Details

Time bar (total: 13.5s)

sample39.0ms

Algorithm
intervals
Results
18.0ms276×body80valid

simplify20.0ms

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)))

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

series164.0ms

Counts
2 → 6
Calls
2 calls:
42.0ms
(fma x.re y.re (* x.im y.im))
122.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

simplify1.9s

Counts
45 → 45
Iterations
IterNodes
done5002
32442
2402
1104
065

prune367.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 26.8b

localize29.0ms

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)))

rewrite11.0ms

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)))
1.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

series338.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(fma x.re y.re (* x.im y.im))
167.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
65.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
56.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

simplify1.1s

Counts
95 → 95
Iterations
IterNodes
done5000
31259
2375
1138
090

prune795.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 25.3b

localize52.0ms

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)))

rewrite66.0ms

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:
46.0ms
(* (/ 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)))))
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)))
2.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

series496.0ms

Counts
4 → 12
Calls
4 calls:
179.0ms
(* (/ 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)))))
200.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
64.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
52.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

simplify2.9s

Counts
170 → 170
Iterations
IterNodes
done5000
22985
1462
0168

prune971.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 25.3b

localize27.0ms

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)))

rewrite16.0ms

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))))
1.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
1.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

series367.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(fma x.re y.re (* x.im y.im))
175.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
86.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
58.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

simplify1.2s

Counts
95 → 95
Iterations
IterNodes
done5000
31259
2375
1138
090

prune595.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 25.3b

regimes455.0ms

Accuracy

-14.4% (3.3b remaining)

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

bsearch53.0ms

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

simplify6.0ms

Iterations
IterNodes
done22
222
121
017

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.1s8473×body80valid