Details

Time bar (total: 13.4s)

sample22.0ms

Algorithm
intervals
Results
7.0ms207×body80valid
2.0ms16×body640valid
2.0ms17×body320valid
1.0ms7×body1280valid
1.0ms9×body160valid

simplify1.8s

Counts
1 → 1
Iterations

Useful iterations: 4 (28.0ms)

IterNodesCost
0811
11611
23511
37611
416110
546610
6186810
done500010

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.7b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- x 1.0) (+ y 1.0))
11.9b
(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
35×*-un-lft-identity
23×add-sqr-sqrt
20×times-frac
13×add-cube-cbrt
6×distribute-lft-out
5×associate-/l* distribute-lft-out-- difference-of-squares
4×add-exp-log associate-/r* add-cbrt-cube
2×pow1 expm1-log1p-u associate-/r/ log1p-expm1-u associate-/l/ add-log-exp
1×cbrt-undiv flip3-- frac-2neg flip3-+ div-sub div-exp clear-num flip-- flip-+ fma-udef div-inv
Counts
2 → 58
Calls
2 calls:
48.0ms
(/ (- x 1.0) (+ y 1.0))
1.0ms
(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

series127.0ms

Counts
2 → 6
Calls
2 calls:
37.0ms
(/ (- x 1.0) (+ y 1.0))
90.0ms
(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

simplify796.0ms

Counts
64 → 64
Iterations

Useful iterations: done (793.0ms)

IterNodesCost
0114834
1282799
21133747
done5002743

prune247.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- 1.0 x) y)
2.8b
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
6.3b
(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity
30×add-sqr-sqrt prod-diff
24×add-cube-cbrt
16×times-frac
10×add-exp-log add-cbrt-cube
8×associate-/r/
5×pow1 associate-*l* distribute-lft-out add-log-exp
4×flip3-+ associate-*l/ associate-/r* flip-+ div-inv
3×expm1-log1p-u flip3-- fma-neg associate-*r* flip-- log1p-expm1-u
2×cbrt-undiv div-exp prod-exp cbrt-unprod associate-/l/ distribute-lft-out-- difference-of-squares
1×sub-neg frac-2neg diff-log pow-prod-down clear-num *-commutative associate-/l* unswap-sqr
Counts
3 → 102
Calls
3 calls:
23.0ms
(* (- 1.0 x) y)
39.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
26.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

series215.0ms

Counts
3 → 9
Calls
3 calls:
58.0ms
(* (- 1.0 x) y)
90.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
68.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

simplify2.6s

Counts
111 → 111
Iterations

Useful iterations: done (2.6s)

IterNodesCost
02022757
15532332
231951872
done50011827

prune301.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ y (sqrt (+ y 1.0)))
0.1b
(/ y (sqrt (+ y 1.0)))
0.1b
(/ y (sqrt (+ y 1.0)))
5.7b
(fma (/ y (sqrt (+ y 1.0))) (- (/ (- 1.0 x) (sqrt (+ y 1.0)))) (pow (cbrt 1.0) 3))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
76×*-un-lft-identity
63×times-frac
52×add-sqr-sqrt add-cube-cbrt
48×sqrt-prod
21×associate-/r*
12×distribute-lft-out
10×add-exp-log add-cbrt-cube
9×associate-/l*
6×sqrt-div associate-/r/
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv frac-2neg flip3-+ div-exp clear-num flip-+ div-inv
1×fma-udef
Counts
4 → 151
Calls
4 calls:
21.0ms
(/ y (sqrt (+ y 1.0)))
19.0ms
(/ y (sqrt (+ y 1.0)))
33.0ms
(/ y (sqrt (+ y 1.0)))
1.0ms
(fma (/ y (sqrt (+ y 1.0))) (- (/ (- 1.0 x) (sqrt (+ y 1.0)))) (pow (cbrt 1.0) 3))

series848.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(/ y (sqrt (+ y 1.0)))
159.0ms
(/ y (sqrt (+ y 1.0)))
188.0ms
(/ y (sqrt (+ y 1.0)))
351.0ms
(fma (/ y (sqrt (+ y 1.0))) (- (/ (- 1.0 x) (sqrt (+ y 1.0)))) (pow (cbrt 1.0) 3))

simplify772.0ms

Counts
163 → 163
Iterations

Useful iterations: done (763.0ms)

IterNodesCost
01352197
12901957
211271850
done50011845

prune893.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cbrt (fma (/ y (sqrt (+ y 1.0))) (- (/ (- 1.0 x) (sqrt (+ y 1.0)))) 1.0)) (cbrt (fma (/ y (sqrt (+ y 1.0))) (- (/ (- 1.0 x) (sqrt (+ y 1.0)))) 1.0)))
5.7b
(fma (/ y (sqrt (+ y 1.0))) (- (/ (- 1.0 x) (sqrt (+ y 1.0)))) 1.0)
5.7b
(fma (/ y (sqrt (+ y 1.0))) (- (/ (- 1.0 x) (sqrt (+ y 1.0)))) 1.0)
5.7b
(fma (/ y (sqrt (+ y 1.0))) (- (/ (- 1.0 x) (sqrt (+ y 1.0)))) 1.0)

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
16×cbrt-prod
12×add-cube-cbrt *-un-lft-identity
11×pow1
6×add-exp-log pow1/3 swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
3×fma-udef
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 72
Calls
4 calls:
19.0ms
(* (cbrt (fma (/ y (sqrt (+ y 1.0))) (- (/ (- 1.0 x) (sqrt (+ y 1.0)))) 1.0)) (cbrt (fma (/ y (sqrt (+ y 1.0))) (- (/ (- 1.0 x) (sqrt (+ y 1.0)))) 1.0)))
0.0ms
(fma (/ y (sqrt (+ y 1.0))) (- (/ (- 1.0 x) (sqrt (+ y 1.0)))) 1.0)
0.0ms
(fma (/ y (sqrt (+ y 1.0))) (- (/ (- 1.0 x) (sqrt (+ y 1.0)))) 1.0)
0.0ms
(fma (/ y (sqrt (+ y 1.0))) (- (/ (- 1.0 x) (sqrt (+ y 1.0)))) 1.0)

series1.8s

Counts
4 → 12
Calls
4 calls:
698.0ms
(* (cbrt (fma (/ y (sqrt (+ y 1.0))) (- (/ (- 1.0 x) (sqrt (+ y 1.0)))) 1.0)) (cbrt (fma (/ y (sqrt (+ y 1.0))) (- (/ (- 1.0 x) (sqrt (+ y 1.0)))) 1.0)))
351.0ms
(fma (/ y (sqrt (+ y 1.0))) (- (/ (- 1.0 x) (sqrt (+ y 1.0)))) 1.0)
381.0ms
(fma (/ y (sqrt (+ y 1.0))) (- (/ (- 1.0 x) (sqrt (+ y 1.0)))) 1.0)
352.0ms
(fma (/ y (sqrt (+ y 1.0))) (- (/ (- 1.0 x) (sqrt (+ y 1.0)))) 1.0)

simplify643.0ms

Counts
84 → 84
Iterations

Useful iterations: done (640.0ms)

IterNodesCost
0992792
12482592
29862304
done50011947

prune520.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

regimes292.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 14.9b

bsearch85.0ms

Steps
ItersRangePoint
8
32715339.804033544
39065373899.41173
166171510.47067747
6
-1.5429656710250222e+19
-3.0444833436098836e+18
-3.0868631627691034e+18

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
01838
12429
done2429

end0.0ms

sample1.0s

Algorithm
intervals
Results
431.0ms6026×body80valid
132.0ms786×body640valid
99.0ms534×body320valid
73.0ms341×body1280valid
27.0ms313×body160valid