Details

Time bar (total: 15.7s)

sample30.0ms

Algorithm
intervals
Results
15.0ms271×body80valid

simplify7.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
011284
117234
221234
done21234

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.0b

localize28.0ms

Local error

Found 1 expressions with local error:

22.6b
(/ (fma a c (* b d)) (fma c c (* d d)))

rewrite9.0ms

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 log1p-expm1-u div-inv add-log-exp
Counts
1 → 29
Calls
1 calls:
8.0ms
(/ (fma a c (* b d)) (fma c c (* d d)))

series151.0ms

Counts
1 → 3
Calls
1 calls:
151.0ms
(/ (fma a c (* b d)) (fma c c (* d d)))

simplify2.8s

Counts
32 → 32
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
05811094
19510821
224010181
390610181
4439610181
done500010181

prune248.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 22.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (fma a c (* b d)) (sqrt (fma c c (* d d)))) (sqrt (fma c c (* d d))))
14.2b
(/ (fma a c (* b d)) (sqrt (fma c c (* d d))))
27.1b
(sqrt (fma c c (* d d)))
27.1b
(sqrt (fma c c (* d d)))

rewrite49.0ms

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 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 → 250
Calls
4 calls:
19.0ms
(/ (/ (fma a c (* b d)) (sqrt (fma c c (* d d)))) (sqrt (fma c c (* d d))))
5.0ms
(/ (fma a c (* b d)) (sqrt (fma c c (* d d))))
1.0ms
(sqrt (fma c c (* d d)))
1.0ms
(sqrt (fma c c (* d d)))

series444.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(/ (/ (fma a c (* b d)) (sqrt (fma c c (* d d)))) (sqrt (fma c c (* d d))))
193.0ms
(/ (fma a c (* b d)) (sqrt (fma c c (* d d))))
55.0ms
(sqrt (fma c c (* d d)))
61.0ms
(sqrt (fma c c (* d d)))

simplify2.1s

Counts
262 → 262
Iterations

Useful iterations: done (2.1s)

IterNodesCost
0259153997
1565143728
22237120927
done5000118367

prune1.4s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 12.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot c d)
0.1b
(/ (hypot c d) (/ (fma a c (* b d)) (hypot c d)))
0.8b
(/ 1 (/ (hypot c d) (/ (fma a c (* b d)) (hypot c d))))
14.2b
(/ (fma a c (* b d)) (hypot c d))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
480×times-frac
239×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
60×associate-/r*
32×add-exp-log
23×div-inv
20×add-cbrt-cube
19×div-exp
10×cbrt-undiv
9×associate-/l*
6×associate-/r/
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rec-exp clear-num frac-2neg 1-exp
1×hypot-udef pow-flip inv-pow
Counts
4 → 317
Calls
4 calls:
0.0ms
(hypot c d)
12.0ms
(/ (hypot c d) (/ (fma a c (* b d)) (hypot c d)))
16.0ms
(/ 1 (/ (hypot c d) (/ (fma a c (* b d)) (hypot c d))))
4.0ms
(/ (fma a c (* b d)) (hypot c d))

series524.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(hypot c d)
101.0ms
(/ (hypot c d) (/ (fma a c (* b d)) (hypot c d)))
215.0ms
(/ 1 (/ (hypot c d) (/ (fma a c (* b d)) (hypot c d))))
157.0ms
(/ (fma a c (* b d)) (hypot c d))

simplify1.6s

Counts
329 → 329
Iterations

Useful iterations: done (1.6s)

IterNodesCost
0439175285
11219152551
done5000150782

prune1.7s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.4b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot c d)
0.1b
(/ (/ 1 (/ (hypot c d) (fma a c (* b d)))) (hypot c d))
0.2b
(/ 1 (/ (hypot c d) (fma a c (* b d))))
14.4b
(/ (hypot c d) (fma a c (* b d)))

rewrite71.0ms

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 log1p-expm1-u add-log-exp
3×clear-num frac-2neg
1×hypot-udef pow-flip inv-pow associate-/l/
Counts
4 → 319
Calls
4 calls:
0.0ms
(hypot c d)
30.0ms
(/ (/ 1 (/ (hypot c d) (fma a c (* b d)))) (hypot c d))
16.0ms
(/ 1 (/ (hypot c d) (fma a c (* b d))))
8.0ms
(/ (hypot c d) (fma a c (* b d)))

series514.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(hypot c d)
220.0ms
(/ (/ 1 (/ (hypot c d) (fma a c (* b d)))) (hypot c d))
133.0ms
(/ 1 (/ (hypot c d) (fma a c (* b d))))
105.0ms
(/ (hypot c d) (fma a c (* b d)))

simplify1.3s

Counts
331 → 331
Iterations

Useful iterations: done (1.3s)

IterNodesCost
0459177395
11314151107
done5000145394

prune1.1s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 6.4b

regimes325.0ms

Accuracy

34.2% (7.5b remaining)

Error of 13.5b against oracle of 6.0b and baseline of 17.4b

bsearch73.0ms

Steps
ItersRangePoint
6
7.997843383138597e+191
8.056208352901572e+192
8.747123436813268e+191
10
-3.959953710600684e+125
-7.632284195501427e+113
-2.0458466692374305e+123

simplify5.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
021697
126697
done26697

end0.0ms

sample1.0s

Algorithm
intervals
Results
789.0ms8463×body80valid