Details

Time bar (total: 14.1s)

sample24.0ms

Algorithm
intervals
Results
8.0ms250×body80valid
2.0ms14×body640valid
1.0ms15×body320valid
1.0ms9×body160valid
0.0ms3×body1280valid
0.0ms1×body2560valid

simplify2.2s

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01113
12313
24512
312212
430312
574112
6165012
7337012
done500012

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.2b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- t x) (- a z))
11.2b
(fma (/ (- t x) (- a z)) (- y z) x)

rewrite17.0ms

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:
13.0ms
(/ (- t x) (- a z))
0.0ms
(fma (/ (- t x) (- a z)) (- y z) x)

series128.0ms

Counts
2 → 6
Calls
2 calls:
47.0ms
(/ (- t x) (- a z))
80.0ms
(fma (/ (- t x) (- a z)) (- y z) x)

simplify894.0ms

Counts
70 → 70
Iterations

Useful iterations: done (891.0ms)

IterNodesCost
0118918
1269890
2701838
32280834
done5001832

prune204.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.4b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 1 (- a z))
0.3b
(* (- t x) (/ 1 (- a z)))
11.1b
(fma (* (- t x) (/ 1 (- a z))) (- y z) x)

rewrite35.0ms

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 z))
25.0ms
(* (- t x) (/ 1 (- a z)))
0.0ms
(fma (* (- t x) (/ 1 (- a z))) (- y z) x)

series165.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(/ 1 (- a z))
48.0ms
(* (- t x) (/ 1 (- a z)))
81.0ms
(fma (* (- t x) (/ 1 (- a z))) (- y z) x)

simplify2.0s

Counts
114 → 114
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01551285
13561096
21171948
33812944
done5001943

prune237.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 7.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ t (- a z))
0.0b
(/ x (- a z))
0.0b
(- (/ t (- a z)) (/ x (- a z)))
11.2b
(fma (- (/ t (- a z)) (/ x (- a z))) (- y z) x)

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
713×*-un-lft-identity
703×add-sqr-sqrt
693×times-frac
441×prod-diff
413×add-cube-cbrt
149×distribute-lft-out--
143×difference-of-squares
94×associate-/r/
48×flip3-- flip--
47×div-inv
21×fma-neg
10×associate-/r*
8×add-exp-log add-cbrt-cube
6×associate-/l* add-log-exp
4×pow1 expm1-log1p-u log1p-expm1-u
3×distribute-rgt-out--
2×cbrt-undiv frac-2neg div-exp clear-num
1×sub-neg diff-log frac-sub fma-udef sub-div
Counts
4 → 581
Calls
4 calls:
7.0ms
(/ t (- a z))
5.0ms
(/ x (- a z))
67.0ms
(- (/ t (- a z)) (/ x (- a z)))
0.0ms
(fma (- (/ t (- a z)) (/ x (- a z))) (- y z) x)

series262.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ t (- a z))
27.0ms
(/ x (- a z))
103.0ms
(- (/ t (- a z)) (/ x (- a z)))
105.0ms
(fma (- (/ t (- a z)) (/ x (- a z))) (- y z) x)

simplify1.4s

Counts
593 → 593
Iterations

Useful iterations: done (1.4s)

IterNodesCost
057428436
1124625539
2324319539
done500019476

prune1.2s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 7.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ t (- a z))
0.0b
(- (/ t (- a z)) (/ x (- a z)))
3.7b
(* (- (/ t (- a z)) (/ x (- a z))) (- y z))
4.3b
(+ (* (- (/ t (- a z)) (/ x (- a z))) (- y z)) x)

rewrite382.0ms

Algorithm
rewrite-expression-head
Rules
751×*-un-lft-identity
733×add-sqr-sqrt
696×times-frac
477×prod-diff
431×add-cube-cbrt
158×distribute-lft-out--
146×difference-of-squares
96×associate-/r/
57×flip3-- flip--
48×div-inv
22×distribute-rgt-in associate-+l+ distribute-lft-in
21×fma-neg
18×associate-*l*
8×add-exp-log frac-times add-cbrt-cube add-log-exp
6×pow1 distribute-rgt-out--
5×sub-neg associate-*r* associate-/r*
4×expm1-log1p-u associate-*l/ frac-sub log1p-expm1-u sub-div
3×associate-/l*
2×associate-*r/
1×cbrt-undiv +-commutative fma-def frac-2neg flip3-+ diff-log div-exp pow-prod-down prod-exp clear-num sum-log *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 641
Calls
4 calls:
5.0ms
(/ t (- a z))
66.0ms
(- (/ t (- a z)) (/ x (- a z)))
171.0ms
(* (- (/ t (- a z)) (/ x (- a z))) (- y z))
79.0ms
(+ (* (- (/ t (- a z)) (/ x (- a z))) (- y z)) x)

series515.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(/ t (- a z))
100.0ms
(- (/ t (- a z)) (/ x (- a z)))
240.0ms
(* (- (/ t (- a z)) (/ x (- a z))) (- y z))
148.0ms
(+ (* (- (/ t (- a z)) (/ x (- a z))) (- y z)) x)

simplify2.0s

Counts
653 → 653
Iterations

Useful iterations: 2 (478.0ms)

IterNodesCost
069630832
1155927597
2478621403
done500021403

prune1.3s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 6.2b

regimes342.0ms

Accuracy

14.9% (6.9b remaining)

Error of 13.4b against oracle of 6.5b and baseline of 14.6b

bsearch49.0ms

Steps
ItersRangePoint
4
5.581274792083229e+225
1.1004066369351343e+226
6.501016910978108e+225
6
-4.356485418338831e+232
-1.0295582727544921e+232
-3.2582793557416086e+232

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01824
12424
done2424

end0.0ms

sample676.0ms

Algorithm
intervals
Results
245.0ms7794×body80valid
57.0ms460×body640valid
41.0ms255×body1280valid
37.0ms435×body320valid
16.0ms280×body160valid
2.0ms14×body2560valid