Details

Time bar (total: 15.6s)

sample215.0ms

Algorithm
intervals
Results
63.0ms133×body1280valid
38.0ms59×body1280nan
27.0ms67×body640nan
22.0ms57×body10240exit
15.0ms47×body640valid
8.0ms192×body80nan
7.0ms31×body320valid
7.0ms27×body320nan
4.0ms91×body80valid
2.0ms14×body160valid
2.0ms14×body160nan

simplify35.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0176
1356
2856
32496
49116
550016

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(pow x (/ 1.0 n))
0.0b
(pow (+ x 1.0) (/ 1.0 n))
2.7b
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite32.0ms

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:
4.0ms
(pow x (/ 1.0 n))
5.0ms
(pow (+ x 1.0) (/ 1.0 n))
16.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series485.0ms

Counts
3 → 9
Calls
3 calls:
56.0ms
(pow x (/ 1.0 n))
149.0ms
(pow (+ x 1.0) (/ 1.0 n))
280.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify72.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
06542164
121641642
250021637

prune349.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)
5.4b
(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)))))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
1×fma-udef
Counts
4 → 49
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
1.0ms
(cbrt x)
1.0ms
(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)))))

series1.8s

Counts
4 → 12
Calls
4 calls:
181.0ms
(cbrt x)
190.0ms
(cbrt x)
182.0ms
(cbrt x)
1.3s
(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)))))

simplify42.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0404566
11474510
25001501

prune379.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 19.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (sqrt x) (/ 1.0 n))
0.0b
(pow (+ x 1.0) (/ 1.0 n))
2.7b
(- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n))))
6.2b
(fma (pow (sqrt x) (/ 1.0 n)) (- (pow (sqrt x) (/ 1.0 n))) (pow (sqrt x) (* 2 (/ 1.0 n))))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
112×unpow-prod-down
93×*-un-lft-identity
84×add-sqr-sqrt
80×prod-diff
67×add-cube-cbrt
30×sqrt-prod
28×sqr-pow
26×pow-unpow
18×times-frac
12×distribute-lft-out difference-of-squares
8×fma-neg
7×pow1
6×add-exp-log add-log-exp
4×expm1-log1p-u pow-pow add-cbrt-cube log1p-expm1-u
2×pow-to-exp pow-exp div-inv
1×sub-neg flip3-- sqrt-pow1 pow1/2 diff-log sqrt-pow2 flip-- fma-udef distribute-lft-out--
Counts
4 → 190
Calls
4 calls:
4.0ms
(pow (sqrt x) (/ 1.0 n))
6.0ms
(pow (+ x 1.0) (/ 1.0 n))
18.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n))))
1.0ms
(fma (pow (sqrt x) (/ 1.0 n)) (- (pow (sqrt x) (/ 1.0 n))) (pow (sqrt x) (* 2 (/ 1.0 n))))

series2.0s

Counts
4 → 12
Calls
4 calls:
227.0ms
(pow (sqrt x) (/ 1.0 n))
149.0ms
(pow (+ x 1.0) (/ 1.0 n))
467.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n))))
1.1s
(fma (pow (sqrt x) (/ 1.0 n)) (- (pow (sqrt x) (/ 1.0 n))) (pow (sqrt x) (* 2 (/ 1.0 n))))

simplify90.0ms

Algorithm
egg-herbie
Counts
202 → 202
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
08364182
128673044
250013025

prune604.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 19.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(sqrt (sqrt x))
0.2b
(sqrt (sqrt x))
2.7b
(- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n))))
5.8b
(fma (pow (sqrt x) (/ 1.0 n)) (- (* (pow (sqrt (sqrt x)) (/ 1.0 n)) (pow (sqrt (sqrt x)) (/ 1.0 n)))) (pow (sqrt x) (* 2 (/ 1.0 n))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
102×unpow-prod-down
80×prod-diff
78×*-un-lft-identity
75×add-sqr-sqrt
54×add-cube-cbrt
47×sqrt-prod
26×sqr-pow
12×difference-of-squares
11×distribute-lft-out
8×pow1 sqrt-pow1 fma-neg
6×add-log-exp
4×add-exp-log expm1-log1p-u rem-sqrt-square pow1/2 add-cbrt-cube log1p-expm1-u
1×sub-neg flip3-- diff-log flip-- fma-udef distribute-lft-out--
Counts
4 → 167
Calls
4 calls:
2.0ms
(sqrt (sqrt x))
2.0ms
(sqrt (sqrt x))
18.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n))))
1.0ms
(fma (pow (sqrt x) (/ 1.0 n)) (- (* (pow (sqrt (sqrt x)) (/ 1.0 n)) (pow (sqrt (sqrt x)) (/ 1.0 n)))) (pow (sqrt x) (* 2 (/ 1.0 n))))

series1.8s

Counts
4 → 12
Calls
4 calls:
142.0ms
(sqrt (sqrt x))
142.0ms
(sqrt (sqrt x))
468.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n))))
1.0s
(fma (pow (sqrt x) (/ 1.0 n)) (- (* (pow (sqrt (sqrt x)) (/ 1.0 n)) (pow (sqrt (sqrt x)) (/ 1.0 n)))) (pow (sqrt x) (* 2 (/ 1.0 n))))

simplify91.0ms

Algorithm
egg-herbie
Counts
179 → 179
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
08124113
128122963
250012962

prune573.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 19.8b

regimes258.0ms

Accuracy

84.5% (1.8b remaining)

Error of 23.6b against oracle of 21.8b and baseline of 33.3b

bsearch2.0ms

simplify6.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
084106
184106

end0.0ms

sample6.6s

Algorithm
intervals
Results
1.9s3981×body1280valid
1.3s2166×body1280nan
744.0ms1811×body640nan
627.0ms1839×body640valid
611.0ms1428×body10240exit
268.0ms6185×body80nan
227.0ms896×body320nan
189.0ms872×body320valid
148.0ms2985×body80valid
69.0ms447×body160nan
63.0ms453×body160valid