Details

Time bar (total: 22.5s)

sample46.0ms

Algorithm
intervals
Results
22.0ms268×body80valid

simplify15.0ms

Counts
1 → 1
Iterations
IterNodes
done21
221
117
011

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma a c (* b d))
27.6b
(/ (fma a c (* b d)) (fma d d (* c c)))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
4×add-cbrt-cube add-exp-log
3×associate-/r* associate-/l*
2×expm1-log1p-u pow1 log1p-expm1-u add-log-exp
1×cbrt-undiv clear-num frac-2neg div-exp fma-udef div-inv
Counts
2 → 39
Calls
2 calls:
0.0ms
(fma a c (* b d))
7.0ms
(/ (fma a c (* b d)) (fma d d (* c c)))

series218.0ms

Counts
2 → 6
Calls
2 calls:
60.0ms
(fma a c (* b d))
158.0ms
(/ (fma a c (* b d)) (fma d d (* c c)))

simplify2.6s

Counts
45 → 45
Iterations
IterNodes
done5015
43383
3969
2291
1107
063

prune351.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 27.3b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))
17.2b
(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
28.8b
(sqrt (fma d d (* c c)))
28.8b
(sqrt (fma d d (* c c)))

rewrite45.0ms

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:
15.0ms
(/ (/ (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)))

series458.0ms

Counts
4 → 12
Calls
4 calls:
165.0ms
(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))
174.0ms
(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
56.0ms
(sqrt (fma d d (* c c)))
63.0ms
(sqrt (fma d d (* c c)))

simplify2.4s

Counts
262 → 262
Iterations
IterNodes
done5000
33674
21121
1549
0259

prune2.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot d c)
0.0b
(fma c a (* b d))
0.1b
(/ (/ (fma c a (* b d)) (hypot d c)) (hypot d c))
17.2b
(/ (fma c a (* b d)) (hypot d c))

rewrite17.0ms

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 log1p-expm1-u add-log-exp
2×clear-num frac-2neg
1×hypot-udef fma-udef associate-/l/
Counts
4 → 121
Calls
4 calls:
0.0ms
(hypot d c)
0.0ms
(fma c a (* b d))
9.0ms
(/ (/ (fma c a (* b d)) (hypot d c)) (hypot d c))
4.0ms
(/ (fma c a (* b d)) (hypot d c))

series484.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(hypot d c)
67.0ms
(fma c a (* b d))
162.0ms
(/ (/ (fma c a (* b d)) (hypot d c)) (hypot d c))
183.0ms
(/ (fma c a (* b d)) (hypot d c))

simplify2.5s

Counts
133 → 133
Iterations
IterNodes
done5061
33599
2910
1344
0167

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.9b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (hypot d c))
0.1b
(/ (/ (/ (fma c a (* b d)) (sqrt (hypot d c))) (sqrt (hypot d c))) (hypot d c))
8.5b
(/ (/ (fma c a (* b d)) (sqrt (hypot d c))) (sqrt (hypot d c)))
8.7b
(/ (fma c a (* b d)) (sqrt (hypot d c)))

rewrite183.0ms

Algorithm
rewrite-expression-head
Rules
1644×times-frac
787×add-sqr-sqrt
786×*-un-lft-identity add-cube-cbrt
627×sqrt-prod
161×associate-/l*
38×div-inv
20×add-cbrt-cube add-exp-log
15×associate-/r*
10×cbrt-undiv div-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×clear-num frac-2neg
2×associate-/l/
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 799
Calls
4 calls:
1.0ms
(sqrt (hypot d c))
74.0ms
(/ (/ (/ (fma c a (* b d)) (sqrt (hypot d c))) (sqrt (hypot d c))) (hypot d c))
21.0ms
(/ (/ (fma c a (* b d)) (sqrt (hypot d c))) (sqrt (hypot d c)))
5.0ms
(/ (fma c a (* b d)) (sqrt (hypot d c)))

series714.0ms

Counts
4 → 12
Calls
4 calls:
131.0ms
(sqrt (hypot d c))
196.0ms
(/ (/ (/ (fma c a (* b d)) (sqrt (hypot d c))) (sqrt (hypot d c))) (hypot d c))
164.0ms
(/ (/ (fma c a (* b d)) (sqrt (hypot d c))) (sqrt (hypot d c)))
222.0ms
(/ (fma c a (* b d)) (sqrt (hypot d c)))

simplify2.8s

Counts
811 → 811
Iterations
IterNodes
done5000
24764
11970
0846

prune4.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.9b

regimes488.0ms

Accuracy

32.9% (7.7b remaining)

Error of 13.9b against oracle of 6.2b and baseline of 17.7b

bsearch125.0ms

Steps
ItersRangePoint
10
1.1063855308468765e+219
1.1167816988421008e+230
1.118997009957087e+219
7
-1.2513451800241158e+129
-6.14118040551932e+127
-1.089461735547702e+128

simplify7.0ms

Iterations
IterNodes
done35
335
234
131
023

end0.0ms

sample1.2s

Algorithm
intervals
Results
947.0ms8480×body80valid