Details

Time bar (total: 6.0s)

sample41.0ms

Algorithm
intervals
Results
21.0ms411×body80valid
4.0ms119×body80nan

simplify104.0ms

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: 2.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (* 10.0 k))
0.0b
(* a (pow k m))
0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
2.2b
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
19×add-exp-log
16×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
7×associate-*r*
6×fma-def prod-exp
4×pow1 expm1-log1p-u unpow-prod-down div-exp sum-log log1p-expm1-u
3×flip3-+ times-frac associate-*l* associate-/r* flip-+ unswap-sqr
2×cbrt-undiv +-commutative pow-to-exp pow-exp associate-/r/ cbrt-unprod sqr-pow
1×associate-+l+ frac-2neg clear-num *-commutative div-inv associate-/l*
Counts
4 → 88
Calls
4 calls:
3.0ms
(+ 1.0 (* 10.0 k))
5.0ms
(* a (pow k m))
5.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
8.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series229.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(+ 1.0 (* 10.0 k))
56.0ms
(* a (pow k m))
18.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
118.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify58.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
0477629
12275544
25001524

prune279.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(* a (pow k m))
0.0b
(fma 10.0 k 1.0)
0.4b
(/ 1 (fma k k (fma 10.0 k 1.0)))
1.9b
(* (* a (pow k m)) (/ 1 (fma k k (fma 10.0 k 1.0))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
57×add-exp-log
31×prod-exp
27×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
20×associate-*r* add-cbrt-cube
18×times-frac
10×div-exp
7×pow1 cbrt-unprod
5×pow-to-exp rec-exp 1-exp pow-exp
4×expm1-log1p-u unpow-prod-down associate-*l* log1p-expm1-u add-log-exp
3×cbrt-undiv associate-/r* associate-/l* unswap-sqr
2×*-commutative div-inv sqr-pow
1×pow-flip frac-2neg associate-*r/ pow-prod-down clear-num un-div-inv fma-udef inv-pow
Counts
4 → 117
Calls
4 calls:
5.0ms
(* a (pow k m))
1.0ms
(fma 10.0 k 1.0)
3.0ms
(/ 1 (fma k k (fma 10.0 k 1.0)))
8.0ms
(* (* a (pow k m)) (/ 1 (fma k k (fma 10.0 k 1.0))))

series253.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(* a (pow k m))
31.0ms
(fma 10.0 k 1.0)
43.0ms
(/ 1 (fma k k (fma 10.0 k 1.0)))
117.0ms
(* (* a (pow k m)) (/ 1 (fma k k (fma 10.0 k 1.0))))

simplify67.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
0512805
12653698
25001671

prune284.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt k)
0.6b
(cbrt k)
0.6b
(* (cbrt k) (cbrt k))
2.2b
(/ (* (* a (pow (* (cbrt k) (cbrt k)) m)) (pow (cbrt k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
60×add-exp-log
31×prod-exp
24×add-sqr-sqrt
22×cbrt-prod
16×add-cube-cbrt *-un-lft-identity div-exp
13×add-cbrt-cube
11×pow1 pow-exp
8×pow-to-exp pow1/3
6×swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u cbrt-unprod log1p-expm1-u add-log-exp unswap-sqr
3×cbrt-undiv times-frac associate-/r*
2×pow-prod-down associate-/r/ pow-sqr pow-prod-up
1×pow2 frac-2neg flip3-+ pow-plus clear-num *-commutative flip-+ div-inv associate-/l*
Counts
4 → 108
Calls
4 calls:
1.0ms
(cbrt k)
1.0ms
(cbrt k)
5.0ms
(* (cbrt k) (cbrt k))
13.0ms
(/ (* (* a (pow (* (cbrt k) (cbrt k)) m)) (pow (cbrt k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series928.0ms

Counts
4 → 12
Calls
4 calls:
173.0ms
(cbrt k)
181.0ms
(cbrt k)
193.0ms
(* (cbrt k) (cbrt k))
381.0ms
(/ (* (* a (pow (* (cbrt k) (cbrt k)) m)) (pow (cbrt k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify76.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
05631055
12772909
25003844

prune368.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

4.6b
(pow (/ 1 k) -2/3)
6.1b
(/ (* 10.0 (* (* (pow (pow (/ 1 k) -2/3) m) a) (pow (pow (/ 1 k) -1/3) m))) (pow k 3))
8.1b
(- (* (/ (* (pow (pow (/ 1 k) -2/3) m) a) k) (/ (pow (pow (/ 1 k) -1/3) m) k)) (/ (* 10.0 (* (* (pow (pow (/ 1 k) -2/3) m) a) (pow (pow (/ 1 k) -1/3) m))) (pow k 3)))
10.7b
(fma 99.0 (/ (* (pow (pow (/ 1 k) -2/3) m) a) (/ (pow k 4) (pow (pow (/ 1 k) -1/3) m))) (- (* (/ (* (pow (pow (/ 1 k) -2/3) m) a) k) (/ (pow (pow (/ 1 k) -1/3) m) k)) (/ (* 10.0 (* (* (pow (pow (/ 1 k) -2/3) m) a) (pow (pow (/ 1 k) -1/3) m))) (pow k 3))))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
955×add-exp-log
627×prod-exp
588×pow-exp
326×div-exp
177×pow-to-exp
52×rec-exp 1-exp
33×times-frac
22×add-sqr-sqrt add-cube-cbrt unpow-prod-down *-un-lft-identity
18×add-cbrt-cube
16×prod-diff
12×associate-/r*
9×cube-prod
6×pow1 cbrt-unprod add-log-exp
4×cbrt-undiv expm1-log1p-u log1p-expm1-u sqr-pow
3×cube-mult pow-unpow pow-pow unpow3 frac-sub div-inv
1×frac-times sub-neg flip3-- pow-flip frac-2neg fma-neg diff-log associate-*r/ associate-*l/ clear-num flip-- fma-udef associate-/l* inv-pow
Counts
4 → 341
Calls
4 calls:
5.0ms
(pow (/ 1 k) -2/3)
28.0ms
(/ (* 10.0 (* (* (pow (pow (/ 1 k) -2/3) m) a) (pow (pow (/ 1 k) -1/3) m))) (pow k 3))
33.0ms
(- (* (/ (* (pow (pow (/ 1 k) -2/3) m) a) k) (/ (pow (pow (/ 1 k) -1/3) m) k)) (/ (* 10.0 (* (* (pow (pow (/ 1 k) -2/3) m) a) (pow (pow (/ 1 k) -1/3) m))) (pow k 3)))
1.0ms
(fma 99.0 (/ (* (pow (pow (/ 1 k) -2/3) m) a) (/ (pow k 4) (pow (pow (/ 1 k) -1/3) m))) (- (* (/ (* (pow (pow (/ 1 k) -2/3) m) a) k) (/ (pow (pow (/ 1 k) -1/3) m) k)) (/ (* 10.0 (* (* (pow (pow (/ 1 k) -2/3) m) a) (pow (pow (/ 1 k) -1/3) m))) (pow k 3))))

series1.3s

Counts
4 → 12
Calls
4 calls:
181.0ms
(pow (/ 1 k) -2/3)
305.0ms
(/ (* 10.0 (* (* (pow (pow (/ 1 k) -2/3) m) a) (pow (pow (/ 1 k) -1/3) m))) (pow k 3))
421.0ms
(- (* (/ (* (pow (pow (/ 1 k) -2/3) m) a) k) (/ (pow (pow (/ 1 k) -1/3) m) k)) (/ (* 10.0 (* (* (pow (pow (/ 1 k) -2/3) m) a) (pow (pow (/ 1 k) -1/3) m))) (pow k 3)))
367.0ms
(fma 99.0 (/ (* (pow (pow (/ 1 k) -2/3) m) a) (/ (pow k 4) (pow (pow (/ 1 k) -1/3) m))) (- (* (/ (* (pow (pow (/ 1 k) -2/3) m) a) k) (/ (pow (pow (/ 1 k) -1/3) m) k)) (/ (* 10.0 (* (* (pow (pow (/ 1 k) -2/3) m) a) (pow (pow (/ 1 k) -1/3) m))) (pow k 3))))

simplify80.0ms

Algorithm
egg-herbie
Counts
353 → 353
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
017325491
150014996

prune585.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes97.0ms

Accuracy

97.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 2.0b

bsearch23.0ms

Steps
ItersRangePoint
3
8.208831046085106e+84
1.1183385225251127e+85
8.766559954678734e+84

simplify7.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04639
14639

end0.0ms

sample1.0s

Algorithm
intervals
Results
528.0ms11874×body80valid
156.0ms4213×body80nan