Details

Time bar (total: 9.2s)

sample19.0ms

Algorithm
intervals
Results
9.0ms277×body80valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01115
11515
done1515

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.9b

localize9.0ms

Local error

Found 2 expressions with local error:

0.2b
(+ (* a c) (* b d))
24.5b
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×flip3-+ associate-/r* flip-+ associate-/l*
2×pow1 associate-/r/ associate-/l/
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 42
Calls
2 calls:
2.0ms
(+ (* a c) (* b d))
11.0ms
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series114.0ms

Counts
2 → 6
Calls
2 calls:
33.0ms
(+ (* a c) (* b d))
81.0ms
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify902.0ms

Counts
48 → 48
Iterations

Useful iterations: 3 (294.0ms)

IterNodesCost
085924
1231906
2718824
32140820
done5000820

prune142.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 24.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (* a c) (* b d))
15.3b
(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
28.1b
(sqrt (+ (* c c) (* d d)))
28.1b
(sqrt (+ (* c c) (* d d)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
18×times-frac sqrt-prod
6×pow1 add-exp-log sqrt-div associate-/r* add-cbrt-cube add-log-exp
5×flip3-+ flip-+
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ associate-/l/
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
4 → 84
Calls
4 calls:
2.0ms
(+ (* a c) (* b d))
12.0ms
(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
3.0ms
(sqrt (+ (* c c) (* d d)))
4.0ms
(sqrt (+ (* c c) (* d d)))

series218.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(+ (* a c) (* b d))
109.0ms
(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
41.0ms
(sqrt (+ (* c c) (* d d)))
35.0ms
(sqrt (+ (* c c) (* d d)))

simplify930.0ms

Counts
96 → 96
Iterations

Useful iterations: 3 (315.0ms)

IterNodesCost
01161780
12741649
27511541
320331525
done50001525

prune303.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 21.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* d b))))
15.4b
(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* d b)))
28.1b
(sqrt (+ (* c c) (* d d)))
28.1b
(sqrt (+ (* c c) (* d d)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
100×add-sqr-sqrt
98×add-cube-cbrt *-un-lft-identity
54×sqrt-prod
27×associate-/r*
17×add-exp-log
11×associate-/r/ add-cbrt-cube
9×associate-/l*
8×flip3-+ div-exp flip-+
7×pow1
6×sqrt-div div-inv
4×cbrt-undiv add-log-exp
2×rem-sqrt-square rec-exp frac-2neg sqrt-pow1 pow1/2 1-exp clear-num associate-/l/
1×pow-flip inv-pow
Counts
4 → 193
Calls
4 calls:
17.0ms
(/ 1 (/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* d b))))
10.0ms
(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* d b)))
3.0ms
(sqrt (+ (* c c) (* d d)))
4.0ms
(sqrt (+ (* c c) (* d d)))

series261.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(/ 1 (/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* d b))))
73.0ms
(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* d b)))
40.0ms
(sqrt (+ (* c c) (* d d)))
37.0ms
(sqrt (+ (* c c) (* d d)))

simplify2.0s

Counts
205 → 205
Iterations

Useful iterations: 3 (983.0ms)

IterNodesCost
02425680
15775078
213444723
337624665
done50004665

prune431.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 21.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (sqrt 1) (/ (+ (* a c) (* d b)) (sqrt (+ (* c c) (* d d))))))
15.3b
(/ (+ (* a c) (* d b)) (sqrt (+ (* c c) (* d d))))
28.1b
(sqrt (+ (* c c) (* d d)))
28.1b
(sqrt (+ (* c c) (* d d)))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
1473×times-frac
681×add-sqr-sqrt
679×add-cube-cbrt *-un-lft-identity
522×sqrt-prod
155×associate-/r*
55×associate-/r/
54×sqrt-div
30×div-inv
28×flip3-+ flip-+
27×add-exp-log
16×div-exp
15×add-cbrt-cube
7×pow1 cbrt-undiv
6×associate-/l*
4×add-log-exp
3×rec-exp 1-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
1×pow-flip inv-pow
Counts
4 → 697
Calls
4 calls:
40.0ms
(/ 1 (/ (sqrt 1) (/ (+ (* a c) (* d b)) (sqrt (+ (* c c) (* d d))))))
11.0ms
(/ (+ (* a c) (* d b)) (sqrt (+ (* c c) (* d d))))
3.0ms
(sqrt (+ (* c c) (* d d)))
4.0ms
(sqrt (+ (* c c) (* d d)))

series324.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(/ 1 (/ (sqrt 1) (/ (+ (* a c) (* d b)) (sqrt (+ (* c c) (* d d))))))
125.0ms
(/ (+ (* a c) (* d b)) (sqrt (+ (* c c) (* d d))))
35.0ms
(sqrt (+ (* c c) (* d d)))
45.0ms
(sqrt (+ (* c c) (* d d)))

simplify1.9s

Counts
709 → 709
Iterations

Useful iterations: 2 (1.3s)

IterNodesCost
084928454
1201020304
2290319173
done500019173

prune708.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 21.1b

regimes223.0ms

Accuracy

1.3% (2.8b remaining)

Error of 25.8b against oracle of 23.0b and baseline of 25.8b

bsearch2.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02356
13056
done3056

end0.0ms

sample485.0ms

Algorithm
intervals
Results
281.0ms8488×body80valid