Details

Time bar (total: 17.0s)

sample30.0ms

Algorithm
intervals
Results
7.0ms256×body80valid
4.0ms296×pre80false
3.0ms256×pre80true

simplify11.0s

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
0813
11913
24811
311111
425511
569011
6346611
done500111

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.6b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (* a a) (* b b))
0.0b
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
14.1b
(/ (- (* a a) (* b b)) (* a a))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
8×add-exp-log add-cbrt-cube
7×add-sqr-sqrt
6×add-cube-cbrt *-un-lft-identity
5×add-log-exp
4×pow1 times-frac associate-/l*
3×expm1-log1p-u sqrt-prod log1p-expm1-u difference-of-squares
2×cbrt-undiv flip3-- div-exp flip-- associate-/l/
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
3 → 60
Calls
3 calls:
3.0ms
(- (* a a) (* b b))
1.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
9.0ms
(/ (- (* a a) (* b b)) (* a a))

series98.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(- (* a a) (* b b))
17.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
52.0ms
(/ (- (* a a) (* b b)) (* a a))

simplify376.0ms

Counts
69 → 69
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
099979
1240843
2982744
done5002744

prune157.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
0.0b
(/ (+ a b) a)
0.1b
(/ (- a b) a)
0.1b
(* (/ (+ a b) a) (/ (- a b) a))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
69×*-un-lft-identity
68×add-sqr-sqrt
58×times-frac
41×add-cube-cbrt
20×add-exp-log add-cbrt-cube
19×associate-*r*
16×associate-*l*
9×associate-/l*
7×pow1 distribute-lft-out distribute-lft-out-- difference-of-squares
6×cbrt-undiv div-exp associate-/r*
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u div-inv associate-/l/ add-log-exp unswap-sqr
3×sqrt-prod
2×frac-2neg clear-num
1×frac-times rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 div-sub associate-*r/ pow-prod-down associate-*l/ *-commutative flip-- flip-+
Counts
4 → 151
Calls
4 calls:
1.0ms
(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
8.0ms
(/ (+ a b) a)
9.0ms
(/ (- a b) a)
31.0ms
(* (/ (+ a b) a) (/ (- a b) a))

series127.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
21.0ms
(/ (+ a b) a)
30.0ms
(/ (- a b) a)
61.0ms
(* (/ (+ a b) a) (/ (- a b) a))

simplify770.0ms

Counts
163 → 163
Iterations

Useful iterations: 2 (157.0ms)

IterNodesCost
01922013
15051917
222261751
done50001751

prune369.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
0.0b
(/ (+ a b) a)
0.1b
(/ (- a b) a)
0.1b
(* (/ (+ a b) a) (/ (- a b) a))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
69×*-un-lft-identity
68×add-sqr-sqrt
58×times-frac
41×add-cube-cbrt
20×add-exp-log add-cbrt-cube
19×associate-*r*
16×associate-*l*
9×associate-/l*
7×pow1 distribute-lft-out distribute-lft-out-- difference-of-squares
6×cbrt-undiv div-exp associate-/r*
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u div-inv associate-/l/ add-log-exp unswap-sqr
3×sqrt-prod
2×frac-2neg clear-num
1×frac-times rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 div-sub associate-*r/ pow-prod-down associate-*l/ *-commutative flip-- flip-+
Counts
4 → 151
Calls
4 calls:
1.0ms
(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
8.0ms
(/ (+ a b) a)
9.0ms
(/ (- a b) a)
31.0ms
(* (/ (+ a b) a) (/ (- a b) a))

series127.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
21.0ms
(/ (+ a b) a)
29.0ms
(/ (- a b) a)
61.0ms
(* (/ (+ a b) a) (/ (- a b) a))

simplify771.0ms

Counts
163 → 163
Iterations

Useful iterations: 2 (156.0ms)

IterNodesCost
01922013
15051917
222261751
done50001751

prune443.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (+ a b) (sqrt a)) (sqrt a))
0.1b
(/ (- a b) a)
0.1b
(* (/ (/ (+ a b) (sqrt a)) (sqrt a)) (/ (- a b) a))
0.4b
(/ (+ a b) (sqrt a))

rewrite184.0ms

Algorithm
rewrite-expression-head
Rules
729×times-frac
534×*-un-lft-identity
419×add-sqr-sqrt
352×sqrt-prod
350×add-cube-cbrt
172×associate-*l*
85×distribute-lft-out
37×associate-/l*
34×add-exp-log add-cbrt-cube
19×associate-*r*
18×div-inv
15×associate-/r*
14×cbrt-undiv div-exp unswap-sqr
7×distribute-lft-out-- difference-of-squares
6×pow1 prod-exp cbrt-unprod
5×associate-/l/
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num
1×frac-times flip3-- flip3-+ div-sub associate-*r/ pow-prod-down associate-*l/ *-commutative flip-- flip-+
Counts
4 → 540
Calls
4 calls:
21.0ms
(/ (/ (+ a b) (sqrt a)) (sqrt a))
8.0ms
(/ (- a b) a)
107.0ms
(* (/ (/ (+ a b) (sqrt a)) (sqrt a)) (/ (- a b) a))
11.0ms
(/ (+ a b) (sqrt a))

series217.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(/ (/ (+ a b) (sqrt a)) (sqrt a))
29.0ms
(/ (- a b) a)
85.0ms
(* (/ (/ (+ a b) (sqrt a)) (sqrt a)) (/ (- a b) a))
61.0ms
(/ (+ a b) (sqrt a))

simplify415.0ms

Counts
552 → 552
Iterations

Useful iterations: done (398.0ms)

IterNodesCost
04589994
113389092
done50028896

prune1.2s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes32.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01115
11315
done1315

end0.0ms

sample606.0ms

Algorithm
intervals
Results
194.0ms8000×body80valid
96.0ms8113×pre80false
92.0ms8000×pre80true