Details

Time bar (total: 21.4s)

sample25.0ms

Algorithm
intervals
Results
7.0ms225×body80valid
2.0ms16×body640valid
2.0ms17×body320valid
2.0ms10×body1280valid
1.0ms9×body160valid

simplify10.0s

Counts
1 → 1
Iterations

Useful iterations: 4 (29.0ms)

IterNodesCost
01113
12213
25113
310313
420512
540812
667612
793912
8112112
9139012
10193612
11291112
12412912
done500012

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.2b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- t z) (- a t))
3.8b
(fma (/ (- t z) (- a t)) y (+ x y))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt *-un-lft-identity
25×times-frac
14×add-cube-cbrt
12×distribute-lft-out-- difference-of-squares
5×associate-/r* associate-/l*
4×add-exp-log add-cbrt-cube
2×pow1 expm1-log1p-u flip3-- associate-/r/ flip-- log1p-expm1-u associate-/l/ add-log-exp
1×cbrt-undiv frac-2neg div-sub div-exp clear-num fma-udef div-inv
Counts
2 → 64
Calls
2 calls:
17.0ms
(/ (- t z) (- a t))
0.0ms
(fma (/ (- t z) (- a t)) y (+ x y))

series221.0ms

Counts
2 → 6
Calls
2 calls:
42.0ms
(/ (- t z) (- a t))
179.0ms
(fma (/ (- t z) (- a t)) y (+ x y))

simplify2.0s

Counts
70 → 70
Iterations

Useful iterations: 4 (1.2s)

IterNodesCost
0113906
1258878
2589826
31517824
44613822
done5000822

prune208.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 1 (- a t))
0.2b
(* (- t z) (/ 1 (- a t)))
5.5b
(fma (* (- t z) (/ 1 (- a t))) y (+ x y))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
40×*-un-lft-identity
32×times-frac
23×add-cube-cbrt
21×associate-*r*
16×add-exp-log
10×add-cbrt-cube
8×distribute-lft-out-- difference-of-squares
6×pow1
5×associate-*l* associate-/r*
4×flip3-- div-exp prod-exp associate-/r/ flip--
3×expm1-log1p-u log1p-expm1-u associate-/l* add-log-exp unswap-sqr
2×cbrt-undiv frac-times rec-exp 1-exp associate-*l/ cbrt-unprod div-inv
1×pow-flip frac-2neg associate-*r/ pow-prod-down clear-num un-div-inv *-commutative fma-udef inv-pow
Counts
3 → 105
Calls
3 calls:
6.0ms
(/ 1 (- a t))
28.0ms
(* (- t z) (/ 1 (- a t)))
0.0ms
(fma (* (- t z) (/ 1 (- a t))) y (+ x y))

series255.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(/ 1 (- a t))
41.0ms
(* (- t z) (/ 1 (- a t)))
177.0ms
(fma (* (- t z) (/ 1 (- a t))) y (+ x y))

simplify2.4s

Counts
114 → 114
Iterations

Useful iterations: done (2.4s)

IterNodesCost
01491273
13351084
2996936
33118934
done5000933

prune279.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (- t z))
0.5b
(cbrt (- t z))
0.5b
(cbrt (- t z))
9.9b
(fma (* (* (cbrt (- t z)) (cbrt (- t z))) (/ (cbrt (- t z)) (- a t))) y (+ x y))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
13×add-sqr-sqrt *-un-lft-identity
7×add-cube-cbrt
6×cbrt-div
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×flip3-- pow1/3 flip-- distribute-lft-out-- difference-of-squares
1×fma-udef
Counts
4 → 61
Calls
4 calls:
2.0ms
(cbrt (- t z))
2.0ms
(cbrt (- t z))
2.0ms
(cbrt (- t z))
0.0ms
(fma (* (* (cbrt (- t z)) (cbrt (- t z))) (/ (cbrt (- t z)) (- a t))) y (+ x y))

series632.0ms

Counts
4 → 12
Calls
4 calls:
153.0ms
(cbrt (- t z))
146.0ms
(cbrt (- t z))
148.0ms
(cbrt (- t z))
185.0ms
(fma (* (* (cbrt (- t z)) (cbrt (- t z))) (/ (cbrt (- t z)) (- a t))) y (+ x y))

simplify1.7s

Counts
73 → 73
Iterations

Useful iterations: 4 (716.0ms)

IterNodesCost
093913
1189895
2409737
31064666
43975630
done5001630

prune295.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (- t z))
0.6b
(cbrt (* (cbrt (- t z)) (cbrt (- t z))))
0.6b
(cbrt (cbrt (- t z)))
10.4b
(fma (* (* (cbrt (- t z)) (* (cbrt (* (cbrt (- t z)) (cbrt (- t z)))) (cbrt (cbrt (- t z))))) (/ (cbrt (- t z)) (- a t))) y (+ x y))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
26×cbrt-div
19×cbrt-prod
11×add-sqr-sqrt *-un-lft-identity
8×flip3-- flip--
7×add-cube-cbrt
4×pow1 add-exp-log expm1-log1p-u frac-times add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
2×associate-*r/ associate-*l/ distribute-lft-out-- difference-of-squares
1×fma-udef
Counts
4 → 66
Calls
4 calls:
2.0ms
(cbrt (- t z))
8.0ms
(cbrt (* (cbrt (- t z)) (cbrt (- t z))))
4.0ms
(cbrt (cbrt (- t z)))
0.0ms
(fma (* (* (cbrt (- t z)) (* (cbrt (* (cbrt (- t z)) (cbrt (- t z)))) (cbrt (cbrt (- t z))))) (/ (cbrt (- t z)) (- a t))) y (+ x y))

series626.0ms

Counts
4 → 12
Calls
4 calls:
160.0ms
(cbrt (- t z))
126.0ms
(cbrt (* (cbrt (- t z)) (cbrt (- t z))))
158.0ms
(cbrt (cbrt (- t z)))
182.0ms
(fma (* (* (cbrt (- t z)) (* (cbrt (* (cbrt (- t z)) (cbrt (- t z)))) (cbrt (cbrt (- t z))))) (/ (cbrt (- t z)) (- a t))) y (+ x y))

simplify910.0ms

Counts
78 → 78
Iterations

Useful iterations: 3 (329.0ms)

IterNodesCost
01891353
13661321
27961213
321331187
done50011187

prune373.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.6b

regimes434.0ms

Accuracy

18% (6.5b remaining)

Error of 9.8b against oracle of 3.3b and baseline of 11.3b

bsearch169.0ms

Steps
ItersRangePoint
8
1.2278762811017799e-28
8.26855449639164e-26
2.8419677495754645e-28
9
4.2464550372131915e-86
1.2201145385644339e-76
8.971627261040967e-84
11
9.806239472655041e-278
1.4981629329511508e-249
1.472628804597749e-249
4
-5.592831531276727e-92
-3.24624944929814e-92
-3.612902899607295e-92

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03584
14284
done4284

end0.0ms

sample655.0ms

Algorithm
intervals
Results
248.0ms7392×body80valid
56.0ms459×body640valid
37.0ms248×body1280valid
36.0ms389×body320valid
13.0ms215×body160valid
4.0ms20×body2560valid