Details

Time bar (total: 11.7s)

sample22.0ms

Algorithm
intervals
Results
9.0ms280×body80valid

simplify66.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
01115
12114
24014
35614
47614
58814
69214
done9214

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.4b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
0.3b
(- (* b c) (* a d))
24.8b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
7×add-log-exp
5×add-exp-log add-cbrt-cube
3×pow1 expm1-log1p-u associate-/r* log1p-expm1-u associate-/l*
2×flip3-- flip3-+ associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative sub-neg fma-def frac-2neg fma-neg diff-log div-sub div-exp prod-diff clear-num sum-log div-inv
Counts
3 → 64
Calls
3 calls:
7.0ms
(+ (* c c) (* d d))
8.0ms
(- (* b c) (* a d))
27.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series161.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(+ (* c c) (* d d))
40.0ms
(- (* b c) (* a d))
91.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify1.5s

Counts
73 → 73
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01111202
13121070
21052961
33487961
done5000960

prune195.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.6b

localize11.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (/ 1 (hypot c d)) (/ (fma b c (- (* d a))) (hypot c d)))
0.3b
(fma b c (- (* d a)))
15.1b
(/ (fma b c (- (* d a))) (hypot c d))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
34×times-frac
27×add-exp-log *-un-lft-identity
25×add-cube-cbrt
17×add-cbrt-cube
13×associate-*r* associate-*l*
9×div-exp
8×prod-exp
6×unswap-sqr
5×pow1 cbrt-undiv
4×cbrt-unprod
3×expm1-log1p-u associate-/r* log1p-expm1-u div-inv associate-/l* add-log-exp
2×rec-exp 1-exp
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative fma-udef
Counts
3 → 97
Calls
3 calls:
22.0ms
(* (/ 1 (hypot c d)) (/ (fma b c (- (* d a))) (hypot c d)))
0.0ms
(fma b c (- (* d a)))
5.0ms
(/ (fma b c (- (* d a))) (hypot c d))

series367.0ms

Counts
3 → 9
Calls
3 calls:
183.0ms
(* (/ 1 (hypot c d)) (/ (fma b c (- (* d a))) (hypot c d)))
45.0ms
(fma b c (- (* d a)))
139.0ms
(/ (fma b c (- (* d a))) (hypot c d))

simplify2.6s

Counts
106 → 106
Iterations

Useful iterations: done (2.6s)

IterNodesCost
01402025
13331894
210821642
342241642
done50011608

prune263.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.6b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (fma b c (- (* d a))) (hypot c d)) (hypot c d))
0.3b
(fma b c (- (* d a)))
15.1b
(/ (fma b c (- (* d a))) (hypot c d))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
53×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×associate-/l*
10×add-exp-log add-cbrt-cube
6×associate-/r* div-inv
4×cbrt-undiv div-exp
3×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
2×frac-2neg clear-num
1×fma-udef associate-/l/
Counts
3 → 111
Calls
3 calls:
10.0ms
(/ (/ (fma b c (- (* d a))) (hypot c d)) (hypot c d))
0.0ms
(fma b c (- (* d a)))
5.0ms
(/ (fma b c (- (* d a))) (hypot c d))

series319.0ms

Counts
3 → 9
Calls
3 calls:
136.0ms
(/ (/ (fma b c (- (* d a))) (hypot c d)) (hypot c d))
45.0ms
(fma b c (- (* d a)))
138.0ms
(/ (fma b c (- (* d a))) (hypot c d))

simplify1.4s

Counts
120 → 120
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01612652
13272592
27502403
325592349
done50002285

prune376.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (hypot c d) (fma b c (- (* d a)))))
0.3b
(* (/ 1 (hypot c d)) (/ 1 (/ (hypot c d) (fma b c (- (* d a))))))
0.3b
(fma b c (- (* d a)))
15.1b
(/ (hypot c d) (fma b c (- (* d a))))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
187×times-frac
143×add-sqr-sqrt
107×*-un-lft-identity
100×add-exp-log
96×add-cube-cbrt
50×div-exp
44×associate-*r*
32×add-cbrt-cube
28×prod-exp
17×rec-exp 1-exp
16×associate-/r*
15×unswap-sqr
13×cbrt-undiv associate-*l*
11×div-inv
9×pow1
6×cbrt-unprod associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-flip pow-prod-down inv-pow
2×frac-2neg clear-num associate-/r/
1×frac-times associate-*r/ associate-*l/ un-div-inv *-commutative fma-udef
Counts
4 → 240
Calls
4 calls:
9.0ms
(/ 1 (/ (hypot c d) (fma b c (- (* d a)))))
42.0ms
(* (/ 1 (hypot c d)) (/ 1 (/ (hypot c d) (fma b c (- (* d a))))))
0.0ms
(fma b c (- (* d a)))
5.0ms
(/ (hypot c d) (fma b c (- (* d a))))

series443.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(/ 1 (/ (hypot c d) (fma b c (- (* d a)))))
182.0ms
(* (/ 1 (hypot c d)) (/ 1 (/ (hypot c d) (fma b c (- (* d a))))))
47.0ms
(fma b c (- (* d a)))
95.0ms
(/ (hypot c d) (fma b c (- (* d a))))

simplify2.4s

Counts
252 → 252
Iterations

Useful iterations: done (2.4s)

IterNodesCost
02925682
17275007
215424342
343974324
done50024246

prune487.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.5b

regimes206.0ms

Accuracy

32.5% (7.7b remaining)

Error of 13.2b against oracle of 5.5b and baseline of 16.9b

bsearch63.0ms

Steps
ItersRangePoint
6
3.0458708391958014e+68
1.5303859857698357e+69
1.5144682182949202e+69
9
-1.5363030971934703e+144
-2.4882870722039588e+138
-8.156571467291585e+143

simplify8.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
02549
13643
23943
34243
44343
done4343

end0.0ms

sample558.0ms

Algorithm
intervals
Results
267.0ms8467×body80valid