Details

Time bar (total: 11.6s)

sample26.0ms

Algorithm
intervals
Results
11.0ms265×body80valid

simplify29.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (10.0ms)

IterNodesCost
01517
12617
23817
35015
46015
56415
done6415

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (fma (/ y t) b a))
1.0b
(fma (/ y t) b a)
2.7b
(fma (/ y t) z x)
12.9b
(/ (fma (/ y t) z x) (+ 1.0 (fma (/ y t) b a)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
14×add-sqr-sqrt add-cube-cbrt
12×times-frac
6×add-exp-log add-cbrt-cube add-log-exp
5×distribute-lft-out
4×pow1 expm1-log1p-u associate-/r* log1p-expm1-u
3×fma-def fma-udef associate-/l*
2×flip3-+ associate-/r/ flip-+
1×cbrt-undiv +-commutative associate-+r+ frac-2neg div-exp clear-num sum-log div-inv
Counts
4 → 73
Calls
4 calls:
2.0ms
(+ 1.0 (fma (/ y t) b a))
0.0ms
(fma (/ y t) b a)
0.0ms
(fma (/ y t) z x)
5.0ms
(/ (fma (/ y t) z x) (+ 1.0 (fma (/ y t) b a)))

series523.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(+ 1.0 (fma (/ y t) b a))
38.0ms
(fma (/ y t) b a)
41.0ms
(fma (/ y t) z x)
409.0ms
(/ (fma (/ y t) z x) (+ 1.0 (fma (/ y t) b a)))

simplify832.0ms

Counts
85 → 85
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
01021281
11971234
26221145
320661145
done50001145

prune284.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (+ 1.0 (fma (/ y t) b a)))
1.0b
(fma (/ y t) b a)
2.7b
(fma (/ y t) z x)
12.9b
(* (fma (/ y t) z x) (/ 1 (+ 1.0 (fma (/ y t) b a))))

rewrite26.0ms

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:
5.0ms
(/ 1 (+ 1.0 (fma (/ y t) b a)))
0.0ms
(fma (/ y t) b a)
0.0ms
(fma (/ y t) z x)
18.0ms
(* (fma (/ y t) z x) (/ 1 (+ 1.0 (fma (/ y t) b a))))

series603.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(/ 1 (+ 1.0 (fma (/ y t) b a)))
38.0ms
(fma (/ y t) b a)
41.0ms
(fma (/ y t) z x)
412.0ms
(* (fma (/ y t) z x) (/ 1 (+ 1.0 (fma (/ y t) b a))))

simplify1.8s

Counts
114 → 114
Iterations

Useful iterations: 2 (95.0ms)

IterNodesCost
01291750
12811592
29561398
331251398
done50001398

prune280.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 12.5b

localize19.0ms

Local error

Found 4 expressions with local error:

12.2b
(cbrt (/ 1 (+ 1.0 (fma (/ y t) b a))))
12.2b
(cbrt (/ 1 (+ 1.0 (fma (/ y t) b a))))
12.2b
(cbrt (/ 1 (+ 1.0 (fma (/ y t) b a))))
12.9b
(* (fma (/ y t) z x) (* (* (cbrt (/ 1 (+ 1.0 (fma (/ y t) b a)))) (cbrt (/ 1 (+ 1.0 (fma (/ y t) b a))))) (cbrt (/ 1 (+ 1.0 (fma (/ y t) b a))))))

rewrite141.0ms

Algorithm
rewrite-expression-head
Rules
54×cbrt-prod
47×*-un-lft-identity
36×times-frac
29×add-sqr-sqrt add-cube-cbrt
15×cbrt-div
13×pow1 add-exp-log
10×associate-*r/
9×add-cbrt-cube distribute-lft-out
6×pow-prod-down prod-exp associate-/r/ cbrt-unprod
5×frac-times associate-*l/
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×flip3-+ pow1/3 associate-*l* flip-+ div-inv
1×associate-*r* *-commutative
Counts
4 → 117
Calls
4 calls:
3.0ms
(cbrt (/ 1 (+ 1.0 (fma (/ y t) b a))))
3.0ms
(cbrt (/ 1 (+ 1.0 (fma (/ y t) b a))))
3.0ms
(cbrt (/ 1 (+ 1.0 (fma (/ y t) b a))))
127.0ms
(* (fma (/ y t) z x) (* (* (cbrt (/ 1 (+ 1.0 (fma (/ y t) b a)))) (cbrt (/ 1 (+ 1.0 (fma (/ y t) b a))))) (cbrt (/ 1 (+ 1.0 (fma (/ y t) b a))))))

series1.1s

Counts
4 → 12
Calls
4 calls:
228.0ms
(cbrt (/ 1 (+ 1.0 (fma (/ y t) b a))))
225.0ms
(cbrt (/ 1 (+ 1.0 (fma (/ y t) b a))))
229.0ms
(cbrt (/ 1 (+ 1.0 (fma (/ y t) b a))))
412.0ms
(* (fma (/ y t) z x) (* (* (cbrt (/ 1 (+ 1.0 (fma (/ y t) b a)))) (cbrt (/ 1 (+ 1.0 (fma (/ y t) b a))))) (cbrt (/ 1 (+ 1.0 (fma (/ y t) b a))))))

simplify3.2s

Counts
129 → 129
Iterations

Useful iterations: 3 (469.0ms)

IterNodesCost
01623366
13403160
210042380
341922222
done50002222

prune357.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 12.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ a 1.0) (/ (* y b) t))
4.6b
(/ (* y b) t)
6.2b
(/ (* y z) t)
12.9b
(/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
64×*-un-lft-identity
26×times-frac
25×distribute-lft-out
20×add-sqr-sqrt add-cube-cbrt
16×add-exp-log add-cbrt-cube
11×associate-/r*
9×add-log-exp
6×associate-/l*
5×cbrt-undiv flip3-+ div-exp flip-+
4×pow1 expm1-log1p-u fma-def frac-add associate-/r/ log1p-expm1-u
3×frac-2neg clear-num sum-log div-inv
2×prod-exp cbrt-unprod associate-/l/
1×+-commutative associate-+l+
Counts
4 → 118
Calls
4 calls:
16.0ms
(+ (+ a 1.0) (/ (* y b) t))
3.0ms
(/ (* y b) t)
3.0ms
(/ (* y z) t)
33.0ms
(/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))

series165.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(+ (+ a 1.0) (/ (* y b) t))
22.0ms
(/ (* y b) t)
17.0ms
(/ (* y z) t)
97.0ms
(/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))

simplify568.0ms

Counts
130 → 130
Iterations

Useful iterations: 2 (149.0ms)

IterNodesCost
01952015
15001928
219171792
done50001792

prune334.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 11.5b

regimes325.0ms

Accuracy

36.1% (2.7b remaining)

Error of 13.2b against oracle of 10.5b and baseline of 14.7b

bsearch136.0ms

Steps
ItersRangePoint
10
1.4922881301407147e-59
7.98403954312571e-44
3.658468748003683e-44
10
-1.554735564942238e+78
-2.8741141712508995e+67
-3.8922922878163137e+68

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
03059
13957
done3957

end0.0ms

sample645.0ms

Algorithm
intervals
Results
354.0ms8298×body80valid