Details

Time bar (total: 18.8s)

sample48.0ms

Algorithm
intervals
Results
19.0ms276×body80valid

simplify12.0ms

Counts
1 → 1
Iterations
IterNodes
done21
221
117
011

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.6b

localize23.0ms

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)))

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 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)))

series202.0ms

Counts
2 → 6
Calls
2 calls:
57.0ms
(fma x.re y.re (* x.im y.im))
145.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

simplify2.2s

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

prune345.0ms

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)))

rewrite19.0ms

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))
6.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
3.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
3.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

series341.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(fma x.re y.re (* x.im y.im))
161.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
60.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
72.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

simplify3.3s

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

prune659.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 25.3b

localize44.0ms

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)))

rewrite71.0ms

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:
50.0ms
(* (/ 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))))
2.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
3.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

series537.0ms

Counts
4 → 12
Calls
4 calls:
194.0ms
(* (/ 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)))))
195.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
81.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
67.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

simplify2.8s

Counts
170 → 170
Iterations
IterNodes
done5000
33830
21387
1456
0168

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 25.3b

localize44.0ms

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)))

rewrite18.0ms

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))
9.0ms
(/ (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)))

series392.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(fma x.re y.re (* x.im y.im))
161.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
80.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
91.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

simplify3.7s

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

prune815.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 25.3b

regimes547.0ms

Accuracy

-14.4% (3.3b remaining)

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

bsearch28.0ms

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

simplify5.0ms

Iterations
IterNodes
done21
121
017

end0.0ms

sample1.6s

Algorithm
intervals
Results
1.1s8473×body80valid