Details

Time bar (total: 6.2s)

sample36.0ms

Algorithm
intervals
Results
15.0ms375×body80valid
5.0ms135×body80nan

simplify104.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
0247
1487
2966
32566
48916
539636
650026

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.8b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
0.0b
(* a (pow k m))
2.8b
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log
13×add-sqr-sqrt
10×add-cbrt-cube
8×add-cube-cbrt *-un-lft-identity add-log-exp
7×associate-*r*
6×prod-exp
4×unpow-prod-down div-exp
3×pow1 times-frac associate-*l* associate-/r* sum-log unswap-sqr
2×cbrt-undiv pow-to-exp flip3-+ pow-exp associate-/r/ cbrt-unprod flip-+ sqr-pow
1×+-commutative associate-+l+ frac-2neg clear-num *-commutative div-inv associate-/l*
Counts
3 → 63
Calls
3 calls:
10.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
6.0ms
(* a (pow k m))
14.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series203.0ms

Counts
3 → 9
Calls
3 calls:
18.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
65.0ms
(* a (pow k m))
120.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify54.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0405548
11965482
25001475

prune210.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 2.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(* a (pow k m))
0.0b
(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
14.7b
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
14.7b
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
114×times-frac
66×sqrt-prod
63×add-sqr-sqrt
56×add-cube-cbrt *-un-lft-identity
25×add-exp-log
20×sqrt-div
16×associate-/r/
15×add-cbrt-cube
12×associate-/l*
10×flip3-+ flip-+
9×div-exp
8×div-inv
7×associate-*r*
6×pow1 prod-exp associate-/r*
5×cbrt-undiv
4×unpow-prod-down add-log-exp
3×associate-*l* unswap-sqr
2×pow-to-exp rem-sqrt-square sqrt-pow1 pow1/2 pow-exp cbrt-unprod sqr-pow
1×frac-2neg clear-num *-commutative associate-/l/
Counts
4 → 166
Calls
4 calls:
6.0ms
(* a (pow k m))
40.0ms
(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
11.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
11.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series288.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(* a (pow k m))
120.0ms
(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
54.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
48.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify100.0ms

Algorithm
egg-herbie
Counts
178 → 178
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
07393131
137082808
250022808

prune527.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 2.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (+ 1.0 (* k (+ 10.0 k))) a) (pow k m))
0.0b
(* k (+ 10.0 k))
0.1b
(/ 1 (/ (/ (+ 1.0 (* k (+ 10.0 k))) a) (pow k m)))
5.9b
(/ (+ 1.0 (* k (+ 10.0 k))) a)

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
1073×times-frac
500×add-sqr-sqrt *-un-lft-identity
498×add-cube-cbrt
198×unpow-prod-down
105×associate-/r*
70×add-exp-log
66×sqr-pow
51×div-exp
43×div-inv
22×add-cbrt-cube
19×associate-/l*
10×cbrt-undiv
8×pow-to-exp pow-exp
7×pow1 rec-exp 1-exp
4×associate-*r* add-log-exp
3×frac-2neg associate-*l* clear-num associate-/l/
2×flip3-+ associate-*r/ flip-+
1×distribute-rgt-in pow-flip distribute-lft-in pow-prod-down prod-exp associate-/r/ *-commutative cbrt-unprod distribute-lft-out inv-pow unswap-sqr
Counts
4 → 602
Calls
4 calls:
15.0ms
(/ (/ (+ 1.0 (* k (+ 10.0 k))) a) (pow k m))
10.0ms
(* k (+ 10.0 k))
32.0ms
(/ 1 (/ (/ (+ 1.0 (* k (+ 10.0 k))) a) (pow k m)))
9.0ms
(/ (+ 1.0 (* k (+ 10.0 k))) a)

series308.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(/ (/ (+ 1.0 (* k (+ 10.0 k))) a) (pow k m))
50.0ms
(* k (+ 10.0 k))
111.0ms
(/ 1 (/ (/ (+ 1.0 (* k (+ 10.0 k))) a) (pow k m)))
40.0ms
(/ (+ 1.0 (* k (+ 10.0 k))) a)

simplify126.0ms

Algorithm
egg-herbie
Counts
614 → 614
Iterations

Useful iterations: 1 (40.0ms)

IterNodesCost
021789172
150028740

prune1.6s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 2.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (/ (+ (/ (pow k 2) a) (+ (* 1.0 (/ 1 a)) (* 10.0 (/ k a)))) (pow k m)))
0.3b
(* 10.0 (/ k a))
0.7b
(+ (/ (pow k 2) a) (+ (* 1.0 (/ 1 a)) (* 10.0 (/ k a))))
9.5b
(/ (pow k 2) a)

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
242×times-frac
184×*-un-lft-identity
131×add-sqr-sqrt
126×add-cube-cbrt
60×unpow-prod-down
36×add-exp-log
35×associate-/r*
29×distribute-lft-out
21×div-exp
20×sqr-pow
16×add-cbrt-cube
13×associate-*r*
11×associate-/l*
9×add-log-exp
7×pow1 div-inv
6×frac-add
5×cbrt-undiv
4×pow-to-exp rec-exp 1-exp associate-*r/ pow-exp unpow2
3×associate-*l* sum-log
2×frac-2neg flip3-+ prod-exp clear-num cbrt-unprod flip-+ unswap-sqr
1×+-commutative associate-+r+ pow-flip pow-prod-down associate-/r/ un-div-inv *-commutative inv-pow
Counts
4 → 257
Calls
4 calls:
58.0ms
(/ 1 (/ (+ (/ (pow k 2) a) (+ (* 1.0 (/ 1 a)) (* 10.0 (/ k a)))) (pow k m)))
8.0ms
(* 10.0 (/ k a))
44.0ms
(+ (/ (pow k 2) a) (+ (* 1.0 (/ 1 a)) (* 10.0 (/ k a))))
7.0ms
(/ (pow k 2) a)

series188.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(/ 1 (/ (+ (/ (pow k 2) a) (+ (* 1.0 (/ 1 a)) (* 10.0 (/ k a)))) (pow k m)))
34.0ms
(* 10.0 (/ k a))
36.0ms
(+ (/ (pow k 2) a) (+ (* 1.0 (/ 1 a)) (* 10.0 (/ k a))))
19.0ms
(/ (pow k 2) a)

simplify62.0ms

Algorithm
egg-herbie
Counts
269 → 269
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
011013778
150023439

prune874.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes72.0ms

Accuracy

0% (1.8b remaining)

Error of 1.9b against oracle of 0.1b and baseline of 1.9b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02512
12712
22712

end0.0ms

sample1.0s

Algorithm
intervals
Results
485.0ms11990×body80valid
146.0ms4349×body80nan