Details

Time bar (total: 13.2s)

sample40.0ms

Algorithm
intervals
Results
24.0ms256×body80valid

simplify41.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (15.0ms)

IterNodesCost
0911
11511
22211
32610
42910
53010
done3010

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 1 expressions with local error:

6.9b
(/ y (+ 1.0 (/ (* x y) 2.0)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
12×times-frac
10×add-sqr-sqrt add-cube-cbrt
4×associate-/r* distribute-lft-out
3×add-exp-log add-cbrt-cube associate-/l*
2×associate-/r/
1×pow1 cbrt-undiv expm1-log1p-u frac-2neg flip3-+ div-exp clear-num flip-+ log1p-expm1-u div-inv add-log-exp
Counts
1 → 35
Calls
1 calls:
17.0ms
(/ y (+ 1.0 (/ (* x y) 2.0)))

series97.0ms

Counts
1 → 3
Calls
1 calls:
97.0ms
(/ y (+ 1.0 (/ (* x y) 2.0)))

simplify1.5s

Counts
38 → 38
Iterations

Useful iterations: 3 (468.0ms)

IterNodesCost
091604
1213582
2611538
31819493
done5001493

prune148.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ 1 (/ (fma (/ x 2.0) y 1.0) y))
6.8b
(/ (fma (/ x 2.0) y 1.0) y)

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
52×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×associate-/r*
15×add-exp-log
9×add-cbrt-cube
8×div-exp
6×div-inv associate-/l*
4×cbrt-undiv
3×pow1
2×expm1-log1p-u rec-exp frac-2neg 1-exp clear-num log1p-expm1-u add-log-exp
1×pow-flip associate-/r/ inv-pow
Counts
2 → 107
Calls
2 calls:
10.0ms
(/ 1 (/ (fma (/ x 2.0) y 1.0) y))
5.0ms
(/ (fma (/ x 2.0) y 1.0) y)

series166.0ms

Counts
2 → 6
Calls
2 calls:
85.0ms
(/ 1 (/ (fma (/ x 2.0) y 1.0) y))
81.0ms
(/ (fma (/ x 2.0) y 1.0) y)

simplify2.2s

Counts
113 → 113
Iterations

Useful iterations: 3 (766.0ms)

IterNodesCost
01842005
13871781
28291580
320601560
done50011560

prune274.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

2.5b
(/ (* (cbrt y) (cbrt y)) (* (cbrt (fma (/ x 2.0) y 1.0)) (cbrt (fma (/ x 2.0) y 1.0))))
7.2b
(cbrt (fma (/ x 2.0) y 1.0))
7.2b
(cbrt (fma (/ x 2.0) y 1.0))
7.2b
(cbrt (fma (/ x 2.0) y 1.0))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
16×add-exp-log
9×cbrt-prod
8×add-cbrt-cube
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 cbrt-undiv expm1-log1p-u div-exp prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×pow1/3
1×frac-2neg times-frac clear-num associate-/r* div-inv associate-/l*
Counts
4 → 62
Calls
4 calls:
31.0ms
(/ (* (cbrt y) (cbrt y)) (* (cbrt (fma (/ x 2.0) y 1.0)) (cbrt (fma (/ x 2.0) y 1.0))))
2.0ms
(cbrt (fma (/ x 2.0) y 1.0))
2.0ms
(cbrt (fma (/ x 2.0) y 1.0))
2.0ms
(cbrt (fma (/ x 2.0) y 1.0))

series1.4s

Counts
4 → 12
Calls
4 calls:
317.0ms
(/ (* (cbrt y) (cbrt y)) (* (cbrt (fma (/ x 2.0) y 1.0)) (cbrt (fma (/ x 2.0) y 1.0))))
297.0ms
(cbrt (fma (/ x 2.0) y 1.0))
367.0ms
(cbrt (fma (/ x 2.0) y 1.0))
378.0ms
(cbrt (fma (/ x 2.0) y 1.0))

simplify1.0s

Counts
74 → 74
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01771716
14661635
214891409
done50001305

prune386.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (* x y) 2.0) (/ (* x y) 2.0))
2.2b
(- (* (/ (* x y) 2.0) (/ (* x y) 2.0)) (* 1.0 (/ (* x y) 2.0)))
3.3b
(/ y (+ (pow 1.0 3) (pow (/ (* x y) 2.0) 3)))
20.4b
(* (/ y (+ (pow 1.0 3) (pow (/ (* x y) 2.0) 3))) (+ (* 1.0 1.0) (- (* (/ (* x y) 2.0) (/ (* x y) 2.0)) (* 1.0 (/ (* x y) 2.0)))))

rewrite724.0ms

Algorithm
rewrite-expression-head
Rules
110×*-un-lft-identity
67×times-frac
47×add-exp-log add-sqr-sqrt add-cbrt-cube
40×add-cube-cbrt associate-*l*
35×distribute-lft-out
28×unpow-prod-down cube-prod
17×prod-exp cbrt-unprod
14×cbrt-undiv div-exp
13×pow1
10×associate-*r/ associate-*r*
9×associate-/r*
7×swap-sqr sum-cubes
6×div-inv add-log-exp
4×expm1-log1p-u frac-times flip3-+ associate-*l/ associate-/r/ flip-+ log1p-expm1-u
3×frac-sub associate-/l* unswap-sqr
2×pow-prod-down *-commutative sub-div
1×pow2 distribute-rgt-in sub-neg flip3-- distribute-rgt-out-- frac-2neg distribute-lft-in pow-plus fma-neg diff-log prod-diff clear-num pow-sqr pow-prod-up flip--
Counts
4 → 195
Calls
4 calls:
47.0ms
(* (/ (* x y) 2.0) (/ (* x y) 2.0))
35.0ms
(- (* (/ (* x y) 2.0) (/ (* x y) 2.0)) (* 1.0 (/ (* x y) 2.0)))
100.0ms
(/ y (+ (pow 1.0 3) (pow (/ (* x y) 2.0) 3)))
526.0ms
(* (/ y (+ (pow 1.0 3) (pow (/ (* x y) 2.0) 3))) (+ (* 1.0 1.0) (- (* (/ (* x y) 2.0) (/ (* x y) 2.0)) (* 1.0 (/ (* x y) 2.0)))))

series593.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(* (/ (* x y) 2.0) (/ (* x y) 2.0))
144.0ms
(- (* (/ (* x y) 2.0) (/ (* x y) 2.0)) (* 1.0 (/ (* x y) 2.0)))
127.0ms
(/ y (+ (pow 1.0 3) (pow (/ (* x y) 2.0) 3)))
256.0ms
(* (/ y (+ (pow 1.0 3) (pow (/ (* x y) 2.0) 3))) (+ (* 1.0 1.0) (- (* (/ (* x y) 2.0) (/ (* x y) 2.0)) (* 1.0 (/ (* x y) 2.0)))))

simplify3.1s

Counts
207 → 207
Iterations

Useful iterations: done (3.1s)

IterNodesCost
03045565
19514472
239073999
done50003991

prune656.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes34.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01012
11212
done1212

end0.0ms

sample735.0ms

Algorithm
intervals
Results
467.0ms7995×body80valid
1.0ms4×body1280valid
0.0ms1×body2560valid