Details

Time bar (total: 16.7s)

sample30.0ms

Algorithm
intervals
Results
15.0ms256×body80valid
7.0ms256×pre80true

simplify287.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
287.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.3b

localize26.0ms

Local error

Found 3 expressions with local error:

7.4b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.3b
(* (/ b a) (/ b a))
0.0b
(- 1 (* (/ b a) (/ b a)))

rewrite43.0ms

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:
Slowest
27.0ms
(* (/ b a) (/ b a))
10.0ms
(- 1 (* (/ b a) (/ b a)))
2.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series112.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
50.0ms
(- 1 (* (/ b a) (/ b a)))
39.0ms
(* (/ b a) (/ b a))
22.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify4.3s

Counts
102 → 118
Calls
102 calls:
Slowest
433.0ms
(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
237.0ms
(/ (exp 1) (exp (* (/ b a) (/ b a))))
233.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
163.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (/ (* (* b b) b) (* (* a a) a)))
141.0ms
(* (/ (* (cbrt b) (cbrt b)) (sqrt a)) (/ (* (cbrt b) (cbrt b)) (sqrt a)))

prune1.0s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 7.3b

localize42.0ms

Local error

Found 4 expressions with local error:

7.4b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
7.4b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.3b
(* (/ b a) (/ b a))
0.3b
(* (/ b a) (/ b a))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
88×add-sqr-sqrt
80×times-frac
62×*-un-lft-identity add-cube-cbrt
28×add-cbrt-cube add-exp-log
26×swap-sqr associate-*r* associate-*l*
20×pow1
8×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
6×sqrt-prod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×pow2 frac-times rem-sqrt-square sqrt-pow1 pow-plus pow1/2 pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
Counts
4 → 172
Calls
4 calls:
Slowest
24.0ms
(* (/ b a) (/ b a))
17.0ms
(* (/ b a) (/ b a))
1.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
1.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series100.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
38.0ms
(* (/ b a) (/ b a))
36.0ms
(* (/ b a) (/ b a))
13.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
13.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify6.8s

Counts
172 → 184
Calls
172 calls:
Slowest
765.0ms
(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
364.0ms
(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
233.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
195.0ms
(* (/ (* (* b b) b) (* (* a a) a)) (* (* (/ b a) (/ b a)) (/ b a)))
183.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))

prune2.4s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 7.3b

regimes74.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample1.3s

Algorithm
intervals
Results
851.0ms8000×body80valid
300.0ms8000×pre80true