Details

Time bar (total: 14.7s)

sample26.0ms

Algorithm
intervals
Results
11.0ms264×body80valid

simplify35.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (11.0ms)

IterNodesCost
01517
12617
23817
35015
46015
56415
done6415

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.3b

localize11.0ms

Local error

Found 3 expressions with local error:

1.9b
(fma (/ y t) b a)
3.1b
(fma (/ y t) z x)
12.0b
(/ (fma (/ y t) z x) (+ (fma (/ y t) b a) 1.0))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
12×add-sqr-sqrt add-cube-cbrt times-frac
5×add-exp-log add-cbrt-cube
4×associate-/r* distribute-lft-out
3×pow1 expm1-log1p-u log1p-expm1-u associate-/l* add-log-exp
2×associate-/r/ fma-udef
1×cbrt-undiv frac-2neg flip3-+ div-exp clear-num flip-+ div-inv
Counts
3 → 55
Calls
3 calls:
0.0ms
(fma (/ y t) b a)
0.0ms
(fma (/ y t) z x)
6.0ms
(/ (fma (/ y t) z x) (+ (fma (/ y t) b a) 1.0))

series548.0ms

Counts
3 → 9
Calls
3 calls:
42.0ms
(fma (/ y t) b a)
42.0ms
(fma (/ y t) z x)
464.0ms
(/ (fma (/ y t) z x) (+ (fma (/ y t) b a) 1.0))

simplify941.0ms

Counts
64 → 64
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
0901058
11641023
2410951
31338951
done5000951

prune245.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (+ (fma (/ y t) b a) 1.0))
1.9b
(fma (/ y t) b a)
3.1b
(fma (/ y t) z x)
12.0b
(* (fma (/ y t) z x) (/ 1 (+ (fma (/ y t) b a) 1.0)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
29×add-sqr-sqrt
26×times-frac
22×add-cube-cbrt
18×associate-*r*
17×add-exp-log
11×add-cbrt-cube
7×pow1 distribute-lft-out
4×expm1-log1p-u div-exp prod-exp associate-/r* associate-/r/ log1p-expm1-u add-log-exp
3×associate-*l* associate-/l* unswap-sqr
2×cbrt-undiv rec-exp flip3-+ 1-exp cbrt-unprod flip-+ fma-udef div-inv
1×pow-flip frac-2neg associate-*r/ pow-prod-down clear-num un-div-inv *-commutative inv-pow
Counts
4 → 102
Calls
4 calls:
10.0ms
(/ 1 (+ (fma (/ y t) b a) 1.0))
0.0ms
(fma (/ y t) b a)
0.0ms
(fma (/ y t) z x)
17.0ms
(* (fma (/ y t) z x) (/ 1 (+ (fma (/ y t) b a) 1.0)))

series689.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(/ 1 (+ (fma (/ y t) b a) 1.0))
43.0ms
(fma (/ y t) b a)
49.0ms
(fma (/ y t) z x)
472.0ms
(* (fma (/ y t) z x) (/ 1 (+ (fma (/ y t) b a) 1.0)))

simplify1.9s

Counts
114 → 114
Iterations

Useful iterations: 2 (97.0ms)

IterNodesCost
01291750
12731556
27161398
326291398
done50001398

prune358.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 11.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (/ (+ (fma (/ y t) b a) 1.0) (fma (/ y t) z x)))
1.9b
(fma (/ y t) b a)
3.1b
(fma (/ y t) z x)
11.8b
(/ (+ (fma (/ y t) b a) 1.0) (fma (/ y t) z x))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
108×times-frac
94×*-un-lft-identity
62×add-sqr-sqrt add-cube-cbrt
19×associate-/r*
17×add-exp-log
16×distribute-lft-out
11×add-cbrt-cube
8×div-exp
7×associate-/l*
6×div-inv
5×pow1
4×cbrt-undiv expm1-log1p-u log1p-expm1-u add-log-exp
2×rec-exp frac-2neg 1-exp clear-num fma-udef associate-/l/
1×pow-flip flip3-+ associate-/r/ flip-+ inv-pow
Counts
4 → 145
Calls
4 calls:
9.0ms
(/ 1 (/ (+ (fma (/ y t) b a) 1.0) (fma (/ y t) z x)))
0.0ms
(fma (/ y t) b a)
0.0ms
(fma (/ y t) z x)
8.0ms
(/ (+ (fma (/ y t) b a) 1.0) (fma (/ y t) z x))

series790.0ms

Counts
4 → 12
Calls
4 calls:
460.0ms
(/ 1 (/ (+ (fma (/ y t) b a) 1.0) (fma (/ y t) z x)))
43.0ms
(fma (/ y t) b a)
51.0ms
(fma (/ y t) z x)
235.0ms
(/ (+ (fma (/ y t) b a) 1.0) (fma (/ y t) z x))

simplify1.8s

Counts
157 → 157
Iterations

Useful iterations: 3 (823.0ms)

IterNodesCost
01863710
13933416
29323121
333743092
done50003092

prune400.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 11.8b

localize16.0ms

Local error

Found 4 expressions with local error:

8.7b
(* (fma (/ y t) z x) (* (cbrt (/ 1 (+ (fma (/ y t) b a) 1.0))) (cbrt (/ 1 (+ (fma (/ y t) b a) 1.0)))))
11.1b
(cbrt (/ 1 (+ (fma (/ y t) b a) 1.0)))
11.1b
(cbrt (/ 1 (+ (fma (/ y t) b a) 1.0)))
11.1b
(cbrt (/ 1 (+ (fma (/ y t) b a) 1.0)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
54×cbrt-prod
47×*-un-lft-identity
36×times-frac
30×add-sqr-sqrt
29×add-cube-cbrt
9×pow1 add-exp-log distribute-lft-out
7×cbrt-div add-cbrt-cube
6×associate-/r/
4×expm1-log1p-u associate-*r/ log1p-expm1-u add-log-exp
3×flip3-+ pow1/3 associate-*l* pow-prod-down prod-exp cbrt-unprod flip-+ div-inv
1×frac-times associate-*r* associate-*l/ *-commutative unswap-sqr
Counts
4 → 111
Calls
4 calls:
31.0ms
(* (fma (/ y t) z x) (* (cbrt (/ 1 (+ (fma (/ y t) b a) 1.0))) (cbrt (/ 1 (+ (fma (/ y t) b a) 1.0)))))
4.0ms
(cbrt (/ 1 (+ (fma (/ y t) b a) 1.0)))
4.0ms
(cbrt (/ 1 (+ (fma (/ y t) b a) 1.0)))
5.0ms
(cbrt (/ 1 (+ (fma (/ y t) b a) 1.0)))

series3.7s

Counts
4 → 12
Calls
4 calls:
2.9s
(* (fma (/ y t) z x) (* (cbrt (/ 1 (+ (fma (/ y t) b a) 1.0))) (cbrt (/ 1 (+ (fma (/ y t) b a) 1.0)))))
263.0ms
(cbrt (/ 1 (+ (fma (/ y t) b a) 1.0)))
261.0ms
(cbrt (/ 1 (+ (fma (/ y t) b a) 1.0)))
263.0ms
(cbrt (/ 1 (+ (fma (/ y t) b a) 1.0)))

simplify1.3s

Counts
123 → 123
Iterations

Useful iterations: 3 (579.0ms)

IterNodesCost
01802974
13902739
29932511
332092431
done50012431

prune440.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 11.8b

regimes569.0ms

Accuracy

52.2% (1.3b remaining)

Error of 12.9b against oracle of 11.5b and baseline of 14.3b

bsearch124.0ms

Steps
ItersRangePoint
9
7.029825254683234e+46
8.775561080507127e+52
1.6691668653093416e+47
7
-4.099996582881451e+41
-1.8478925286023206e+39
-5.213978647468733e+39

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03360
14460
done4460

end0.0ms

sample641.0ms

Algorithm
intervals
Results
357.0ms8300×body80valid