Details

Time bar (total: 16.2s)

sample49.0ms

Algorithm
intervals
Results
26.0ms272×body80valid

simplify71.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
011284
121259
240259
356259
476259
590259
694259
done94259

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.7b

localize33.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (* b c) (* a d))
23.2b
(/ (- (* b c) (* a d)) (fma c c (* d d)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
4×add-cbrt-cube add-exp-log add-log-exp
3×associate-/r* associate-/l*
2×expm1-log1p-u pow1 flip3-- log1p-expm1-u flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg fma-neg diff-log div-sub div-exp prod-diff div-inv
Counts
2 → 48
Calls
2 calls:
8.0ms
(- (* b c) (* a d))
29.0ms
(/ (- (* b c) (* a d)) (fma c c (* d d)))

series230.0ms

Counts
2 → 6
Calls
2 calls:
77.0ms
(- (* b c) (* a d))
154.0ms
(/ (- (* b c) (* a d)) (fma c c (* d d)))

simplify2.5s

Counts
54 → 54
Iterations

Useful iterations: done (2.5s)

IterNodesCost
08616946
121816132
279815492
3364015452
done500115427

prune431.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 23.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- (* b c) (* a d)) (sqrt (fma c c (* d d)))) (sqrt (fma c c (* d d))))
14.8b
(/ (- (* b c) (* a d)) (sqrt (fma c c (* d d))))
27.1b
(sqrt (fma c c (* d d)))
27.1b
(sqrt (fma c c (* d d)))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
276×times-frac
160×add-sqr-sqrt
158×*-un-lft-identity add-cube-cbrt
150×sqrt-prod
25×associate-/l*
12×associate-/r*
11×add-cbrt-cube add-exp-log
9×div-inv
6×pow1
4×expm1-log1p-u cbrt-undiv div-exp log1p-expm1-u add-log-exp
3×div-sub associate-/l/
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 fma-udef hypot-def
1×flip3-- flip--
Counts
4 → 254
Calls
4 calls:
30.0ms
(/ (/ (- (* b c) (* a d)) (sqrt (fma c c (* d d)))) (sqrt (fma c c (* d d))))
15.0ms
(/ (- (* b c) (* a d)) (sqrt (fma c c (* d d))))
1.0ms
(sqrt (fma c c (* d d)))
1.0ms
(sqrt (fma c c (* d d)))

series395.0ms

Counts
4 → 12
Calls
4 calls:
123.0ms
(/ (/ (- (* b c) (* a d)) (sqrt (fma c c (* d d)))) (sqrt (fma c c (* d d))))
132.0ms
(/ (- (* b c) (* a d)) (sqrt (fma c c (* d d))))
62.0ms
(sqrt (fma c c (* d d)))
76.0ms
(sqrt (fma c c (* d d)))

simplify2.0s

Counts
266 → 266
Iterations

Useful iterations: done (1.9s)

IterNodesCost
0273163498
1678152978
23354129777
done5000129697

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 17.9b

localize47.0ms

Local error

Found 4 expressions with local error:

14.4b
(/ (/ (* (cbrt (- (* b c) (* a d))) (cbrt (- (* b c) (* a d)))) 1) (* (hypot c d) (/ (hypot c d) (cbrt (- (* b c) (* a d))))))
15.4b
(cbrt (- (* b c) (* a d)))
15.4b
(cbrt (- (* b c) (* a d)))
15.4b
(cbrt (- (* b c) (* a d)))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
61×add-exp-log
32×div-exp
31×add-cbrt-cube
18×cbrt-undiv
16×prod-exp
13×times-frac
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×cbrt-prod cbrt-unprod
7×associate-/l*
6×cbrt-div 1-exp
4×expm1-log1p-u pow1 log1p-expm1-u add-log-exp
3×flip3-- pow1/3 div-inv flip--
1×clear-num associate-/r* frac-2neg associate-*r/ associate-/r/ associate-/l/
Counts
4 → 98
Calls
4 calls:
49.0ms
(/ (/ (* (cbrt (- (* b c) (* a d))) (cbrt (- (* b c) (* a d)))) 1) (* (hypot c d) (/ (hypot c d) (cbrt (- (* b c) (* a d))))))
8.0ms
(cbrt (- (* b c) (* a d)))
8.0ms
(cbrt (- (* b c) (* a d)))
9.0ms
(cbrt (- (* b c) (* a d)))

series710.0ms

Counts
4 → 12
Calls
4 calls:
159.0ms
(/ (/ (* (cbrt (- (* b c) (* a d))) (cbrt (- (* b c) (* a d)))) 1) (* (hypot c d) (/ (hypot c d) (cbrt (- (* b c) (* a d))))))
187.0ms
(cbrt (- (* b c) (* a d)))
163.0ms
(cbrt (- (* b c) (* a d)))
200.0ms
(cbrt (- (* b c) (* a d)))

simplify3.4s

Counts
110 → 110
Iterations

Useful iterations: done (3.4s)

IterNodesCost
017953161
156146503
2390644699
done500242992

prune714.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 13.5b

localize40.0ms

Local error

Found 4 expressions with local error:

4.1b
(/ (* (cbrt (- (* b c) (* a d))) (cbrt (- (* b c) (* a d)))) (hypot c d))
15.4b
(cbrt (- (* b c) (* a d)))
15.4b
(cbrt (- (* b c) (* a d)))
15.4b
(cbrt (- (* b c) (* a d)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
9×cbrt-prod add-sqr-sqrt *-un-lft-identity flip3-- add-exp-log add-cube-cbrt flip--
8×associate-/l/
7×add-cbrt-cube
4×expm1-log1p-u frac-times pow1 log1p-expm1-u add-log-exp
3×associate-/r* times-frac pow1/3
2×cbrt-undiv div-exp associate-*l/ associate-*r/
1×clear-num frac-2neg prod-exp cbrt-unprod div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
23.0ms
(/ (* (cbrt (- (* b c) (* a d))) (cbrt (- (* b c) (* a d)))) (hypot c d))
14.0ms
(cbrt (- (* b c) (* a d)))
6.0ms
(cbrt (- (* b c) (* a d)))
5.0ms
(cbrt (- (* b c) (* a d)))

series706.0ms

Counts
4 → 12
Calls
4 calls:
300.0ms
(/ (* (cbrt (- (* b c) (* a d))) (cbrt (- (* b c) (* a d)))) (hypot c d))
130.0ms
(cbrt (- (* b c) (* a d)))
134.0ms
(cbrt (- (* b c) (* a d)))
141.0ms
(cbrt (- (* b c) (* a d)))

simplify1.1s

Counts
88 → 88
Iterations

Useful iterations: done (1.1s)

IterNodesCost
014435389
138033036
2149932771
done500031904

prune504.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 13.5b

regimes523.0ms

Accuracy

0% (3.4b remaining)

Error of 17.6b against oracle of 14.2b and baseline of 17.6b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
013419
115419
done15419

end0.0ms

sample996.0ms

Algorithm
intervals
Results
771.0ms8438×body80valid