Details

Time bar (total: 12.7s)

sample23.0ms

Algorithm
intervals
Results
12.0ms268×body80valid

simplify73.0ms

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

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
1.4b
(- (* b c) (* a d))
24.9b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite45.0ms

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:
8.0ms
(+ (* c c) (* d d))
9.0ms
(- (* b c) (* a d))
27.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series217.0ms

Counts
3 → 9
Calls
3 calls:
44.0ms
(+ (* c c) (* d d))
67.0ms
(- (* b c) (* a d))
106.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify2.1s

Counts
73 → 73
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01111202
13121070
21052961
33487961
done5000960

prune292.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 16.0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (/ 1 (hypot c d)) (/ (fma b c (- (* d a))) (hypot c d)))
0.8b
(fma b c (- (* d a)))
15.6b
(/ (fma b c (- (* d a))) (hypot c d))

rewrite47.0ms

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:
37.0ms
(* (/ 1 (hypot c d)) (/ (fma b c (- (* d a))) (hypot c d)))
0.0ms
(fma b c (- (* d a)))
6.0ms
(/ (fma b c (- (* d a))) (hypot c d))

series487.0ms

Counts
3 → 9
Calls
3 calls:
259.0ms
(* (/ 1 (hypot c d)) (/ (fma b c (- (* d a))) (hypot c d)))
53.0ms
(fma b c (- (* d a)))
175.0ms
(/ (fma b c (- (* d a))) (hypot c d))

simplify2.9s

Counts
106 → 106
Iterations

Useful iterations: done (2.9s)

IterNodesCost
01402025
13331894
210821642
342241642
done50011608

prune282.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (fma b c (- (* d a))) (hypot c d)) (hypot c d))
0.8b
(fma b c (- (* d a)))
15.6b
(/ (fma b c (- (* d a))) (hypot c d))

rewrite27.0ms

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:
11.0ms
(/ (/ (fma b c (- (* d a))) (hypot c d)) (hypot c d))
0.0ms
(fma b c (- (* d a)))
6.0ms
(/ (fma b c (- (* d a))) (hypot c d))

series353.0ms

Counts
3 → 9
Calls
3 calls:
151.0ms
(/ (/ (fma b c (- (* d a))) (hypot c d)) (hypot c d))
52.0ms
(fma b c (- (* d a)))
150.0ms
(/ (fma b c (- (* d a))) (hypot c d))

simplify1.6s

Counts
120 → 120
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01612652
13272592
27502403
325592349
done50002285

prune368.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1 (/ (hypot c d) (fma b c (- (* d a))))) (hypot c d))
0.2b
(/ 1 (/ (hypot c d) (fma b c (- (* d a)))))
0.8b
(fma b c (- (* d a)))
15.6b
(/ (hypot c d) (fma b c (- (* d a))))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
480×times-frac
239×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
50×associate-/l*
36×add-exp-log
23×div-inv
22×div-exp
20×add-cbrt-cube
19×associate-/r*
10×cbrt-undiv
5×pow1 associate-/r/
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u add-log-exp
3×frac-2neg clear-num
1×pow-flip fma-udef associate-/l/ inv-pow
Counts
4 → 319
Calls
4 calls:
24.0ms
(/ (/ 1 (/ (hypot c d) (fma b c (- (* d a))))) (hypot c d))
16.0ms
(/ 1 (/ (hypot c d) (fma b c (- (* d a)))))
0.0ms
(fma b c (- (* d a)))
6.0ms
(/ (hypot c d) (fma b c (- (* d a))))

series495.0ms

Counts
4 → 12
Calls
4 calls:
204.0ms
(/ (/ 1 (/ (hypot c d) (fma b c (- (* d a))))) (hypot c d))
132.0ms
(/ 1 (/ (hypot c d) (fma b c (- (* d a)))))
53.0ms
(fma b c (- (* d a)))
105.0ms
(/ (hypot c d) (fma b c (- (* d a))))

simplify1.3s

Counts
331 → 331
Iterations

Useful iterations: done (1.2s)

IterNodesCost
04599298
110188210
219127632
done50007450

prune620.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.9b

regimes220.0ms

Accuracy

35.9% (7.1b remaining)

Error of 12.6b against oracle of 5.5b and baseline of 16.6b

bsearch87.0ms

Steps
ItersRangePoint
11
1.3202626764746345e+144
1.2662851632966894e+177
3.3678318389903335e+157
8
-7.066707918776839e+146
-1.0923850232644114e+143
-4.468015220407937e+144

simplify6.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
02442
13536
24136
done4136

end0.0ms

sample1.1s

Algorithm
intervals
Results
834.0ms8530×body80valid