Details

Time bar (total: 21.3s)

sample24.0ms

Algorithm
intervals
Results
8.0ms256×body80valid
6.0ms256×pre80true

simplify1.2s

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
08242
118242
247203
3100203
4319203
51561203
done5000203

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.5b

localize16.0ms

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)))))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
40×times-frac
33×*-un-lft-identity
32×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×sqrt-prod
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 → 94
Calls
3 calls:
9.0ms
(- 1 (* (/ b a) (/ b a)))
34.0ms
(* (/ b a) (/ b a))
2.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series126.0ms

Counts
3 → 9
Calls
3 calls:
47.0ms
(- 1 (* (/ b a) (/ b a)))
50.0ms
(* (/ b a) (/ b a))
29.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify3.7s

Counts
103 → 103
Iterations

Useful iterations: done (3.7s)

IterNodesCost
015125441
148920163
2375519200
done500119120

prune501.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 5.5b

localize34.0ms

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))))))

rewrite103.0ms

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×pow-prod-down associate-*l/ div-inv add-log-exp
3×rem-sqrt-square
2×cbrt-undiv cube-unmult div-exp *-commutative
Counts
4 → 143
Calls
4 calls:
3.0ms
(sqrt (/ b a))
60.0ms
(* (sqrt (/ b a)) (* (sqrt (/ b a)) (/ b a)))
34.0ms
(* (sqrt (/ b a)) (/ b a))
2.0ms
(sqrt (fabs (- 1 (* (sqrt (/ b a)) (* (sqrt (/ b a)) (/ b a))))))

series273.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(sqrt (/ b a))
44.0ms
(* (sqrt (/ b a)) (* (sqrt (/ b a)) (/ b a)))
142.0ms
(* (sqrt (/ b a)) (/ b a))
25.0ms
(sqrt (fabs (- 1 (* (sqrt (/ b a)) (* (sqrt (/ b a)) (/ b a))))))

simplify2.9s

Counts
155 → 155
Iterations

Useful iterations: done (2.9s)

IterNodesCost
019539061
150532734
2319428850
done500128450

prune846.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 5.3b

localize37.0ms

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)))))))

rewrite272.0ms

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×div-inv add-log-exp
3×cbrt-undiv div-exp *-commutative
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 175
Calls
4 calls:
169.0ms
(* (sqrt (/ b a)) (* (sqrt (/ (sqrt b) 1)) (* (sqrt (/ (sqrt b) a)) (/ b a))))
26.0ms
(* (sqrt (/ (sqrt b) a)) (/ b a))
64.0ms
(* (sqrt (/ (sqrt b) 1)) (* (sqrt (/ (sqrt b) a)) (/ b a)))
1.0ms
(sqrt (fabs (- 1 (* (sqrt (/ b a)) (* (sqrt (/ (sqrt b) 1)) (* (sqrt (/ (sqrt b) a)) (/ b a)))))))

series654.0ms

Counts
4 → 12
Calls
4 calls:
229.0ms
(* (sqrt (/ b a)) (* (sqrt (/ (sqrt b) 1)) (* (sqrt (/ (sqrt b) a)) (/ b a))))
210.0ms
(* (sqrt (/ (sqrt b) a)) (/ b a))
179.0ms
(* (sqrt (/ (sqrt b) 1)) (* (sqrt (/ (sqrt b) a)) (/ b a)))
35.0ms
(sqrt (fabs (- 1 (* (sqrt (/ b a)) (* (sqrt (/ (sqrt b) 1)) (* (sqrt (/ (sqrt b) a)) (/ b a)))))))

simplify1.4s

Counts
187 → 187
Iterations

Useful iterations: done (1.3s)

IterNodesCost
033876160
186664549
done500162644

prune1.3s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 5.3b

localize51.0ms

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))))

rewrite77.0ms

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×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 → 187
Calls
4 calls:
24.0ms
(* (/ b a) (/ b a))
26.0ms
(* (/ b a) (/ b a))
1.0ms
(sqrt (fabs (/ (- 1 (* (* (/ b a) (/ b a)) (* (/ b a) (/ b a)))) (+ 1 (* (/ b a) (/ b a))))))
18.0ms
(/ (- 1 (* (* (/ b a) (/ b a)) (* (/ b a) (/ b a)))) (+ 1 (* (/ b a) (/ b a))))

series234.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (/ b a) (/ b a))
29.0ms
(* (/ b a) (/ b a))
44.0ms
(sqrt (fabs (/ (- 1 (* (* (/ b a) (/ b a)) (* (/ b a) (/ b a)))) (+ 1 (* (/ b a) (/ b a))))))
115.0ms
(/ (- 1 (* (* (/ b a) (/ b a)) (* (/ b a) (/ b a)))) (+ 1 (* (/ b a) (/ b a))))

simplify5.0s

Counts
199 → 199
Iterations

Useful iterations: 2 (2.3s)

IterNodesCost
021357066
166347665
2490245619
done500145619

prune1.1s

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 5.3b

regimes124.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
08203
110203
done10203

end0.0ms

sample1.3s

Algorithm
intervals
Results
831.0ms8000×body80valid
223.0ms8000×pre80true