Details

Time bar (total: 15.5s)

sample50.0ms

Algorithm
intervals
Results
22.0ms265×body80valid

simplify7.0ms

Counts
1 → 1
Iterations
IterNodes
done15
115
011

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.6b

localize26.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* a c) (* b d))
24.1b
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite68.0ms

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* flip3-+ flip-+ associate-/l*
2×pow1 associate-/r/ associate-/l/
1×cbrt-undiv +-commutative clear-num sum-log frac-2neg div-exp div-inv
Counts
2 → 42
Calls
2 calls:
11.0ms
(+ (* a c) (* b d))
55.0ms
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series174.0ms

Counts
2 → 6
Calls
2 calls:
45.0ms
(+ (* a c) (* b d))
128.0ms
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify2.0s

Counts
48 → 48
Iterations
IterNodes
done5000
34513
2925
1235
083

prune334.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 23.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (+ (* b d) (* a c)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
15.4b
(/ (+ (* b d) (* a c)) (sqrt (+ (* c c) (* d d))))
26.2b
(sqrt (+ (* c c) (* d d)))
26.2b
(sqrt (+ (* c c) (* d d)))

rewrite161.0ms

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* flip3-+ flip-+
11×add-cbrt-cube add-exp-log
9×div-inv
6×pow1
4×cbrt-undiv div-exp add-log-exp
3×associate-/l/
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2
Counts
4 → 264
Calls
4 calls:
67.0ms
(/ (/ (+ (* b d) (* a c)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
57.0ms
(/ (+ (* b d) (* a c)) (sqrt (+ (* c c) (* d d))))
12.0ms
(sqrt (+ (* c c) (* d d)))
9.0ms
(sqrt (+ (* c c) (* d d)))

series414.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(/ (/ (+ (* b d) (* a c)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
208.0ms
(/ (+ (* b d) (* a c)) (sqrt (+ (* c c) (* d d))))
55.0ms
(sqrt (+ (* c c) (* d d)))
58.0ms
(sqrt (+ (* c c) (* d d)))

simplify1.5s

Counts
276 → 276
Iterations
IterNodes
done5000
23738
1755
0302

prune1.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 19.8b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1 (sqrt (+ (* c c) (* d d)))) (/ (+ (* b d) (* a c)) (sqrt (+ (* c c) (* d d)))))
15.4b
(/ (+ (* b d) (* a c)) (sqrt (+ (* c c) (* d d))))
26.2b
(sqrt (+ (* c c) (* d d)))
26.2b
(sqrt (+ (* c c) (* d d)))

rewrite163.0ms

Algorithm
rewrite-expression-head
Rules
95×add-sqr-sqrt
76×times-frac
53×*-un-lft-identity
47×add-cube-cbrt sqrt-prod
28×add-exp-log
24×associate-*r* associate-*l*
18×add-cbrt-cube
15×unswap-sqr
10×sqrt-div
9×div-exp
8×pow1 prod-exp
6×associate-/r* flip3-+ associate-/r/ flip-+
5×cbrt-undiv
4×cbrt-unprod add-log-exp
3×div-inv associate-/l*
2×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-/l/
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 160
Calls
4 calls:
99.0ms
(* (/ 1 (sqrt (+ (* c c) (* d d)))) (/ (+ (* b d) (* a c)) (sqrt (+ (* c c) (* d d)))))
36.0ms
(/ (+ (* b d) (* a c)) (sqrt (+ (* c c) (* d d))))
11.0ms
(sqrt (+ (* c c) (* d d)))
7.0ms
(sqrt (+ (* c c) (* d d)))

series468.0ms

Counts
4 → 12
Calls
4 calls:
198.0ms
(* (/ 1 (sqrt (+ (* c c) (* d d)))) (/ (+ (* b d) (* a c)) (sqrt (+ (* c c) (* d d)))))
177.0ms
(/ (+ (* b d) (* a c)) (sqrt (+ (* c c) (* d d))))
44.0ms
(sqrt (+ (* c c) (* d d)))
49.0ms
(sqrt (+ (* c c) (* d d)))

simplify3.1s

Counts
172 → 172
Iterations
IterNodes
done5000
24169
1609
0193

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 19.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1 (sqrt (+ (* c c) (* d d)))) (/ 1 (/ (sqrt (+ (* c c) (* d d))) (+ (* d b) (* a c)))))
15.4b
(/ (sqrt (+ (* c c) (* d d))) (+ (* d b) (* a c)))
26.2b
(sqrt (+ (* c c) (* d d)))
26.2b
(sqrt (+ (* c c) (* d d)))

rewrite224.0ms

Algorithm
rewrite-expression-head
Rules
240×times-frac
219×add-sqr-sqrt
127×*-un-lft-identity
98×add-cube-cbrt
89×add-exp-log
78×sqrt-prod
77×associate-*r*
43×div-exp
35×unswap-sqr
28×prod-exp
27×add-cbrt-cube
24×associate-*l*
15×rec-exp 1-exp
11×associate-/r/
10×pow1 cbrt-undiv
8×flip3-+ sqrt-div flip-+
6×cbrt-unprod div-inv associate-/l*
4×add-log-exp
3×associate-/r* pow-prod-down
2×rem-sqrt-square sqrt-pow1 pow1/2 pow-flip inv-pow associate-/l/
1×frac-times clear-num frac-2neg associate-*l/ associate-*r/ un-div-inv *-commutative
Counts
4 → 258
Calls
4 calls:
149.0ms
(* (/ 1 (sqrt (+ (* c c) (* d d)))) (/ 1 (/ (sqrt (+ (* c c) (* d d))) (+ (* d b) (* a c)))))
39.0ms
(/ (sqrt (+ (* c c) (* d d))) (+ (* d b) (* a c)))
13.0ms
(sqrt (+ (* c c) (* d d)))
9.0ms
(sqrt (+ (* c c) (* d d)))

series442.0ms

Counts
4 → 12
Calls
4 calls:
184.0ms
(* (/ 1 (sqrt (+ (* c c) (* d d)))) (/ 1 (/ (sqrt (+ (* c c) (* d d))) (+ (* d b) (* a c)))))
137.0ms
(/ (sqrt (+ (* c c) (* d d))) (+ (* d b) (* a c)))
59.0ms
(sqrt (+ (* c c) (* d d)))
62.0ms
(sqrt (+ (* c c) (* d d)))

simplify756.0ms

Counts
270 → 270
Iterations
IterNodes
done5000
11249
0343

prune1.3s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 19.8b

regimes422.0ms

Accuracy

12.3% (2.6b remaining)

Error of 25.4b against oracle of 22.9b and baseline of 25.8b

bsearch85.0ms

Steps
ItersRangePoint
8
2.586892949274192e+85
1.392645936715808e+88
1.3785256020459088e+88
7
-4.1468841507459867e+123
-2.615624459402513e+121
-5.577210106748075e+122

simplify2.0ms

Iterations
IterNodes
done27
127
022

end0.0ms

sample1.2s

Algorithm
intervals
Results
760.0ms8448×body80valid