Details

Time bar (total: 17.6s)

sample25.0ms

Algorithm
intervals
Results
12.0ms272×body80valid

simplify18.0ms

Counts
1 → 1
Iterations
IterNodes
done21
221
117
011

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.2b

localize36.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma d d (* c c))
0.3b
(fma a c (* b d))
26.2b
(/ (fma a c (* b d)) (fma d d (* c c)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
5×add-cbrt-cube add-exp-log
3×expm1-log1p-u pow1 associate-/r* insert-posit16 log1p-expm1-u associate-/l* add-log-exp
2×fma-udef
1×cbrt-undiv clear-num frac-2neg div-exp div-inv
Counts
3 → 52
Calls
3 calls:
1.0ms
(fma d d (* c c))
1.0ms
(fma a c (* b d))
11.0ms
(/ (fma a c (* b d)) (fma d d (* c c)))

series221.0ms

Counts
3 → 9
Calls
3 calls:
56.0ms
(fma d d (* c c))
52.0ms
(fma a c (* b d))
112.0ms
(/ (fma a c (* b d)) (fma d d (* c c)))

simplify2.6s

Counts
61 → 61
Iterations
IterNodes
done5000
44024
31082
2340
1123
075

prune436.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 25.8b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(fma a c (* b d))
16.8b
(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
28.9b
(sqrt (fma d d (* c c)))
28.9b
(sqrt (fma d d (* c c)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
6×pow1 associate-/r* add-cbrt-cube add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×fma-udef associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 hypot-def
1×cbrt-undiv clear-num frac-2neg div-exp div-inv
Counts
4 → 87
Calls
4 calls:
0.0ms
(fma a c (* b d))
17.0ms
(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
1.0ms
(sqrt (fma d d (* c c)))
2.0ms
(sqrt (fma d d (* c c)))

series298.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(fma a c (* b d))
122.0ms
(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
49.0ms
(sqrt (fma d d (* c c)))
60.0ms
(sqrt (fma d d (* c c)))

simplify3.0s

Counts
99 → 99
Iterations
IterNodes
done5000
42818
3974
2304
1146
091

prune593.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 24.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (fma b d (* c a)) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))
16.8b
(/ (fma b d (* c a)) (sqrt (fma d d (* c c))))
28.9b
(sqrt (fma d d (* c c)))
28.9b
(sqrt (fma d d (* c c)))

rewrite36.0ms

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:
17.0ms
(/ (/ (fma b d (* c a)) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))
6.0ms
(/ (fma b d (* c a)) (sqrt (fma d d (* c c))))
1.0ms
(sqrt (fma d d (* c c)))
2.0ms
(sqrt (fma d d (* c c)))

series444.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(/ (/ (fma b d (* c a)) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))
163.0ms
(/ (fma b d (* c a)) (sqrt (fma d d (* c c))))
69.0ms
(sqrt (fma d d (* c c)))
70.0ms
(sqrt (fma d d (* c c)))

simplify2.4s

Counts
266 → 266
Iterations
IterNodes
done5064
34078
21154
1547
0262

prune1.5s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 15.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (hypot d c) (fma c a (* b d))) (hypot d c))
0.3b
(fma c a (* b d))
0.5b
(/ 1 (* (/ (hypot d c) (fma c a (* b d))) (hypot d c)))
16.9b
(/ (hypot d c) (fma c a (* b d)))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
27×add-sqr-sqrt
22×*-un-lft-identity times-frac add-cube-cbrt
20×add-cbrt-cube
13×associate-*l*
11×div-exp
9×pow1
8×prod-exp
6×cbrt-undiv associate-/l*
4×expm1-log1p-u associate-/r* cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×rec-exp 1-exp associate-*r* div-inv
2×clear-num frac-2neg pow-prod-down associate-*l/ pow-flip unswap-sqr
1×associate-/r/ *-commutative fma-udef inv-pow
Counts
4 → 112
Calls
4 calls:
28.0ms
(* (/ (hypot d c) (fma c a (* b d))) (hypot d c))
0.0ms
(fma c a (* b d))
26.0ms
(/ 1 (* (/ (hypot d c) (fma c a (* b d))) (hypot d c)))
9.0ms
(/ (hypot d c) (fma c a (* b d)))

series559.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(* (/ (hypot d c) (fma c a (* b d))) (hypot d c))
44.0ms
(fma c a (* b d))
241.0ms
(/ 1 (* (/ (hypot d c) (fma c a (* b d))) (hypot d c)))
124.0ms
(/ (hypot d c) (fma c a (* b d)))

simplify2.8s

Counts
124 → 124
Iterations
IterNodes
done5077
33511
21073
1308
0137

prune676.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 14.6b

regimes368.0ms

Accuracy

0% (3.2b remaining)

Error of 16.3b against oracle of 13.1b and baseline of 16.3b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done10
110
09

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.1s8467×body80valid