Details

Time bar (total: 22.9s)

sample49.0ms

Algorithm
intervals
Results
16.0ms256×body80valid
14.0ms256×pre80true

simplify1.9s

Counts
1 → 1
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
08242
119242
248203
3103203
4330203
51622203
done5001203

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.5b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b
(- 1 (* (/ b a) (/ b a)))
0.4b
(* (/ b a) (/ b a))
5.2b
(sqrt (fabs (- 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 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 → 106
Calls
3 calls:
5.0ms
(- 1 (* (/ b a) (/ b a)))
28.0ms
(* (/ b a) (/ b a))
2.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series121.0ms

Counts
3 → 9
Calls
3 calls:
47.0ms
(- 1 (* (/ b a) (/ b a)))
48.0ms
(* (/ b a) (/ b a))
26.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify4.0s

Counts
115 → 115
Iterations

Useful iterations: done (4.0s)

IterNodesCost
016428328
151422820
2391721427
done500021355

prune584.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 5.5b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (/ b a))
0.3b
(* (sqrt (/ b a)) (* (sqrt (/ b a)) (/ b a)))
0.3b
(* (sqrt (/ b a)) (/ b a))
5.2b
(sqrt (fabs (- 1 (* (sqrt (/ b a)) (* (sqrt (/ b a)) (/ b a))))))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt
46×sqrt-prod
42×times-frac
35×*-un-lft-identity add-cube-cbrt
32×associate-*l*
30×pow1
18×add-cbrt-cube add-exp-log
15×pow-prod-up
14×associate-*r*
12×sqrt-pow1 pow1/2
11×sqrt-div
7×prod-exp cbrt-unprod
6×frac-times pow-plus associate-*r/ unswap-sqr
4×expm1-log1p-u pow-prod-down associate-*l/ log1p-expm1-u div-inv add-log-exp
3×rem-sqrt-square
2×cbrt-undiv cube-unmult div-exp *-commutative
Counts
4 → 151
Calls
4 calls:
3.0ms
(sqrt (/ b a))
55.0ms
(* (sqrt (/ b a)) (* (sqrt (/ b a)) (/ b a)))
24.0ms
(* (sqrt (/ b a)) (/ b a))
1.0ms
(sqrt (fabs (- 1 (* (sqrt (/ b a)) (* (sqrt (/ b a)) (/ b a))))))

series305.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(sqrt (/ b a))
37.0ms
(* (sqrt (/ b a)) (* (sqrt (/ b a)) (/ b a)))
182.0ms
(* (sqrt (/ b a)) (/ b a))
18.0ms
(sqrt (fabs (- 1 (* (sqrt (/ b a)) (* (sqrt (/ b a)) (/ b a))))))

simplify3.1s

Counts
163 → 163
Iterations

Useful iterations: done (3.1s)

IterNodesCost
020340999
151334432
2321930508
done500130068

prune966.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 5.3b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (/ b a)) (* (sqrt (/ (sqrt b) 1)) (* (sqrt (/ (sqrt b) a)) (/ b a))))
0.3b
(* (sqrt (/ (sqrt b) a)) (/ b a))
0.8b
(* (sqrt (/ (sqrt b) 1)) (* (sqrt (/ (sqrt b) a)) (/ b a)))
5.2b
(sqrt (fabs (- 1 (* (sqrt (/ b a)) (* (sqrt (/ (sqrt b) 1)) (* (sqrt (/ (sqrt b) a)) (/ b a)))))))

rewrite327.0ms

Algorithm
rewrite-expression-head
Rules
86×sqrt-prod
73×add-sqr-sqrt
66×associate-*l*
62×times-frac
48×*-un-lft-identity add-cube-cbrt
34×sqrt-div
32×add-cbrt-cube add-exp-log
23×frac-times associate-*r/
21×pow1
16×prod-exp cbrt-unprod
15×associate-*r*
11×associate-*l/
10×pow-prod-down
8×unswap-sqr
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×cbrt-undiv div-exp *-commutative
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 183
Calls
4 calls:
187.0ms
(* (sqrt (/ b a)) (* (sqrt (/ (sqrt b) 1)) (* (sqrt (/ (sqrt b) a)) (/ b a))))
37.0ms
(* (sqrt (/ (sqrt b) a)) (/ b a))
93.0ms
(* (sqrt (/ (sqrt b) 1)) (* (sqrt (/ (sqrt b) a)) (/ b a)))
2.0ms
(sqrt (fabs (- 1 (* (sqrt (/ b a)) (* (sqrt (/ (sqrt b) 1)) (* (sqrt (/ (sqrt b) a)) (/ b a)))))))

series664.0ms

Counts
4 → 12
Calls
4 calls:
256.0ms
(* (sqrt (/ b a)) (* (sqrt (/ (sqrt b) 1)) (* (sqrt (/ (sqrt b) a)) (/ b a))))
177.0ms
(* (sqrt (/ (sqrt b) a)) (/ b a))
199.0ms
(* (sqrt (/ (sqrt b) 1)) (* (sqrt (/ (sqrt b) a)) (/ b a)))
31.0ms
(sqrt (fabs (- 1 (* (sqrt (/ b a)) (* (sqrt (/ (sqrt b) 1)) (* (sqrt (/ (sqrt b) a)) (/ b a)))))))

simplify1.1s

Counts
195 → 195
Iterations

Useful iterations: done (1.1s)

IterNodesCost
034679702
187967847
done500065785

prune1.5s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 5.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ b a) (/ b a))
0.4b
(* (/ b a) (/ b a))
5.2b
(sqrt (fabs (/ (- 1 (* (* (/ b a) (/ b a)) (* (/ b a) (/ b a)))) (+ 1 (* (/ b a) (/ b a))))))
13.8b
(/ (- 1 (* (* (/ b a) (/ b a)) (* (/ b a) (/ b a)))) (+ 1 (* (/ b a) (/ b a))))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
100×add-sqr-sqrt
95×times-frac
75×*-un-lft-identity
71×add-cube-cbrt
30×add-cbrt-cube add-exp-log
26×swap-sqr associate-*r* associate-*l*
19×pow1
9×cbrt-undiv div-exp div-inv
8×prod-exp cbrt-unprod difference-of-squares unswap-sqr
5×associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r* sqrt-prod
2×pow2 frac-times pow-plus pow-prod-down associate-*l/ associate-*r/ associate-/r/ pow-sqr *-commutative pow-prod-up associate-/l/
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 flip3-+ flip3-- pow1/2 div-sub flip-+ flip--
Counts
4 → 195
Calls
4 calls:
23.0ms
(* (/ b a) (/ b a))
22.0ms
(* (/ b a) (/ b a))
1.0ms
(sqrt (fabs (/ (- 1 (* (* (/ b a) (/ b a)) (* (/ b a) (/ b a)))) (+ 1 (* (/ b a) (/ b a))))))
22.0ms
(/ (- 1 (* (* (/ b a) (/ b a)) (* (/ b a) (/ b a)))) (+ 1 (* (/ b a) (/ b a))))

series227.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(* (/ b a) (/ b a))
38.0ms
(* (/ b a) (/ b a))
34.0ms
(sqrt (fabs (/ (- 1 (* (* (/ b a) (/ b a)) (* (/ b a) (/ b a)))) (+ 1 (* (/ b a) (/ b a))))))
119.0ms
(/ (- 1 (* (* (/ b a) (/ b a)) (* (/ b a) (/ b a)))) (+ 1 (* (/ b a) (/ b a))))

simplify5.0s

Counts
207 → 207
Iterations

Useful iterations: 2 (2.4s)

IterNodesCost
021959166
167449505
2485047071
done500047071

prune1.1s

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 5.3b

regimes88.0ms

Accuracy

0% (0.3b remaining)

Error of 8.1b against oracle of 7.8b and baseline of 8.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08203
110203
done10203

end0.0ms

sample1.3s

Algorithm
intervals
Results
883.0ms8000×body80valid
193.0ms8000×pre80true