Details

Time bar (total: 20.8s)

sample43.0ms

Algorithm
intervals
Results
18.0ms261×body80valid

simplify58.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (24.0ms)

IterNodesCost
01517
12617
23817
35015
46015
56415
done6415

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.9b

localize26.0ms

Local error

Found 3 expressions with local error:

1.6b
(fma (/ y t) b a)
3.2b
(fma (/ y t) z x)
11.6b
(/ (fma (/ y t) z x) (+ (fma (/ y t) b a) 1.0))

rewrite30.0ms

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:
1.0ms
(fma (/ y t) b a)
1.0ms
(fma (/ y t) z x)
25.0ms
(/ (fma (/ y t) z x) (+ (fma (/ y t) b a) 1.0))

series941.0ms

Counts
3 → 9
Calls
3 calls:
72.0ms
(fma (/ y t) b a)
84.0ms
(fma (/ y t) z x)
785.0ms
(/ (fma (/ y t) z x) (+ (fma (/ y t) b a) 1.0))

simplify1.4s

Counts
64 → 64
Iterations

Useful iterations: 2 (106.0ms)

IterNodesCost
0901058
11661023
2439951
31585951
done5000951

prune346.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 11.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ 1 (+ (fma (/ y t) b a) 1.0))
1.6b
(fma (/ y t) b a)
3.2b
(fma (/ y t) z x)
11.2b
(* (fma (/ y t) z x) (/ 1 (+ (fma (/ y t) b a) 1.0)))

rewrite85.0ms

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:
22.0ms
(/ 1 (+ (fma (/ y t) b a) 1.0))
0.0ms
(fma (/ y t) b a)
0.0ms
(fma (/ y t) z x)
55.0ms
(* (fma (/ y t) z x) (/ 1 (+ (fma (/ y t) b a) 1.0)))

series1.1s

Counts
4 → 12
Calls
4 calls:
197.0ms
(/ 1 (+ (fma (/ y t) b a) 1.0))
70.0ms
(fma (/ y t) b a)
63.0ms
(fma (/ y t) z x)
741.0ms
(* (fma (/ y t) z x) (/ 1 (+ (fma (/ y t) b a) 1.0)))

simplify3.6s

Counts
114 → 114
Iterations

Useful iterations: 2 (172.0ms)

IterNodesCost
01291750
12681556
27471398
329281398
done50001398

prune504.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 11.4b

localize31.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1 (/ (+ (fma (/ y t) b a) 1.0) (fma (/ y t) z x)))
1.6b
(fma (/ y t) b a)
3.2b
(fma (/ y t) z x)
11.4b
(/ (+ (fma (/ y t) b a) 1.0) (fma (/ y t) z x))

rewrite75.0ms

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:
26.0ms
(/ 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)
40.0ms
(/ (+ (fma (/ y t) b a) 1.0) (fma (/ y t) z x))

series1.3s

Counts
4 → 12
Calls
4 calls:
713.0ms
(/ 1 (/ (+ (fma (/ y t) b a) 1.0) (fma (/ y t) z x)))
70.0ms
(fma (/ y t) b a)
71.0ms
(fma (/ y t) z x)
417.0ms
(/ (+ (fma (/ y t) b a) 1.0) (fma (/ y t) z x))

simplify2.9s

Counts
157 → 157
Iterations

Useful iterations: 3 (1.3s)

IterNodesCost
01863710
13803416
29343121
336343092
done50013092

prune567.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 11.4b

localize27.0ms

Local error

Found 4 expressions with local error:

11.2b
(* (fma (/ y t) z x) (/ (/ 1 (* (cbrt (+ (fma (/ y t) b a) 1.0)) (cbrt (+ (fma (/ y t) b a) 1.0)))) (cbrt (+ (fma (/ y t) b a) 1.0))))
11.6b
(cbrt (+ (fma (/ y t) b a) 1.0))
11.6b
(cbrt (+ (fma (/ y t) b a) 1.0))
11.6b
(cbrt (+ (fma (/ y t) b a) 1.0))

rewrite211.0ms

Algorithm
rewrite-expression-head
Rules
136×times-frac
111×associate-*r*
92×cbrt-div
91×*-un-lft-identity
75×cbrt-prod
71×add-sqr-sqrt
58×associate-/r/
53×add-cube-cbrt
46×flip3-+ flip-+
32×add-exp-log
28×frac-times
18×distribute-lft-out
15×associate-*r/
14×associate-*l/
13×add-cbrt-cube
11×div-exp prod-exp
8×div-inv
7×unswap-sqr
6×pow1
5×cbrt-undiv cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow1/3 associate-*l*
2×rec-exp 1-exp
1×pow-prod-down *-commutative
Counts
4 → 193
Calls
4 calls:
161.0ms
(* (fma (/ y t) z x) (/ (/ 1 (* (cbrt (+ (fma (/ y t) b a) 1.0)) (cbrt (+ (fma (/ y t) b a) 1.0)))) (cbrt (+ (fma (/ y t) b a) 1.0))))
19.0ms
(cbrt (+ (fma (/ y t) b a) 1.0))
8.0ms
(cbrt (+ (fma (/ y t) b a) 1.0))
8.0ms
(cbrt (+ (fma (/ y t) b a) 1.0))

series1.8s

Counts
4 → 12
Calls
4 calls:
677.0ms
(* (fma (/ y t) z x) (/ (/ 1 (* (cbrt (+ (fma (/ y t) b a) 1.0)) (cbrt (+ (fma (/ y t) b a) 1.0)))) (cbrt (+ (fma (/ y t) b a) 1.0))))
379.0ms
(cbrt (+ (fma (/ y t) b a) 1.0))
396.0ms
(cbrt (+ (fma (/ y t) b a) 1.0))
359.0ms
(cbrt (+ (fma (/ y t) b a) 1.0))

simplify2.2s

Counts
205 → 205
Iterations

Useful iterations: done (2.1s)

IterNodesCost
03457290
18776948
227655987
done50005816

prune1.2s

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 11.4b

regimes635.0ms

Accuracy

51.3% (1.3b remaining)

Error of 13.3b against oracle of 12.0b and baseline of 14.8b

bsearch157.0ms

Steps
ItersRangePoint
8
1.983818873629023e-62
8.443715870529883e-60
8.239083667014754e-61
8
-4.694015096128857e+76
-1.0846075904783298e+74
-2.328380613761226e+75

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
02655
13541
done3541

end0.0ms

sample1.5s

Algorithm
intervals
Results
798.0ms8273×body80valid