Details

Time bar (total: 17.8s)

sample46.0ms

Algorithm
intervals
Results
25.0ms271×body80valid

simplify3.2s

Counts
1 → 1
Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
01417
12416
24315
37515
412715
518215
621515
729115
860015
9174815
done500015

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.7b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b
(* z (- t a))
0.5b
(fma x y (* z (- t a)))
22.0b
(/ (fma x y (* z (- t a))) (fma z (- b y) y))

rewrite68.0ms

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:
49.0ms
(* z (- t a))
1.0ms
(fma x y (* z (- t a)))
12.0ms
(/ (fma x y (* z (- t a))) (fma z (- b y) y))

series757.0ms

Counts
3 → 9
Calls
3 calls:
49.0ms
(* z (- t a))
79.0ms
(fma x y (* z (- t a)))
629.0ms
(/ (fma x y (* z (- t a))) (fma z (- b y) y))

simplify739.0ms

Counts
94 → 94
Iterations

Useful iterations: done (735.0ms)

IterNodesCost
01631562
13371384
210971192
done50011164

prune394.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 22.0b

localize35.0ms

Local error

Found 3 expressions with local error:

0.5b
(fma x y (+ (* z t) (* z (- a))))
2.0b
(+ (* z t) (* z (- a)))
22.0b
(/ (fma x y (+ (* z t) (* z (- a)))) (fma z (- b y) y))

rewrite33.0ms

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:
1.0ms
(fma x y (+ (* z t) (* z (- a))))
18.0ms
(+ (* z t) (* z (- a)))
11.0ms
(/ (fma x y (+ (* z t) (* z (- a)))) (fma z (- b y) y))

series714.0ms

Counts
3 → 9
Calls
3 calls:
86.0ms
(fma x y (+ (* z t) (* z (- a))))
54.0ms
(+ (* z t) (* z (- a)))
574.0ms
(/ (fma x y (+ (* z t) (* z (- a)))) (fma z (- b y) y))

simplify3.5s

Counts
65 → 65
Iterations

Useful iterations: 3 (1.2s)

IterNodesCost
0961209
1220976
2831883
34716879
done5000879

prune293.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 22.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (fma z (- b y) y))
0.5b
(fma x y (+ (* z t) (* z (- a))))
2.0b
(+ (* z t) (* z (- a)))
21.5b
(* (fma x y (+ (* z t) (* z (- a)))) (/ 1 (fma z (- b y) y)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
21×*-un-lft-identity
20×add-cube-cbrt times-frac
17×add-exp-log
13×associate-*r*
11×add-cbrt-cube
7×pow1
6×add-log-exp
4×expm1-log1p-u div-exp prod-exp log1p-expm1-u
3×associate-*l* associate-/r* associate-/l* unswap-sqr
2×cbrt-undiv rec-exp 1-exp distribute-rgt-neg-out cbrt-unprod div-inv
1×+-commutative pow-flip fma-def frac-2neg flip3-+ associate-*r/ unsub-neg pow-prod-down clear-num sum-log un-div-inv *-commutative flip-+ fma-udef distribute-lft-out inv-pow
Counts
4 → 98
Calls
4 calls:
6.0ms
(/ 1 (fma z (- b y) y))
0.0ms
(fma x y (+ (* z t) (* z (- a))))
9.0ms
(+ (* z t) (* z (- a)))
27.0ms
(* (fma x y (+ (* z t) (* z (- a)))) (/ 1 (fma z (- b y) y)))

series710.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(/ 1 (fma z (- b y) y))
89.0ms
(fma x y (+ (* z t) (* z (- a))))
58.0ms
(+ (* z t) (* z (- a)))
495.0ms
(* (fma x y (+ (* z t) (* z (- a)))) (/ 1 (fma z (- b y) y)))

simplify999.0ms

Counts
110 → 110
Iterations

Useful iterations: done (995.0ms)

IterNodesCost
01331792
13271416
213941247
done50001242

prune447.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 22.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* z (- t a))
0.4b
(/ 1 (/ (fma z (- b y) y) (fma x y (* z (- t a)))))
0.5b
(fma x y (* z (- t a)))
21.9b
(/ (fma z (- b y) y) (fma x y (* z (- t a))))

rewrite77.0ms

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:
38.0ms
(* z (- t a))
21.0ms
(/ 1 (/ (fma z (- b y) y) (fma x y (* z (- t a)))))
0.0ms
(fma x y (* z (- t a)))
6.0ms
(/ (fma z (- b y) y) (fma x y (* z (- t a))))

series1.1s

Counts
4 → 12
Calls
4 calls:
66.0ms
(* z (- t a))
801.0ms
(/ 1 (/ (fma z (- b y) y) (fma x y (* z (- t a)))))
70.0ms
(fma x y (* z (- t a)))
190.0ms
(/ (fma z (- b y) y) (fma x y (* z (- t a))))

simplify1.8s

Counts
175 → 175
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02643896
15993513
224473184
done50013080

prune588.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 11.5b

regimes573.0ms

Accuracy

33.2% (8.3b remaining)

Error of 19.4b against oracle of 11.0b and baseline of 23.5b

bsearch104.0ms

Steps
ItersRangePoint
7
5.6044378618353505e+103
2.2349872733644533e+105
1.680173933349987e+105
6
-6.239041997477821e+124
-3.931503708037643e+123
-1.6650384260519124e+124

simplify10.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
02340
13134
23534
33634
done3634

end0.0ms

sample1.4s

Algorithm
intervals
Results
716.0ms8393×body80valid