Details

Time bar (total: 36.7s)

sample55.0ms

Algorithm
intervals
Results
29.0ms256×body80valid
12.0ms256×pre80true

simplify366.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
366.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.5b

localize26.0ms

Local error

Found 3 expressions with local error:

8.6b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.3b
(* (/ b a) (/ b a))
0.0b
(- 1 (* (/ b a) (/ b a)))

rewrite39.0ms

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
24.0ms
(* (/ b a) (/ b a))
10.0ms
(- 1 (* (/ b a) (/ b a)))
2.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series107.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
48.0ms
(- 1 (* (/ b a) (/ b a)))
37.0ms
(* (/ b a) (/ b a))
22.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify4.7s

Counts
102 → 118
Calls
102 calls:
Slowest
485.0ms
(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
253.0ms
(/ (exp 1) (exp (* (/ b a) (/ b a))))
216.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
203.0ms
(* (/ (* (* b b) b) (* (* a a) a)) (* (* (/ b a) (/ b a)) (/ b a)))
149.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (/ (* (* b b) b) (* (* a a) a)))

prune1.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 8.5b

localize18.0ms

Local error

Found 4 expressions with local error:

8.6b
(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
6.4b
(/ (* b (/ b a)) a)
0.2b
(* b (/ b a))
0.0b
(- 1 (/ (* b (/ b a)) a))

rewrite36.0ms

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-*r*
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-*l* sqrt-prod
2×associate-*r/ 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:
Slowest
13.0ms
(* b (/ b a))
11.0ms
(/ (* b (/ b a)) a)
9.0ms
(- 1 (/ (* b (/ b a)) a))
1.0ms
(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))

series119.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
43.0ms
(- 1 (/ (* b (/ b a)) a))
35.0ms
(/ (* b (/ b a)) a)
21.0ms
(* b (/ b a))
19.0ms
(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))

simplify13.8s

Counts
106 → 132
Calls
106 calls:
Slowest
673.0ms
(fma (- (/ (* b (/ b a)) a)) 1 (* (/ (* b (/ b a)) a) 1))
492.0ms
(fma (- (/ (* b (/ b a)) a)) 1 (* (/ (* b (/ b a)) a) 1))
449.0ms
(fma (sqrt 1) (sqrt 1) (- (* (/ (* b (/ b a)) a) 1)))
449.0ms
(fma (* (cbrt 1) (cbrt 1)) (cbrt 1) (- (* (/ (* b (/ b a)) a) 1)))
445.0ms
(fma 1 1 (- (* (/ (* b (/ b a)) a) 1)))

prune1.4s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 8.4b

localize42.0ms

Local error

Found 4 expressions with local error:

8.6b
(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
8.6b
(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
6.4b
(/ (* b (/ b a)) a)
6.4b
(/ (* b (/ b a)) a)

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
22×add-cbrt-cube add-exp-log
12×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
8×cbrt-undiv div-exp
6×pow1 associate-/r* times-frac sqrt-prod
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-*r/ div-inv associate-/l* associate-/l/
Counts
4 → 86
Calls
4 calls:
Slowest
22.0ms
(/ (* b (/ b a)) a)
12.0ms
(/ (* b (/ b a)) a)
2.0ms
(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
2.0ms
(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))

series112.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
50.0ms
(/ (* b (/ b a)) a)
33.0ms
(/ (* b (/ b a)) a)
16.0ms
(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
13.0ms
(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))

simplify3.4s

Counts
52 → 98
Calls
52 calls:
Slowest
251.0ms
(/ (* (* (* b (/ b a)) (* b (/ b a))) (* b (/ b a))) (* (* a a) a))
244.0ms
(/ (* (* (* b b) b) (/ (* (* b b) b) (* (* a a) a))) (* (* a a) a))
226.0ms
(/ (* (* (* b (/ b a)) (* b (/ b a))) (* b (/ b a))) (* (* a a) a))
225.0ms
(/ (* (* (* b b) b) (/ (* (* b b) b) (* (* a a) a))) (* (* a a) a))
208.0ms
(/ (* (* (* b b) b) (* (* (/ b a) (/ b a)) (/ b a))) (* (* a a) a))

prune1.3s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 8.4b

localize33.0ms

Local error

Found 4 expressions with local error:

9.4b
(* b (/ (/ b a) a))
8.6b
(sqrt (fabs (- 1 (* b (/ (/ b a) a)))))
0.2b
(/ (/ b a) a)
0.0b
(- 1 (* b (/ (/ b a) a)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
95×add-sqr-sqrt
85×*-un-lft-identity add-cube-cbrt
43×associate-*r*
18×add-cbrt-cube add-exp-log
13×associate-/l*
9×div-inv
7×pow1
6×cbrt-undiv div-exp add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r* fma-neg associate-*l* prod-diff prod-exp sqrt-prod cbrt-unprod unswap-sqr
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log pow-prod-down associate-*r/ *-commutative flip-- associate-/l/
Counts
4 → 178
Calls
4 calls:
Slowest
26.0ms
(* b (/ (/ b a) a))
9.0ms
(/ (/ b a) a)
5.0ms
(- 1 (* b (/ (/ b a) a)))
2.0ms
(sqrt (fabs (- 1 (* b (/ (/ b a) a)))))

series144.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
57.0ms
(- 1 (* b (/ (/ b a) a)))
40.0ms
(* b (/ (/ b a) a))
34.0ms
(/ (/ b a) a)
12.0ms
(sqrt (fabs (- 1 (* b (/ (/ b a) a)))))

simplify6.5s

Counts
179 → 190
Calls
179 calls:
Slowest
410.0ms
(* (* (* b b) b) (* (* (/ (/ b a) a) (/ (/ b a) a)) (/ (/ b a) a)))
396.0ms
(/ (/ (* (* b b) b) (* (* a a) a)) (* (* a a) a))
285.0ms
(/ (exp 1) (exp (* b (/ (/ b a) a))))
269.0ms
(/ (* (* (/ b a) (/ b a)) (/ b a)) (* (* a a) a))
202.0ms
(* (* (* b b) b) (/ (/ (* (* b b) b) (* (* a a) a)) (* (* a a) a)))

prune1.8s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 8.4b

regimes122.0ms

Accuracy

0% (0.1b remaining)

Error of 7.5b against oracle of 7.4b and baseline of 7.5b

bsearch3.0ms

end0.0ms

sample1.3s

Algorithm
intervals
Results
870.0ms8000×body80valid
298.0ms8000×pre80true