Details

Time bar (total: 18.6s)

sample43.0ms

Algorithm
intervals
Results
20.0ms276×body80valid

simplify10.0ms

Counts
1 → 1
Iterations
IterNodes
done21
221
117
011

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.6b

localize22.0ms

Local error

Found 2 expressions with local error:

0.3b
(fma x.re y.re (* x.im y.im))
27.2b
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

rewrite8.0ms

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 x.re y.re (* x.im y.im))
7.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

series191.0ms

Counts
2 → 6
Calls
2 calls:
47.0ms
(fma x.re y.re (* x.im y.im))
144.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

simplify2.4s

Counts
45 → 45
Iterations
IterNodes
done5001
42350
3700
2244
1104
065

prune346.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 26.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b
(fma x.re y.re (* x.im y.im))
15.3b
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
31.3b
(sqrt (fma y.im y.im (* y.re y.re)))
31.3b
(sqrt (fma y.im y.im (* y.re y.re)))

rewrite10.0ms

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 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 → 83
Calls
4 calls:
0.0ms
(fma x.re y.re (* x.im y.im))
5.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
1.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
2.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

series356.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(fma x.re y.re (* x.im y.im))
185.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
49.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
74.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

simplify3.5s

Counts
95 → 95
Iterations
IterNodes
done5000
54414
41335
3532
2242
1138
090

prune757.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 25.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1 (sqrt (fma y.im y.im (* y.re y.re)))) (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))))
15.3b
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
31.3b
(sqrt (fma y.im y.im (* y.re y.re)))
31.3b
(sqrt (fma y.im y.im (* y.re y.re)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
95×add-sqr-sqrt
76×times-frac
53×*-un-lft-identity
47×add-cube-cbrt sqrt-prod
28×add-exp-log
22×associate-*r* associate-*l*
18×add-cbrt-cube
15×unswap-sqr
9×div-exp
8×pow1 prod-exp
6×associate-/r*
5×cbrt-undiv
4×expm1-log1p-u cbrt-unprod log1p-expm1-u add-log-exp
3×div-inv associate-/l*
2×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp fma-udef hypot-def
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 158
Calls
4 calls:
39.0ms
(* (/ 1 (sqrt (fma y.im y.im (* y.re y.re)))) (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))))
5.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
1.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
1.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

series451.0ms

Counts
4 → 12
Calls
4 calls:
188.0ms
(* (/ 1 (sqrt (fma y.im y.im (* y.re y.re)))) (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))))
154.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
61.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
48.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

simplify2.7s

Counts
170 → 170
Iterations
IterNodes
done5000
33830
21387
1456
0168

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 25.3b

localize55.0ms

Local error

Found 4 expressions with local error:

0.3b
(fma x.re y.re (* x.im y.im))
15.3b
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
31.3b
(sqrt (fma y.im y.im (* y.re y.re)))
31.3b
(sqrt (fma y.im y.im (* y.re y.re)))

rewrite20.0ms

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 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 → 83
Calls
4 calls:
0.0ms
(fma x.re y.re (* x.im y.im))
10.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
2.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
3.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

series384.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(fma x.re y.re (* x.im y.im))
163.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
83.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
81.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

simplify3.3s

Counts
95 → 95
Iterations
IterNodes
done5000
54414
41335
3532
2242
1138
090

prune739.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 25.3b

regimes565.0ms

Accuracy

-14.4% (3.3b remaining)

Error of 26.2b against oracle of 22.9b and baseline of 25.8b

bsearch26.0ms

Steps
ItersRangePoint
5
1.34232255763024e+37
2.8506796103821506e+37
2.814854621501251e+37

simplify4.0ms

Iterations
IterNodes
done21
121
017

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.1s8473×body80valid