7×body160nan

simplify289.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
289.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.7b

localize16.0ms

Local error

Found 3 expressions with local error:

1.8b
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
0.9b
(pow (+ x 1) (/ 1 n))
0.0b
(pow x (/ 1 n))

rewrite103.0ms

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
80.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
14.0ms
(pow (+ x 1) (/ 1 n))
5.0ms
(pow x (/ 1 n))

series463.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
280.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
109.0ms
(pow (+ x 1) (/ 1 n))
74.0ms
(pow x (/ 1 n))

simplify39.7s

Counts
188 → 161
Calls
188 calls:
Slowest
844.0ms
(fma (* (cbrt (pow (+ x 1) (/ 1 n))) (cbrt (pow (+ x 1) (/ 1 n)))) (cbrt (pow (+ x 1) (/ 1 n))) (- (* (pow (sqrt x) (/ 1 n)) (pow (sqrt x) (/ 1 n)))))
567.0ms
(+ (pow (sqrt (+ x 1)) (/ 1 n)) (sqrt (pow x (/ 1 n))))
564.0ms
(fma (pow 1 (/ 1 n)) (pow (+ x 1) (/ 1 n)) (- (* (pow (sqrt x) (/ 1 n)) (pow (sqrt x) (/ 1 n)))))
499.0ms
(fma (pow 1 (/ 1 n)) (pow (+ x 1) (/ 1 n)) (- (* (pow (sqrt x) (/ 1 n)) (pow (sqrt x) (/ 1 n)))))
484.0ms
(+ (pow (sqrt (+ x 1)) (/ 1 n)) (pow (sqrt x) (/ 1 n)))

prune1.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.8b

localize21.0ms

Local error

Found 4 expressions with local error:

1.8b
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.8b
(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
0.9b
(pow (+ x 1) (/ 1 n))
0.0b
(exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))))

rewrite348.0ms

Algorithm
rewrite-expression-head
Rules
194×unpow-prod-down
174×*-un-lft-identity
168×prod-diff
143×add-sqr-sqrt
116×exp-sum
107×add-cube-cbrt
65×sqr-pow
61×log-prod
30×exp-prod
27×difference-of-squares
26×distribute-lft-out
16×log-pow
13×pow-unpow
9×times-frac distribute-lft-out-- add-log-exp
8×fma-neg
6×pow1
5×add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u
3×sub-neg
2×exp-diff diff-log rem-exp-log
1×pow-to-exp log-div pow-pow flip3-- rem-log-exp pow-exp div-inv flip--
Counts
4 → 297
Calls
4 calls:
Slowest
160.0ms
(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
107.0ms
(exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))))
67.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
7.0ms
(pow (+ x 1) (/ 1 n))

series904.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
319.0ms
(exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))))
242.0ms
(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
235.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
108.0ms
(pow (+ x 1) (/ 1 n))

simplify1.4m

Counts
328 → 309
Calls
328 calls:
Slowest
853.0ms
(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)))))
767.0ms
(exp (fma 1 (pow (+ x 1) (/ 1 n)) (- (* (pow x (/ 1 n)) (pow 1 (/ 1 n))))))
662.0ms
(log (exp (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)))))))
599.0ms
(- (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow x (/ 1 n))))
588.0ms
(- (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow x (/ 1 n))))

prune4.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.8b

localize36.0ms

Local error

Found 4 expressions with local error:

1.8b
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.8b
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.8b
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.8b
(log (exp (* (* (cbrt (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))) (cbrt (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))))) (cbrt (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))))

rewrite280.0ms

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
96.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
92.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
82.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
4.0ms
(log (exp (* (* (cbrt (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))) (cbrt (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))))) (cbrt (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
279.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
274.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
264.0ms
(log (exp (* (* (cbrt (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))) (cbrt (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))))) (cbrt (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))))
256.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

simplify2.0m

Counts
447 → 302
Calls
447 calls:
Slowest
950.0ms
(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)))))
725.0ms
(cbrt (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))))
670.0ms
(fma (- (sqrt (pow x (/ 1 n)))) (sqrt (pow x (/ 1 n))) (* (sqrt (pow x (/ 1 n))) (sqrt (pow x (/ 1 n)))))
583.0ms
(fma (- (cbrt (pow x (/ 1 n)))) (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))) (* (cbrt (pow x (/ 1 n))) (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n))))))
581.0ms
(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow (sqrt x) (/ 1 n)) (pow (sqrt x) (/ 1 n)))))

prune4.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.8b

localize47.0ms

Local error

Found 4 expressions with local error:

1.9b
(- (pow (+ x 1) (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))
0.9b
(pow (+ x 1) (/ (/ 1 n) 2))
0.9b
(pow (+ x 1) (/ (/ 1 n) 2))
0.2b
(/ (/ 1 n) 2)

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
207×times-frac
177×*-un-lft-identity
162×add-sqr-sqrt
150×add-cube-cbrt
86×pow-unpow
74×unpow-prod-down
56×prod-diff
24×sqr-pow
15×add-exp-log
13×div-inv associate-/l*
11×distribute-lft-out
9×add-cbrt-cube difference-of-squares
8×fma-neg
6×pow1 div-exp add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-/r* distribute-lft-out--
2×pow-to-exp pow-pow pow-exp
1×rec-exp clear-num sub-neg frac-2neg flip3-- diff-log 1-exp flip-- associate-/l/
Counts
4 → 288
Calls
4 calls:
Slowest
72.0ms
(- (pow (+ x 1) (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))
11.0ms
(/ (/ 1 n) 2)
8.0ms
(pow (+ x 1) (/ (/ 1 n) 2))
7.0ms
(pow (+ x 1) (/ (/ 1 n) 2))

series588.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
309.0ms
(- (pow (+ x 1) (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))
146.0ms
(pow (+ x 1) (/ (/ 1 n) 2))
115.0ms
(pow (+ x 1) (/ (/ 1 n) 2))
18.0ms
(/ (/ 1 n) 2)

simplify44.2s

Counts
350 → 300
Calls
350 calls:
Slowest
581.0ms
(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)))))
560.0ms
(fma (- (pow x (/ (/ 1 n) 2))) (pow 1 (/ (/ 1 n) 2)) (* (pow x (/ (/ 1 n) 2)) (pow 1 (/ (/ 1 n) 2))))
506.0ms
(pow (+ x 1) (/ (/ (/ 1 n) 2) 2))
505.0ms
(- (+ (* 1/2 (/ (log -1) n)) (+ 1 (* 1/2 (/ 1 (* x n))))) (* 1/2 (/ (log (/ -1 x)) n)))
500.0ms
(fma (pow (sqrt (+ x 1)) (/ (/ 1 n) 2)) (pow (sqrt (+ x 1)) (/ (/ 1 n) 2)) (- (* (sqrt (pow x (/ (/ 1 n) 2))) (sqrt (pow x (/ (/ 1 n) 2))))))

prune3.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.6b

regimes431.0ms

Accuracy

89.2% (1.3b remaining)

Error of 18.6b against oracle of 17.3b and baseline of 29.0b

bsearch437.0ms

end0.0ms

sample10.5s

Algorithm
intervals
Results
3.7s3122×body1280valid
1.3s1183×body10240exit
1.3s1613×body640valid
990.0ms5028×body80nan
776.0ms4854×body80valid
759.0ms618×body1280nan
448.0ms611×body640nan
431.0ms828×body320valid
217.0ms320×body320nan
127.0ms417×body160valid
104.0ms205×body160nan