Details

Time bar (total: 53.9s)

sample198.0ms

Algorithm
intervals
Results
55.0ms90×body1280valid
32.0ms67×body640valid
22.0ms39×body10240exit
14.0ms172×body80valid
10.0ms21×body640nan
9.0ms31×body320valid
9.0ms169×body80nan
8.0ms14×body1280nan
4.0ms11×body320nan
2.0ms9×body160valid
1.0ms5×body160nan

simplify3.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0813
11713
23513
38613
424513
573013
6368813
done500013

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.8b
(pow (+ x 1.0) (/ 1.0 n))
0.8b
(pow x (/ 1.0 n))
1.8b
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite168.0ms

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 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 → 149
Calls
3 calls:
13.0ms
(pow (+ x 1.0) (/ 1.0 n))
4.0ms
(pow x (/ 1.0 n))
143.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series693.0ms

Counts
3 → 9
Calls
3 calls:
215.0ms
(pow (+ x 1.0) (/ 1.0 n))
108.0ms
(pow x (/ 1.0 n))
370.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.6s

Counts
158 → 158
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02714785
16473566
216203020
done50002646

prune544.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 23.0b

localize68.0ms

Local error

Found 4 expressions with local error:

0.8b
(pow (cbrt x) (/ 1.0 n))
0.8b
(pow (cbrt x) (/ 1.0 n))
0.8b
(pow (cbrt x) (/ 1.0 n))
3.3b
(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
39×pow-unpow
31×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
27×times-frac
18×unpow-prod-down
9×cbrt-prod
7×pow1 add-exp-log
6×pow-pow
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow-to-exp pow1/3 pow-exp div-inv sqr-pow
1×fma-udef
Counts
4 → 109
Calls
4 calls:
11.0ms
(pow (cbrt x) (/ 1.0 n))
13.0ms
(pow (cbrt x) (/ 1.0 n))
5.0ms
(pow (cbrt x) (/ 1.0 n))
0.0ms
(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))

series2.6s

Counts
4 → 12
Calls
4 calls:
161.0ms
(pow (cbrt x) (/ 1.0 n))
139.0ms
(pow (cbrt x) (/ 1.0 n))
143.0ms
(pow (cbrt x) (/ 1.0 n))
2.1s
(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))

simplify1.2s

Counts
121 → 121
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02101967
15611804
216931673
done50001649

prune928.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 22.9b

localize74.0ms

Local error

Found 4 expressions with local error:

0.8b
(pow (cbrt x) (/ 1.0 n))
1.8b
(- (/ (/ 1.0 n) x) (/ 0.5 (* (pow x 2) n)))
6.4b
(* (/ 1.0 (pow n 2)) (+ (/ (* (- (log x)) -1/3) x) (/ -2/3 (/ x (- (log x))))))
8.7b
(* (pow x 2) n)

rewrite642.0ms

Algorithm
rewrite-expression-head
Rules
697×times-frac
425×add-sqr-sqrt
402×*-un-lft-identity
398×add-cube-cbrt
301×prod-diff
77×div-inv
43×fma-neg
36×associate-*l*
20×add-exp-log unpow-prod-down
13×pow-unpow
11×add-cbrt-cube
9×unswap-sqr
7×pow1 associate-*r* prod-exp sqr-pow
6×unpow2 add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×cbrt-prod frac-times pow-to-exp associate-*r/ div-exp pow-exp cbrt-unprod difference-of-squares
2×pow-pow flip3-+ frac-add *-commutative flip-+
1×cbrt-undiv distribute-rgt-in sub-neg flip3-- distribute-lft-in pow1/3 diff-log pow-prod-down associate-*l/ frac-sub flip-- distribute-lft-out distribute-lft-out--
Counts
4 → 488
Calls
4 calls:
5.0ms
(pow (cbrt x) (/ 1.0 n))
114.0ms
(- (/ (/ 1.0 n) x) (/ 0.5 (* (pow x 2) n)))
459.0ms
(* (/ 1.0 (pow n 2)) (+ (/ (* (- (log x)) -1/3) x) (/ -2/3 (/ x (- (log x))))))
16.0ms
(* (pow x 2) n)

series362.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(pow (cbrt x) (/ 1.0 n))
99.0ms
(- (/ (/ 1.0 n) x) (/ 0.5 (* (pow x 2) n)))
95.0ms
(* (/ 1.0 (pow n 2)) (+ (/ (* (- (log x)) -1/3) x) (/ -2/3 (/ x (- (log x))))))
28.0ms
(* (pow x 2) n)

simplify1.2s

Counts
500 → 500
Iterations

Useful iterations: done (1.2s)

IterNodesCost
074721047
1193316770
done500114030

prune3.9s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 22.8b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 0.5 (* (pow x 2) n))
0.8b
(/ (- (log x)) (pow n 2))
2.1b
(* (/ 1.0 x) (- (/ 1 n) (/ (- (log x)) (pow n 2))))
8.7b
(* (pow x 2) n)

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
4433×times-frac
2796×add-sqr-sqrt
2763×*-un-lft-identity
2744×add-cube-cbrt
2600×prod-diff
1303×distribute-rgt-in distribute-lft-in
982×unpow-prod-down
870×distribute-rgt-neg-in
868×distribute-lft-neg-in
441×pow1
435×log-pow
330×unpow2 sqr-pow
230×div-inv
217×neg-mul-1
29×add-exp-log
26×associate-*r*
21×associate-*l*
18×add-cbrt-cube
15×associate-/l* difference-of-squares
9×associate-/r*
8×div-exp prod-exp
6×unswap-sqr
5×distribute-lft-out--
4×cbrt-undiv expm1-log1p-u cbrt-unprod log1p-expm1-u add-log-exp
3×neg-sub0 frac-times pow-to-exp div-sub associate-*r/ pow-exp
2×sub-neg flip3-- frac-2neg clear-num *-commutative frac-sub flip-- associate--r-
1×distribute-frac-neg pow-prod-down associate-*l/
Counts
4 → 2854
Calls
4 calls:
9.0ms
(/ 0.5 (* (pow x 2) n))
14.0ms
(/ (- (log x)) (pow n 2))
934.0ms
(* (/ 1.0 x) (- (/ 1 n) (/ (- (log x)) (pow n 2))))
24.0ms
(* (pow x 2) n)

series361.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(/ 0.5 (* (pow x 2) n))
98.0ms
(/ (- (log x)) (pow n 2))
206.0ms
(* (/ 1.0 x) (- (/ 1 n) (/ (- (log x)) (pow n 2))))
26.0ms
(* (pow x 2) n)

simplify10.1s

Counts
2866 → 2866
Iterations

Useful iterations: done (9.8s)

IterNodesCost
03603192576
done5001173755

prune16.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 22.8b

regimes482.0ms

Accuracy

83.8% (1.4b remaining)

Error of 22.1b against oracle of 20.7b and baseline of 29.5b

bsearch270.0ms

Steps
ItersRangePoint
5
65877241274.64672
241918210538.82648
96674705739.32524
10
-8534861749055764.0
-1.8687997873074387
-23787117.005651087

simplify35.0ms

Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
059175
180175
289174
390174
done90174

end0.0ms

sample7.4s

Algorithm
intervals
Results
2.1s3159×body1280valid
878.0ms635×body1280nan
830.0ms1602×body640valid
793.0ms1125×body10240exit
775.0ms662×body640nan
435.0ms4813×body80valid
325.0ms5108×body80nan
297.0ms882×body320valid
130.0ms337×body320nan
82.0ms444×body160valid
30.0ms187×body160nan