Details

Time bar (total: 20.6s)

sample56.0ms

Algorithm
intervals
Results
16.0ms256×body80valid
6.0ms252×pre80false
6.0ms256×pre80true

simplify5.8s

Counts
1 → 1
Iterations

Useful iterations: 2 (11.0ms)

IterNodesCost
0813
11913
24811
310111
419811
537611
661811
7165311
done500111

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.1b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (* a a) (* b b))
0.0b
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
11.7b
(/ (- (* a a) (* b b)) (* a a))

rewrite52.0ms

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:
11.0ms
(- (* a a) (* b b))
2.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
36.0ms
(/ (- (* a a) (* b b)) (* a a))

series152.0ms

Counts
3 → 9
Calls
3 calls:
41.0ms
(- (* a a) (* b b))
27.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
84.0ms
(/ (- (* a a) (* b b)) (* a a))

simplify2.3s

Counts
69 → 69
Iterations

Useful iterations: 3 (1.0s)

IterNodesCost
099979
1230843
2698744
33365735
done5001735

prune239.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
19×times-frac
13×associate-*r*
10×add-exp-log add-cbrt-cube
6×pow1
3×expm1-log1p-u associate-*l* associate-/r* sqrt-prod log1p-expm1-u associate-/l* add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
1×rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 div-sub associate-*r/ pow-prod-down clear-num *-commutative flip--
Counts
3 → 81
Calls
3 calls:
16.0ms
(/ (- a (* b (/ b a))) a)
1.0ms
(sqrt (fabs (/ (- a (* b (/ b a))) a)))
20.0ms
(* b (/ b a))

series112.0ms

Counts
3 → 9
Calls
3 calls:
74.0ms
(/ (- a (* b (/ b a))) a)
17.0ms
(sqrt (fabs (/ (- a (* b (/ b a))) a)))
21.0ms
(* b (/ b a))

simplify2.5s

Counts
90 → 90
Iterations

Useful iterations: done (2.5s)

IterNodesCost
01381060
1296997
2790912
32121908
done5000903

prune321.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite212.0ms

Algorithm
rewrite-expression-head
Rules
302×add-sqr-sqrt
260×times-frac
243×sqrt-prod
137×add-cube-cbrt *-un-lft-identity
68×swap-sqr
66×associate-*r*
46×associate-*l*
29×unswap-sqr
26×add-exp-log add-cbrt-cube
16×pow1
8×prod-exp cbrt-unprod
6×cbrt-undiv div-exp div-inv
4×expm1-log1p-u sqrt-undiv log1p-expm1-u add-log-exp
3×associate-*r/ pow-prod-down *-commutative
1×pow2 frac-times rem-sqrt-square sqrt-pow1 pow-plus pow1/2 sqrt-unprod associate-*l/ rem-square-sqrt pow-sqr pow-prod-up
Counts
4 → 284
Calls
4 calls:
3.0ms
(sqrt (fabs (* (/ (sqrt (- a (* b (/ b a)))) (sqrt a)) (/ (sqrt (- a (* b (/ b a)))) (sqrt a)))))
146.0ms
(* (/ (sqrt (- a (* b (/ b a)))) (sqrt a)) (/ (sqrt (- a (* b (/ b a)))) (sqrt a)))
14.0ms
(* b (/ b a))
20.0ms
(* b (/ b a))

series199.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(sqrt (fabs (* (/ (sqrt (- a (* b (/ b a)))) (sqrt a)) (/ (sqrt (- a (* b (/ b a)))) (sqrt a)))))
116.0ms
(* (/ (sqrt (- a (* b (/ b a)))) (sqrt a)) (/ (sqrt (- a (* b (/ b a)))) (sqrt a)))
35.0ms
(* b (/ b a))
22.0ms
(* b (/ b a))

simplify2.2s

Counts
296 → 296
Iterations

Useful iterations: done (2.1s)

IterNodesCost
02808947
17927677
223955956
done50015506

prune1.1s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(expm1 (log1p (sqrt (fabs (/ (- a (* b (/ b a))) a)))))
0.0b
(sqrt (fabs (/ (- a (* b (/ b a))) a)))
0.0b
(/ (- a (* b (/ b a))) a)
0.1b
(* b (/ b a))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
19×times-frac
13×associate-*r*
11×add-exp-log add-cbrt-cube
7×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*l* associate-/r* sqrt-prod associate-/l*
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
1×rem-sqrt-square expm1-log1p flip3-- frac-2neg sqrt-pow1 pow1/2 div-sub associate-*r/ pow-prod-down clear-num *-commutative flip-- expm1-udef
Counts
4 → 92
Calls
4 calls:
1.0ms
(expm1 (log1p (sqrt (fabs (/ (- a (* b (/ b a))) a)))))
3.0ms
(sqrt (fabs (/ (- a (* b (/ b a))) a)))
37.0ms
(/ (- a (* b (/ b a))) a)
28.0ms
(* b (/ b a))

series246.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(expm1 (log1p (sqrt (fabs (/ (- a (* b (/ b a))) a)))))
34.0ms
(sqrt (fabs (/ (- a (* b (/ b a))) a)))
79.0ms
(/ (- a (* b (/ b a))) a)
33.0ms
(* b (/ b a))

simplify2.7s

Counts
104 → 104
Iterations

Useful iterations: done (2.7s)

IterNodesCost
01491274
13071174
27941080
321131076
done50001071

prune392.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes30.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01125
11225
done1225

end0.0ms

sample1.7s

Algorithm
intervals
Results
368.0ms8000×body80valid
175.0ms8293×pre80false
169.0ms8000×pre80true