Details

Time bar (total: 15.9s)

sample55.0ms

Algorithm
intervals
Results
23.0ms272×body80valid

simplify58.0ms

Counts
1 → 1
Iterations
IterNodes
done72
572
466
348
236
119
011

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.7b

localize18.0ms

Local error

Found 2 expressions with local error:

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

rewrite49.0ms

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×pow1 flip3-- associate-/r/ flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg flip3-+ diff-log div-sub div-exp flip-+ div-inv
Counts
2 → 44
Calls
2 calls:
12.0ms
(- (* b c) (* a d))
34.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series183.0ms

Counts
2 → 6
Calls
2 calls:
57.0ms
(- (* b c) (* a d))
126.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify2.0s

Counts
50 → 50
Iterations
IterNodes
done5001
34329
2980
1254
086

prune309.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 23.0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
288×times-frac
164×add-sqr-sqrt
162×*-un-lft-identity add-cube-cbrt
156×sqrt-prod
27×associate-/l*
22×sqrt-div
18×associate-/r/
12×associate-/r*
11×flip3-+ add-cbrt-cube add-exp-log flip-+
9×div-inv
6×pow1
4×cbrt-undiv div-exp add-log-exp
3×div-sub associate-/l/
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2
1×flip3-- flip--
Counts
4 → 266
Calls
4 calls:
48.0ms
(/ (/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
21.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
6.0ms
(sqrt (+ (* c c) (* d d)))
11.0ms
(sqrt (+ (* c c) (* d d)))

series336.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(/ (/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
139.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
40.0ms
(sqrt (+ (* c c) (* d d)))
52.0ms
(sqrt (+ (* c c) (* d d)))

simplify1.8s

Counts
278 → 278
Iterations
IterNodes
done5000
23205
1764
0307

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 21.3b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (* b c) (* a d))
0.6b
(/ 1 (/ (+ (* c c) (* d d)) (- (* b c) (* a d))))
22.8b
(/ (+ (* c c) (* d d)) (- (* b c) (* a d)))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
55×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×associate-/r*
16×add-exp-log
11×associate-/r/
10×add-cbrt-cube
8×div-exp
6×flip3-- div-inv flip-- associate-/l*
5×add-log-exp
4×pow1 cbrt-undiv
2×rec-exp clear-num frac-2neg 1-exp associate-/l/
1×sub-neg flip3-+ diff-log flip-+ pow-flip inv-pow
Counts
3 → 127
Calls
3 calls:
6.0ms
(- (* b c) (* a d))
29.0ms
(/ 1 (/ (+ (* c c) (* d d)) (- (* b c) (* a d))))
49.0ms
(/ (+ (* c c) (* d d)) (- (* b c) (* a d)))

series275.0ms

Counts
3 → 9
Calls
3 calls:
55.0ms
(- (* b c) (* a d))
155.0ms
(/ 1 (/ (+ (* c c) (* d d)) (- (* b c) (* a d))))
65.0ms
(/ (+ (* c c) (* d d)) (- (* b c) (* a d)))

simplify1.6s

Counts
136 → 136
Iterations
IterNodes
done5002
22790
1533
0192

prune664.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 21.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ 1 (sqrt (+ (* c c) (* d d)))) (/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d))))
14.8b
(/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d)))
27.1b
(sqrt (+ (* c c) (* d d)))
27.1b
(sqrt (+ (* c c) (* d d)))

rewrite173.0ms

Algorithm
rewrite-expression-head
Rules
1494×times-frac
673×add-sqr-sqrt
671×*-un-lft-identity add-cube-cbrt
468×sqrt-prod
103×associate-/r/
56×sqrt-div
52×div-inv
30×associate-/l*
28×flip3-+ add-exp-log flip-+
27×associate-/r*
26×flip3-- flip--
18×add-cbrt-cube
17×div-exp
9×cbrt-undiv
6×pow1
4×add-log-exp
3×associate-/l/
2×rem-sqrt-square rec-exp clear-num frac-2neg sqrt-pow1 pow1/2 1-exp
Counts
4 → 721
Calls
4 calls:
74.0ms
(/ (/ 1 (sqrt (+ (* c c) (* d d)))) (/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d))))
19.0ms
(/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d)))
11.0ms
(sqrt (+ (* c c) (* d d)))
10.0ms
(sqrt (+ (* c c) (* d d)))

series369.0ms

Counts
4 → 12
Calls
4 calls:
164.0ms
(/ (/ 1 (sqrt (+ (* c c) (* d d)))) (/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d))))
116.0ms
(/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d)))
44.0ms
(sqrt (+ (* c c) (* d d)))
45.0ms
(sqrt (+ (* c c) (* d d)))

simplify3.2s

Counts
733 → 733
Iterations
IterNodes
done5002
13402
0890

prune2.1s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 21.3b

regimes271.0ms

Accuracy

0% (2.8b remaining)

Error of 26.3b against oracle of 23.6b and baseline of 26.3b

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done16
116
013

end0.0ms

sample880.0ms

Algorithm
intervals
Results
520.0ms8438×body80valid