Details

Time bar (total: 15.1s)

sample31.0ms

Algorithm
intervals
Results
16.0ms256×body80valid
7.0ms256×pre80true

simplify1.1s

Counts
1 → 1
Iterations
IterNodes
done2002
62002
5808
4236
388
244
119
08

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.2b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b
(- 1 (* (/ b a) (/ b a)))
0.4b
(* (/ b a) (/ b a))
9.2b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
48×add-sqr-sqrt
40×times-frac
35×*-un-lft-identity
34×add-cube-cbrt
15×add-cbrt-cube add-exp-log
13×swap-sqr associate-*r* associate-*l*
11×pow1
5×add-log-exp
4×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
3×expm1-log1p-u fma-neg prod-diff sqrt-prod insert-posit16 log1p-expm1-u
2×difference-of-squares
1×pow2 frac-times rem-sqrt-square sub-neg sqrt-pow1 pow-plus flip3-- pow1/2 diff-log pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up flip--
Counts
3 → 109
Calls
3 calls:
5.0ms
(- 1 (* (/ b a) (/ b a)))
17.0ms
(* (/ b a) (/ b a))
1.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series104.0ms

Counts
3 → 9
Calls
3 calls:
55.0ms
(- 1 (* (/ b a) (/ b a)))
30.0ms
(* (/ b a) (/ b a))
18.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify1.2s

Counts
118 → 118
Iterations
IterNodes
done2002
32002
21597
1496
0167

prune1.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 9.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(- 1 (/ (* (/ b a) b) a))
0.2b
(* (/ b a) b)
6.4b
(/ (* (/ b a) b) a)
9.2b
(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
32×*-un-lft-identity
29×add-cube-cbrt
22×times-frac
21×prod-diff
18×add-cbrt-cube add-exp-log
13×associate-*l*
7×pow1
6×add-log-exp
5×cbrt-undiv div-exp div-inv
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u
3×associate-/r* fma-neg associate-*r* sqrt-prod
2×associate-*l/ difference-of-squares unswap-sqr
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log pow-prod-down *-commutative flip-- associate-/l* distribute-lft-out-- associate-/l/
Counts
4 → 120
Calls
4 calls:
14.0ms
(- 1 (/ (* (/ b a) b) a))
20.0ms
(* (/ b a) b)
20.0ms
(/ (* (/ b a) b) a)
1.0ms
(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))

series147.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(- 1 (/ (* (/ b a) b) a))
33.0ms
(* (/ b a) b)
51.0ms
(/ (* (/ b a) b) a)
24.0ms
(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))

simplify1.1s

Counts
132 → 132
Iterations
IterNodes
done2024
32024
21432
1478
0194

prune1.4s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 9.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (/ b a))
0.3b
(* (* (/ b a) (sqrt (/ b a))) (sqrt (/ b a)))
0.3b
(* (/ b a) (sqrt (/ b a)))
9.2b
(sqrt (fabs (- 1 (* (* (/ b a) (sqrt (/ b a))) (sqrt (/ b a))))))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
46×sqrt-prod
42×times-frac
35×*-un-lft-identity add-cube-cbrt
32×associate-*r*
25×pow1
18×add-cbrt-cube add-exp-log
14×associate-*l*
11×sqrt-div pow-prod-up
7×sqrt-pow1 pow1/2 prod-exp cbrt-unprod
6×frac-times associate-*l/ unswap-sqr
4×expm1-log1p-u pow-prod-down associate-*r/ insert-posit16 log1p-expm1-u div-inv add-log-exp
3×rem-sqrt-square pow3
2×cbrt-undiv div-exp *-commutative
1×pow-plus
Counts
4 → 150
Calls
4 calls:
5.0ms
(sqrt (/ b a))
71.0ms
(* (* (/ b a) (sqrt (/ b a))) (sqrt (/ b a)))
35.0ms
(* (/ b a) (sqrt (/ b a)))
2.0ms
(sqrt (fabs (- 1 (* (* (/ b a) (sqrt (/ b a))) (sqrt (/ b a))))))

series261.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(sqrt (/ b a))
46.0ms
(* (* (/ b a) (sqrt (/ b a))) (sqrt (/ b a)))
135.0ms
(* (/ b a) (sqrt (/ b a)))
21.0ms
(sqrt (fabs (- 1 (* (* (/ b a) (sqrt (/ b a))) (sqrt (/ b a))))))

simplify1.4s

Counts
162 → 162
Iterations
IterNodes
done2009
32009
21873
1521
0210

prune1.8s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 9.1b

localize40.0ms

Local error

Found 4 expressions with local error:

6.4b
(/ (* (/ b a) b) a)
6.4b
(/ (* (/ b a) b) a)
9.2b
(sqrt (fabs (/ (- (* 1 1) (* (/ (* (/ b a) b) a) (/ (* (/ b a) b) a))) (+ 1 (/ (* (/ b a) b) a)))))
18.9b
(/ (- (* 1 1) (* (/ (* (/ b a) b) a) (/ (* (/ b a) b) a))) (+ 1 (/ (* (/ b a) b) a)))

rewrite202.0ms

Algorithm
rewrite-expression-head
Rules
29×*-un-lft-identity
24×add-cbrt-cube add-exp-log
22×times-frac
20×add-sqr-sqrt
19×add-cube-cbrt
10×associate-/r*
9×cbrt-undiv div-exp
6×associate-/l*
5×pow1 distribute-lft-out difference-of-squares
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp associate-/l/
3×clear-num frac-2neg sqrt-prod div-inv
2×associate-*l/ associate-/r/
1×rem-sqrt-square sqrt-pow1 flip3-+ flip3-- pow1/2 div-sub flip-+ flip--
Counts
4 → 114
Calls
4 calls:
25.0ms
(/ (* (/ b a) b) a)
24.0ms
(/ (* (/ b a) b) a)
2.0ms
(sqrt (fabs (/ (- (* 1 1) (* (/ (* (/ b a) b) a) (/ (* (/ b a) b) a))) (+ 1 (/ (* (/ b a) b) a)))))
149.0ms
(/ (- (* 1 1) (* (/ (* (/ b a) b) a) (/ (* (/ b a) b) a))) (+ 1 (/ (* (/ b a) b) a)))

series248.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(/ (* (/ b a) b) a)
54.0ms
(/ (* (/ b a) b) a)
36.0ms
(sqrt (fabs (/ (- (* 1 1) (* (/ (* (/ b a) b) a) (/ (* (/ b a) b) a))) (+ 1 (/ (* (/ b a) b) a)))))
126.0ms
(/ (- (* 1 1) (* (/ (* (/ b a) b) a) (/ (* (/ b a) b) a))) (+ 1 (/ (* (/ b a) b) a)))

simplify1.6s

Counts
126 → 126
Iterations
IterNodes
done2085
32085
21388
1415
0164

prune1.5s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 9.1b

regimes128.0ms

Accuracy

0% (0.1b remaining)

Error of 7.5b against oracle of 7.3b and baseline of 7.5b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done12
112
09

end0.0ms

sample1.5s

Algorithm
intervals
Results
903.0ms8000×body80valid
375.0ms8000×pre80true