Details

Time bar (total: 10.8s)

sample18.0ms

Algorithm
intervals
Results
8.0ms264×body80valid

simplify51.0ms

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: 25.5b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma c c (* d d))
1.2b
(- (* b c) (* a d))
25.0b
(/ (- (* b c) (* a d)) (fma c c (* d d)))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
5×add-exp-log add-cbrt-cube add-log-exp
3×pow1 expm1-log1p-u associate-/r* log1p-expm1-u associate-/l*
2×flip3-- flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg fma-neg diff-log div-sub div-exp prod-diff clear-num fma-udef div-inv
Counts
3 → 58
Calls
3 calls:
0.0ms
(fma c c (* d d))
3.0ms
(- (* b c) (* a d))
7.0ms
(/ (- (* b c) (* a d)) (fma c c (* d d)))

series163.0ms

Counts
3 → 9
Calls
3 calls:
34.0ms
(fma c c (* d d))
41.0ms
(- (* b c) (* a d))
88.0ms
(/ (- (* b c) (* a d)) (fma c c (* d d)))

simplify1.0s

Counts
67 → 67
Iterations

Useful iterations: done (1.0s)

IterNodesCost
0961039
12231011
2745892
32701892
done5000890

prune197.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot d c)
0.2b
(* (/ 1 (hypot d c)) (/ (fma b c (- (* d a))) (hypot d c)))
0.3b
(fma b c (- (* d a)))
15.9b
(/ (fma b c (- (* d a))) (hypot d c))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
34×times-frac
28×add-exp-log *-un-lft-identity
26×add-cube-cbrt
18×add-cbrt-cube
13×associate-*r* associate-*l*
9×div-exp
8×prod-exp
6×pow1 unswap-sqr
5×cbrt-undiv
4×expm1-log1p-u cbrt-unprod log1p-expm1-u add-log-exp
3×associate-/r* div-inv associate-/l*
2×rec-exp 1-exp
1×frac-times hypot-udef frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative fma-udef
Counts
4 → 107
Calls
4 calls:
0.0ms
(hypot d c)
14.0ms
(* (/ 1 (hypot d c)) (/ (fma b c (- (* d a))) (hypot d c)))
0.0ms
(fma b c (- (* d a)))
2.0ms
(/ (fma b c (- (* d a))) (hypot d c))

series387.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(hypot d c)
166.0ms
(* (/ 1 (hypot d c)) (/ (fma b c (- (* d a))) (hypot d c)))
42.0ms
(fma b c (- (* d a)))
131.0ms
(/ (fma b c (- (* d a))) (hypot d c))

simplify3.0s

Counts
119 → 119
Iterations

Useful iterations: 2 (155.0ms)

IterNodesCost
01472085
13651952
210881694
347761694
done50001694

prune341.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot d c)
0.1b
(/ (/ (fma b c (- (* d a))) (hypot d c)) (hypot d c))
0.3b
(fma b c (- (* d a)))
15.9b
(/ (fma b c (- (* d a))) (hypot d c))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
54×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×associate-/l*
11×add-exp-log add-cbrt-cube
6×associate-/r* div-inv
4×pow1 cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
2×frac-2neg clear-num
1×hypot-udef fma-udef associate-/l/
Counts
4 → 121
Calls
4 calls:
0.0ms
(hypot d c)
6.0ms
(/ (/ (fma b c (- (* d a))) (hypot d c)) (hypot d c))
0.0ms
(fma b c (- (* d a)))
2.0ms
(/ (fma b c (- (* d a))) (hypot d c))

series354.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(hypot d c)
132.0ms
(/ (/ (fma b c (- (* d a))) (hypot d c)) (hypot d c))
44.0ms
(fma b c (- (* d a)))
134.0ms
(/ (fma b c (- (* d a))) (hypot d c))

simplify1.4s

Counts
133 → 133
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01682712
13442650
28342455
326682401
done50002399

prune438.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1 (/ (hypot d c) (fma b c (- (* d a))))) (hypot d c))
0.2b
(/ 1 (/ (hypot d c) (fma b c (- (* d a)))))
0.3b
(fma b c (- (* d a)))
16.0b
(/ (hypot d c) (fma b c (- (* d a))))

rewrite44.0ms

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:
15.0ms
(/ (/ 1 (/ (hypot d c) (fma b c (- (* d a))))) (hypot d c))
5.0ms
(/ 1 (/ (hypot d c) (fma b c (- (* d a)))))
0.0ms
(fma b c (- (* d a)))
2.0ms
(/ (hypot d c) (fma b c (- (* d a))))

series449.0ms

Counts
4 → 12
Calls
4 calls:
164.0ms
(/ (/ 1 (/ (hypot d c) (fma b c (- (* d a))))) (hypot d c))
151.0ms
(/ 1 (/ (hypot d c) (fma b c (- (* d a)))))
42.0ms
(fma b c (- (* d a)))
91.0ms
(/ (hypot d c) (fma b c (- (* d a))))

simplify1.4s

Counts
331 → 331
Iterations

Useful iterations: done (1.4s)

IterNodesCost
04589296
110788209
221857631
done50007559

prune656.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 1.9b

regimes212.0ms

Accuracy

28.7% (10.0b remaining)

Error of 12.5b against oracle of 2.5b and baseline of 16.5b

bsearch77.0ms

Steps
ItersRangePoint
6
2.364246562673592e+136
1.4357828132925017e+137
2.5019882417216274e+136
10
-1.4584171055257321e+175
-1.1045029026290381e+161
-5.9876509466672635e+162

simplify7.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
02760
13854
24154
34454
44854
done4854

end0.0ms

sample468.0ms

Algorithm
intervals
Results
270.0ms8495×body80valid