Details

Time bar (total: 18.3s)

sample32.0ms

Algorithm
intervals
Results
21.0ms268×body80valid

simplify8.0ms

Counts
1 → 1
Iterations
IterNodes
done21
221
117
011

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.8b

localize18.0ms

Local error

Found 1 expressions with local error:

27.8b
(/ (fma a c (* b d)) (fma d d (* c c)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
3×associate-/r* add-cbrt-cube add-exp-log associate-/l*
1×expm1-log1p-u pow1 cbrt-undiv clear-num frac-2neg div-exp insert-posit16 log1p-expm1-u div-inv add-log-exp
Counts
1 → 30
Calls
1 calls:
19.0ms
(/ (fma a c (* b d)) (fma d d (* c c)))

series124.0ms

Counts
1 → 3
Calls
1 calls:
124.0ms
(/ (fma a c (* b d)) (fma d d (* c c)))

simplify1.1s

Counts
33 → 33
Iterations
IterNodes
done2007
42007
3770
2232
196
059

prune405.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 27.3b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))
18.6b
(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
28.3b
(sqrt (fma d d (* c c)))
28.3b
(sqrt (fma d d (* c c)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
276×times-frac
160×add-sqr-sqrt
158×*-un-lft-identity add-cube-cbrt
150×sqrt-prod
25×associate-/l*
12×associate-/r*
11×add-cbrt-cube add-exp-log
9×div-inv
6×pow1
4×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 fma-udef hypot-def
1×associate-/l/
Counts
4 → 254
Calls
4 calls:
10.0ms
(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))
5.0ms
(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
1.0ms
(sqrt (fma d d (* c c)))
1.0ms
(sqrt (fma d d (* c c)))

series365.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))
144.0ms
(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
47.0ms
(sqrt (fma d d (* c c)))
58.0ms
(sqrt (fma d d (* c c)))

simplify1.2s

Counts
266 → 266
Iterations
IterNodes
done2006
32006
21154
1547
0262

prune4.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 16.8b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot d c)
0.0b
(fma b d (* c a))
0.0b
(/ (/ (fma b d (* c a)) (hypot d c)) (hypot d c))
18.6b
(/ (fma b d (* c a)) (hypot d c))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
54×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
16×associate-/l*
11×add-cbrt-cube add-exp-log
6×associate-/r* div-inv
4×expm1-log1p-u pow1 cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg
1×hypot-udef fma-udef associate-/l/
Counts
4 → 125
Calls
4 calls:
1.0ms
(hypot d c)
1.0ms
(fma b d (* c a))
24.0ms
(/ (/ (fma b d (* c a)) (hypot d c)) (hypot d c))
9.0ms
(/ (fma b d (* c a)) (hypot d c))

series469.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(hypot d c)
54.0ms
(fma b d (* c a))
158.0ms
(/ (/ (fma b d (* c a)) (hypot d c)) (hypot d c))
184.0ms
(/ (fma b d (* c a)) (hypot d c))

simplify1.1s

Counts
137 → 137
Iterations
IterNodes
done2001
32001
2919
1346
0171

prune1.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma b d (* c a))
0.0b
(/ (/ 1 (/ (hypot d c) (fma b d (* c a)))) (hypot d c))
0.2b
(/ 1 (/ (hypot d c) (fma b d (* c a))))
18.7b
(/ (hypot d c) (fma b d (* c a)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
480×times-frac
239×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
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 insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg
1×fma-udef pow-flip inv-pow associate-/l/
Counts
4 → 323
Calls
4 calls:
0.0ms
(fma b d (* c a))
11.0ms
(/ (/ 1 (/ (hypot d c) (fma b d (* c a)))) (hypot d c))
7.0ms
(/ 1 (/ (hypot d c) (fma b d (* c a))))
5.0ms
(/ (hypot d c) (fma b d (* c a)))

series527.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(fma b d (* c a))
226.0ms
(/ (/ 1 (/ (hypot d c) (fma b d (* c a)))) (hypot d c))
132.0ms
(/ 1 (/ (hypot d c) (fma b d (* c a))))
112.0ms
(/ (hypot d c) (fma b d (* c a)))

simplify1.2s

Counts
335 → 335
Iterations
IterNodes
done2001
22001
11263
0462

prune3.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.3b

regimes300.0ms

Accuracy

31.5% (7.9b remaining)

Error of 13.0b against oracle of 5.2b and baseline of 16.6b

bsearch100.0ms

Steps
ItersRangePoint
11
3.256921449474541e+176
7.122284858877049e+195
4.711008584896772e+178
6
-8.126158358066474e+96
-1.2737663299885354e+96
-7.67400831190257e+96

simplify10.0ms

Iterations
IterNodes
done34
334
233
130
023

end0.0ms

sample1.6s

Algorithm
intervals
Results
895.0ms8453×body80valid