Details

Time bar (total: 30.5s)

sample46.0ms

Algorithm
intervals
Results
11.0ms237×body80valid
3.0ms18×body640valid
3.0ms20×body320valid
1.0ms7×body1280valid
1.0ms11×body160valid
0.0ms1×body2560valid

simplify12.6s

Counts
1 → 1
Iterations

Useful iterations: 4 (48.0ms)

IterNodesCost
01113
12213
25213
310913
420312
545112
674812
7107812
8140012
9165512
10215312
11268312
12384712
done500112

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.7b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- t z) (- a t))
4.8b
(fma (/ (- t z) (- a t)) y (+ x y))

rewrite58.0ms

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:
53.0ms
(/ (- t z) (- a t))
0.0ms
(fma (/ (- t z) (- a t)) y (+ x y))

series356.0ms

Counts
2 → 6
Calls
2 calls:
75.0ms
(/ (- t z) (- a t))
281.0ms
(fma (/ (- t z) (- a t)) y (+ x y))

simplify1.5s

Counts
70 → 70
Iterations

Useful iterations: 3 (535.0ms)

IterNodesCost
0113906
1258878
2622826
31643824
done5000824

prune276.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.8b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- a t) (- t z))
0.3b
(/ 1 (/ (- a t) (- t z)))
4.8b
(fma (/ 1 (/ (- a t) (- t z))) y (+ x y))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
218×times-frac
195×add-sqr-sqrt *-un-lft-identity
91×add-cube-cbrt
52×distribute-lft-out-- difference-of-squares
36×associate-/r*
16×add-exp-log
11×associate-/r/
10×add-cbrt-cube
8×div-exp associate-/l*
6×flip3-- flip-- div-inv
4×pow1 cbrt-undiv
3×expm1-log1p-u log1p-expm1-u add-log-exp
2×rec-exp frac-2neg 1-exp clear-num associate-/l/
1×pow-flip div-sub fma-udef inv-pow
Counts
3 → 214
Calls
3 calls:
39.0ms
(/ (- a t) (- t z))
41.0ms
(/ 1 (/ (- a t) (- t z)))
1.0ms
(fma (/ 1 (/ (- a t) (- t z))) y (+ x y))

series399.0ms

Counts
3 → 9
Calls
3 calls:
79.0ms
(/ (- a t) (- t z))
195.0ms
(/ 1 (/ (- a t) (- t z)))
125.0ms
(fma (/ 1 (/ (- a t) (- t z))) y (+ x y))

simplify2.8s

Counts
223 → 223
Iterations

Useful iterations: 3 (1.5s)

IterNodesCost
02723776
16153262
213982939
339722863
done50022863

prune486.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ a (- t z))
0.0b
(- (/ a (- t z)) (/ t (- t z)))
0.3b
(/ 1 (- (/ a (- t z)) (/ t (- t z))))
4.8b
(fma (/ 1 (- (/ a (- t z)) (/ t (- t z)))) y (+ x y))

rewrite401.0ms

Algorithm
rewrite-expression-head
Rules
830×*-un-lft-identity
804×times-frac
780×add-sqr-sqrt
441×prod-diff
434×add-cube-cbrt
193×distribute-lft-out--
163×difference-of-squares
112×associate-/r/
56×flip3-- flip--
55×div-inv
23×associate-/r*
21×fma-neg
15×distribute-rgt-out--
10×add-exp-log
8×add-cbrt-cube
6×associate-/l* add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×div-exp
2×cbrt-undiv frac-2neg clear-num frac-sub sub-div
1×sub-neg rec-exp pow-flip diff-log 1-exp fma-udef inv-pow
Counts
4 → 639
Calls
4 calls:
19.0ms
(/ a (- t z))
135.0ms
(- (/ a (- t z)) (/ t (- t z)))
162.0ms
(/ 1 (- (/ a (- t z)) (/ t (- t z))))
0.0ms
(fma (/ 1 (- (/ a (- t z)) (/ t (- t z)))) y (+ x y))

series546.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(/ a (- t z))
98.0ms
(- (/ a (- t z)) (/ t (- t z)))
241.0ms
(/ 1 (- (/ a (- t z)) (/ t (- t z))))
168.0ms
(fma (/ 1 (- (/ a (- t z)) (/ t (- t z)))) y (+ x y))

simplify2.1s

Counts
651 → 651
Iterations

Useful iterations: done (2.1s)

IterNodesCost
066230127
1137826953
2287820903
done500118446

prune1.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ t (- t z))
0.0b
(- (/ a (- t z)) (/ t (- t z)))
1.4b
(/ y (- (/ a (- t z)) (/ t (- t z))))
3.6b
(+ (/ y (- (/ a (- t z)) (/ t (- t z)))) (+ x y))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
941×*-un-lft-identity
912×times-frac
856×add-sqr-sqrt
462×add-cube-cbrt
441×prod-diff
229×distribute-lft-out--
181×difference-of-squares
128×associate-/r/
63×flip3-- flip--
62×fma-def div-inv
24×distribute-rgt-out--
23×associate-/r*
21×fma-neg
11×add-log-exp
8×add-exp-log add-cbrt-cube
6×associate-/l*
4×pow1 expm1-log1p-u log1p-expm1-u
3×sum-log frac-sub distribute-lft-out sub-div
2×cbrt-undiv frac-2neg flip3-+ div-exp frac-add clear-num flip-+
1×+-commutative sub-neg associate-+r+ diff-log
Counts
4 → 706
Calls
4 calls:
15.0ms
(/ t (- t z))
160.0ms
(- (/ a (- t z)) (/ t (- t z)))
177.0ms
(/ y (- (/ a (- t z)) (/ t (- t z))))
637.0ms
(+ (/ y (- (/ a (- t z)) (/ t (- t z)))) (+ x y))

series855.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(/ t (- t z))
67.0ms
(- (/ a (- t z)) (/ t (- t z)))
254.0ms
(/ y (- (/ a (- t z)) (/ t (- t z))))
489.0ms
(+ (/ y (- (/ a (- t z)) (/ t (- t z)))) (+ x y))

simplify1.9s

Counts
718 → 718
Iterations

Useful iterations: 2 (811.0ms)

IterNodesCost
070630387
1153527335
2377121367
done500021367

prune2.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.7b

regimes384.0ms

Accuracy

38.9% (5.0b remaining)

Error of 8.4b against oracle of 3.4b and baseline of 11.6b

bsearch114.0ms

Steps
ItersRangePoint
8
2.1173889327764862e+51
1.1230196676476993e+56
5.547130691672523e+55
8
-5.143611643359078e+88
-3.61369871224165e+84
-2.7798277110681646e+85

simplify6.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
02552
13147
done3147

end0.0ms

sample1.1s

Algorithm
intervals
Results
338.0ms7375×body80valid
79.0ms488×body640valid
53.0ms266×body1280valid
43.0ms357×body320valid
26.0ms276×body160valid
3.0ms12×body2560valid