Details

Time bar (total: 4.4s)

sample36.0ms

Algorithm
intervals
Results
14.0ms367×body80valid
4.0ms133×body80nan

simplify107.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0247
1535
21065
32695
49045
539765
650015

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.9b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1.0 (* 10.0 k))
0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
1.9b
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
13×add-exp-log
10×add-log-exp
8×add-cbrt-cube
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×fma-def
4×div-exp sum-log
3×pow1 expm1-log1p-u flip3-+ times-frac prod-exp associate-/r* flip-+ log1p-expm1-u
2×cbrt-undiv +-commutative associate-/r/
1×pow-to-exp associate-+l+ frac-2neg pow-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
3 → 61
Calls
3 calls:
5.0ms
(+ 1.0 (* 10.0 k))
23.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
34.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series153.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(+ 1.0 (* 10.0 k))
21.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
103.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify52.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0421510
11910434
25001411

prune193.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma 1 1.0 (* 10.0 k))
0.0b
(+ (fma 1 1.0 (* 10.0 k)) (* k k))
1.9b
(/ (* a (pow k m)) (+ (fma 1 1.0 (* 10.0 k)) (* k k)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
13×add-exp-log
8×add-cbrt-cube
6×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
5×add-log-exp
4×div-exp
3×pow1 expm1-log1p-u fma-def times-frac prod-exp associate-/r* log1p-expm1-u
2×cbrt-undiv flip3-+ associate-/r/ flip-+ fma-udef
1×+-commutative pow-to-exp associate-+l+ frac-2neg pow-exp clear-num sum-log cbrt-unprod div-inv associate-/l*
Counts
3 → 54
Calls
3 calls:
0.0ms
(fma 1 1.0 (* 10.0 k))
9.0ms
(+ (fma 1 1.0 (* 10.0 k)) (* k k))
15.0ms
(/ (* a (pow k m)) (+ (fma 1 1.0 (* 10.0 k)) (* k k)))

series157.0ms

Counts
3 → 9
Calls
3 calls:
32.0ms
(fma 1 1.0 (* 10.0 k))
17.0ms
(+ (fma 1 1.0 (* 10.0 k)) (* k k))
109.0ms
(/ (* a (pow k m)) (+ (fma 1 1.0 (* 10.0 k)) (* k k)))

simplify48.0ms

Algorithm
egg-herbie
Counts
63 → 63
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0355491
11648414
25001382

prune180.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (fma 1 1.0 (* 10.0 k)) (* k k))
0.0b
(/ (/ (* a (pow k m)) (sqrt (+ (fma 1 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (fma 1 1.0 (* 10.0 k)) (* k k))))
15.0b
(sqrt (+ (fma 1 1.0 (* 10.0 k)) (* k k)))
15.0b
(sqrt (+ (fma 1 1.0 (* 10.0 k)) (* k k)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
114×times-frac
66×sqrt-prod
58×add-sqr-sqrt
54×add-cube-cbrt *-un-lft-identity
20×add-exp-log sqrt-div
16×associate-/r/
13×add-cbrt-cube
12×associate-/l*
11×flip3-+ flip-+
9×div-exp
8×div-inv
6×pow1 associate-/r* add-log-exp
5×cbrt-undiv
4×expm1-log1p-u log1p-expm1-u
3×fma-def prod-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 hypot-def
1×+-commutative pow-to-exp associate-+l+ frac-2neg pow-exp clear-num sum-log cbrt-unprod fma-udef associate-/l/
Counts
4 → 166
Calls
4 calls:
6.0ms
(+ (fma 1 1.0 (* 10.0 k)) (* k k))
32.0ms
(/ (/ (* a (pow k m)) (sqrt (+ (fma 1 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (fma 1 1.0 (* 10.0 k)) (* k k))))
5.0ms
(sqrt (+ (fma 1 1.0 (* 10.0 k)) (* k k)))
5.0ms
(sqrt (+ (fma 1 1.0 (* 10.0 k)) (* k k)))

series218.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(+ (fma 1 1.0 (* 10.0 k)) (* k k))
110.0ms
(/ (/ (* a (pow k m)) (sqrt (+ (fma 1 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (fma 1 1.0 (* 10.0 k)) (* k k))))
42.0ms
(sqrt (+ (fma 1 1.0 (* 10.0 k)) (* k k)))
49.0ms
(sqrt (+ (fma 1 1.0 (* 10.0 k)) (* k k)))

simplify96.0ms

Algorithm
egg-herbie
Counts
178 → 178
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
07253177
132002816
250012802

prune503.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (* a (pow k m)) (sqrt (+ (fma 1 1.0 (* 10.0 k)) (* k k)))) (sqrt (sqrt (+ (fma 1 1.0 (* 10.0 k)) (* k k)))))
15.0b
(sqrt (+ (fma 1 1.0 (* 10.0 k)) (* k k)))
15.0b
(sqrt (+ (fma 1 1.0 (* 10.0 k)) (* k k)))
15.0b
(sqrt (+ (fma 1 1.0 (* 10.0 k)) (* k k)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
168×times-frac
156×sqrt-prod
82×add-sqr-sqrt
76×add-cube-cbrt *-un-lft-identity
30×sqrt-div
22×associate-/r/
20×add-exp-log
14×flip3-+ flip-+
13×add-cbrt-cube
12×associate-/l*
11×div-inv
9×div-exp associate-/r*
7×pow1
5×cbrt-undiv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 prod-exp hypot-def
1×pow-to-exp frac-2neg pow-exp clear-num cbrt-unprod associate-/l/
Counts
4 → 206
Calls
4 calls:
31.0ms
(/ (/ (* a (pow k m)) (sqrt (+ (fma 1 1.0 (* 10.0 k)) (* k k)))) (sqrt (sqrt (+ (fma 1 1.0 (* 10.0 k)) (* k k)))))
5.0ms
(sqrt (+ (fma 1 1.0 (* 10.0 k)) (* k k)))
5.0ms
(sqrt (+ (fma 1 1.0 (* 10.0 k)) (* k k)))
8.0ms
(sqrt (+ (fma 1 1.0 (* 10.0 k)) (* k k)))

series375.0ms

Counts
4 → 12
Calls
4 calls:
237.0ms
(/ (/ (* a (pow k m)) (sqrt (+ (fma 1 1.0 (* 10.0 k)) (* k k)))) (sqrt (sqrt (+ (fma 1 1.0 (* 10.0 k)) (* k k)))))
48.0ms
(sqrt (+ (fma 1 1.0 (* 10.0 k)) (* k k)))
42.0ms
(sqrt (+ (fma 1 1.0 (* 10.0 k)) (* k k)))
48.0ms
(sqrt (+ (fma 1 1.0 (* 10.0 k)) (* k k)))

simplify108.0ms

Algorithm
egg-herbie
Counts
218 → 218
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
08304633
136864316
250024264

prune688.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes80.0ms

Accuracy

98.8% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 2.1b

bsearch70.0ms

Steps
ItersRangePoint
9
4.496645835834823e+132
2.7823386642853144e+138
1.517993931788378e+137

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04734
15334
25334

end0.0ms

sample1.1s

Algorithm
intervals
Results
464.0ms11821×body80valid
144.0ms4195×body80nan