Details

Time bar (total: 11.4s)

sample24.0ms

Algorithm
intervals
Results
10.0ms265×body80valid

simplify2.3s

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01417
12416
24315
36515
49615
513015
616315
723915
839615
980515
10287115
done500015

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.7b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(* z (- t a))
0.8b
(fma x y (* z (- t a)))
24.0b
(/ (fma x y (* z (- t a))) (fma z (- b y) y))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
27×*-un-lft-identity
25×add-cube-cbrt
18×prod-diff
11×distribute-rgt-in distribute-lft-in
9×times-frac
7×add-exp-log add-cbrt-cube
5×pow1 associate-*r*
3×expm1-log1p-u associate-*l* associate-/r* log1p-expm1-u associate-/l* add-log-exp
2×sub-neg associate-*r/
1×cbrt-undiv flip3-- frac-2neg div-exp pow-prod-down prod-exp clear-num *-commutative flip-- cbrt-unprod fma-udef div-inv distribute-lft-out-- difference-of-squares unswap-sqr
Counts
3 → 85
Calls
3 calls:
12.0ms
(* z (- t a))
0.0ms
(fma x y (* z (- t a)))
2.0ms
(/ (fma x y (* z (- t a))) (fma z (- b y) y))

series412.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(* z (- t a))
50.0ms
(fma x y (* z (- t a)))
326.0ms
(/ (fma x y (* z (- t a))) (fma z (- b y) y))

simplify1.7s

Counts
94 → 94
Iterations

Useful iterations: 3 (531.0ms)

IterNodesCost
01631562
12881378
28621170
336111146
done50001146

prune295.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 24.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.5b
(+ (* z t) (* z (- a)))
0.8b
(fma x y (+ (* z t) (* z (- a))))
24.0b
(/ (fma x y (+ (* z t) (* z (- a)))) (fma z (- b y) y))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
5×add-exp-log add-cbrt-cube add-log-exp
3×pow1 expm1-log1p-u associate-/r* log1p-expm1-u associate-/l*
2×distribute-rgt-neg-out
1×cbrt-undiv +-commutative fma-def frac-2neg flip3-+ div-exp unsub-neg clear-num sum-log flip-+ fma-udef div-inv distribute-lft-out
Counts
3 → 56
Calls
3 calls:
3.0ms
(+ (* z t) (* z (- a)))
0.0ms
(fma x y (+ (* z t) (* z (- a))))
2.0ms
(/ (fma x y (+ (* z t) (* z (- a)))) (fma z (- b y) y))

series418.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(+ (* z t) (* z (- a)))
46.0ms
(fma x y (+ (* z t) (* z (- a))))
335.0ms
(/ (fma x y (+ (* z t) (* z (- a)))) (fma z (- b y) y))

simplify1.4s

Counts
65 → 65
Iterations

Useful iterations: 3 (324.0ms)

IterNodesCost
0961209
1217976
2705883
32758879
done5001879

prune220.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 24.0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.5b
(+ (* z t) (* z (- a)))
1.3b
(+ (* x y) (+ (* z t) (* z (- a))))
24.0b
(/ (+ (* x y) (+ (* z t) (* z (- a)))) (fma z (- b y) y))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
10×add-log-exp
9×times-frac
6×distribute-rgt-neg-out
5×add-exp-log add-cbrt-cube
4×associate-+r- sum-log
3×pow1 expm1-log1p-u flip3-+ unsub-neg associate-/r* flip-+ log1p-expm1-u associate-/l*
2×+-commutative fma-def div-sub associate-/l/
1×cbrt-undiv associate-+r+ frac-2neg div-exp clear-num div-inv distribute-lft-out
Counts
3 → 68
Calls
3 calls:
3.0ms
(+ (* z t) (* z (- a)))
7.0ms
(+ (* x y) (+ (* z t) (* z (- a))))
26.0ms
(/ (+ (* x y) (+ (* z t) (* z (- a)))) (fma z (- b y) y))

series415.0ms

Counts
3 → 9
Calls
3 calls:
34.0ms
(+ (* z t) (* z (- a)))
48.0ms
(+ (* x y) (+ (* z t) (* z (- a))))
332.0ms
(/ (+ (* x y) (+ (* z t) (* z (- a)))) (fma z (- b y) y))

simplify617.0ms

Counts
77 → 77
Iterations

Useful iterations: done (615.0ms)

IterNodesCost
01141513
13101148
211931069
done50001065

prune254.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 24.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(* z (- t a))
0.2b
(/ 1 (/ (fma z (- b y) y) (fma x y (* z (- t a)))))
0.8b
(fma x y (* z (- t a)))
24.0b
(/ (fma z (- b y) y) (fma x y (* z (- t a))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
72×add-sqr-sqrt
70×*-un-lft-identity
68×add-cube-cbrt
19×add-exp-log
18×prod-diff
16×associate-/r*
13×add-cbrt-cube
11×distribute-rgt-in distribute-lft-in
8×div-exp
7×pow1
6×div-inv associate-/l*
5×associate-*r*
4×cbrt-undiv expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*l*
2×sub-neg rec-exp frac-2neg 1-exp associate-*r/ clear-num
1×flip3-- pow-flip pow-prod-down prod-exp associate-/r/ *-commutative flip-- cbrt-unprod fma-udef distribute-lft-out-- inv-pow difference-of-squares unswap-sqr
Counts
4 → 163
Calls
4 calls:
12.0ms
(* z (- t a))
5.0ms
(/ 1 (/ (fma z (- b y) y) (fma x y (* z (- t a)))))
0.0ms
(fma x y (* z (- t a)))
2.0ms
(/ (fma z (- b y) y) (fma x y (* z (- t a))))

series658.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(* z (- t a))
470.0ms
(/ 1 (/ (fma z (- b y) y) (fma x y (* z (- t a)))))
49.0ms
(fma x y (* z (- t a)))
101.0ms
(/ (fma z (- b y) y) (fma x y (* z (- t a))))

simplify902.0ms

Counts
175 → 175
Iterations

Useful iterations: done (897.0ms)

IterNodesCost
02643896
15193507
214073100
done50003058

prune404.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 12.2b

regimes447.0ms

Accuracy

32.2% (8.9b remaining)

Error of 19.6b against oracle of 10.7b and baseline of 23.8b

bsearch99.0ms

Steps
ItersRangePoint
9
2.2108085494553437e+120
6.680833282765864e+126
1.621555450877592e+125
8
-7.928120464220808e+174
-1.214019913834516e+172
-1.285204343974009e+172

simplify5.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
02441
13435
23735
33835
done3835

end0.0ms

sample645.0ms

Algorithm
intervals
Results
350.0ms8413×body80valid