Details

Time bar (total: 10.0s)

sample139.0ms

Algorithm
intervals
Results
44.0ms101×body1280valid
17.0ms30×body10240exit
15.0ms46×body640valid
13.0ms29×body1280nan
8.0ms23×body640nan
8.0ms141×body80valid
7.0ms33×body320valid
6.0ms179×body80nan
2.0ms15×body160valid
2.0ms9×body320nan
1.0ms8×body160nan

simplify34.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0176
1346
2806
32366
48686
550016

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize8.0ms

Local error

Found 3 expressions with local error:

1.0b
(pow (+ x 1.0) (/ 1.0 n))
1.2b
(pow x (/ 1.0 n))
2.3b
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
28×*-un-lft-identity
26×pow-unpow
19×add-cube-cbrt
18×times-frac
17×unpow-prod-down
9×difference-of-squares
8×sqr-pow
5×pow1 add-exp-log add-log-exp
3×add-cbrt-cube distribute-lft-out--
2×pow-to-exp pow-pow pow-exp div-inv distribute-lft-out
1×sub-neg flip3-- diff-log flip--
Counts
3 → 79
Calls
3 calls:
5.0ms
(pow (+ x 1.0) (/ 1.0 n))
2.0ms
(pow x (/ 1.0 n))
45.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series489.0ms

Counts
3 → 9
Calls
3 calls:
154.0ms
(pow (+ x 1.0) (/ 1.0 n))
60.0ms
(pow x (/ 1.0 n))
275.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify64.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
0476639
11600623
25001609

prune231.0ms

Filtered
88 candidates to 70 candidates (79.5%)
Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 19.5b

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b
(pow (+ x 1.0) (/ 1.0 n))
1.2b
(pow x (/ 1.0 n))
1.2b
(pow x (/ 1.0 n))
2.3b
(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))

rewrite191.0ms

Algorithm
rewrite-expression-head
Rules
52×add-sqr-sqrt
39×pow-unpow *-un-lft-identity
30×sqrt-prod
28×add-cube-cbrt
27×times-frac
22×unpow-prod-down
16×difference-of-squares
11×sqr-pow
7×pow1 add-exp-log
6×add-log-exp
4×add-cbrt-cube distribute-lft-out--
3×pow-to-exp pow-pow pow-exp div-inv
2×distribute-lft-out
1×sub-neg flip3-- diff-log flip--
Counts
4 → 114
Calls
4 calls:
5.0ms
(pow (+ x 1.0) (/ 1.0 n))
2.0ms
(pow x (/ 1.0 n))
2.0ms
(pow x (/ 1.0 n))
45.0ms
(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))

series607.0ms

Counts
4 → 12
Calls
4 calls:
146.0ms
(pow (+ x 1.0) (/ 1.0 n))
57.0ms
(pow x (/ 1.0 n))
54.0ms
(pow x (/ 1.0 n))
349.0ms
(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))

simplify46.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
05021017
11683983
25002969

prune443.0ms

Filtered
126 candidates to 94 candidates (74.6%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.4b

localize19.0ms

Local error

Found 4 expressions with local error:

1.2b
(pow x (/ 1.0 n))
1.2b
(pow x (/ (/ 1.0 n) 2))
1.2b
(pow x (/ (/ 1.0 n) 2))
2.5b
(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
141×times-frac
99×pow-unpow
94×add-sqr-sqrt
86×*-un-lft-identity
84×add-cube-cbrt
11×unpow-prod-down
10×sqrt-prod
9×div-inv
8×difference-of-squares
7×pow1 add-exp-log
6×add-log-exp
5×sqr-pow
4×add-cbrt-cube
3×pow-to-exp pow-pow pow-exp
1×sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 162
Calls
4 calls:
2.0ms
(pow x (/ 1.0 n))
5.0ms
(pow x (/ (/ 1.0 n) 2))
5.0ms
(pow x (/ (/ 1.0 n) 2))
44.0ms
(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))))

series570.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(pow x (/ 1.0 n))
60.0ms
(pow x (/ (/ 1.0 n) 2))
55.0ms
(pow x (/ (/ 1.0 n) 2))
395.0ms
(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))))

simplify66.0ms

Algorithm
egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
07791369
128841323
250011321

prune803.0ms

Filtered
174 candidates to 143 candidates (82.2%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 19.4b

localize30.0ms

Local error

Found 4 expressions with local error:

1.7b
(* (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n)))) (+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))))) (/ (/ 0.5 n) x)))
1.8b
(+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))))) (/ (/ 0.5 n) x))
7.1b
(* x (pow n 2))
9.2b
(* (pow x 2) n)

rewrite230.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
25×*-un-lft-identity
18×associate-*l*
17×associate-*r/
16×add-exp-log frac-add
15×associate-*r*
14×flip3-+ flip-+
12×add-cube-cbrt unpow-prod-down distribute-neg-frac
10×frac-times add-cbrt-cube
9×unswap-sqr
8×add-log-exp
7×prod-exp distribute-lft-out
6×pow1 sqrt-prod
4×unpow2 sqr-pow
3×*-commutative cbrt-unprod
2×distribute-rgt-in pow-to-exp associate-+l+ distribute-neg-in distribute-lft-in associate-*l/ pow-exp sum-log
1×+-commutative neg-sub0 associate-+l- pow-prod-down neg-log
Counts
4 → 115
Calls
4 calls:
191.0ms
(* (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n)))) (+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))))) (/ (/ 0.5 n) x)))
24.0ms
(+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))))) (/ (/ 0.5 n) x))
5.0ms
(* x (pow n 2))
6.0ms
(* (pow x 2) n)

series590.0ms

Counts
4 → 12
Calls
4 calls:
457.0ms
(* (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n)))) (+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))))) (/ (/ 0.5 n) x)))
86.0ms
(+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))))) (/ (/ 0.5 n) x))
29.0ms
(* x (pow n 2))
18.0ms
(* (pow x 2) n)

simplify53.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09442456
150012289

prune610.0ms

Filtered
127 candidates to 93 candidates (73.2%)
Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 19.3b

regimes320.0ms

Accuracy

79.4% (1.9b remaining)

Error of 22.3b against oracle of 20.4b and baseline of 29.5b

bsearch211.0ms

Steps
ItersRangePoint
6
927621.7061119184
6803969.331336576
2460917.9181734445
11
-4240874295.0135207
-2.472407816558163e-13
-3965823.9428030387

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05745
15745

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.4s3157×body1280valid
540.0ms1608×body640valid
487.0ms1158×body10240exit
267.0ms596×body1280nan
250.0ms4755×body80valid
209.0ms647×body640nan
199.0ms5185×body80nan
184.0ms852×body320valid
66.0ms358×body320nan
61.0ms436×body160valid
21.0ms190×body160nan