Details

Time bar (total: 24.1s)

sample40.0ms

Algorithm
intervals
Results
25.0ms272×body80valid

simplify55.0ms

Counts
1 → 1
Iterations
IterNodes
done80
580
476
356
240
121
011

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.6b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma y.im y.im (* y.re y.re))
0.2b
(- (* x.im y.re) (* x.re y.im))
22.6b
(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

rewrite285.0ms

Algorithm
rewrite-expression-head
Rules
204×add-sqr-sqrt
144×prod-diff
134×*-un-lft-identity
95×associate-*l*
94×add-cube-cbrt
75×associate-*r*
45×unswap-sqr
33×times-frac
25×*-commutative
20×distribute-lft-out-- difference-of-squares
12×fma-neg
11×associate-/l*
5×add-cbrt-cube add-exp-log add-log-exp
3×expm1-log1p-u pow1 associate-/r* insert-posit16 log1p-expm1-u
2×flip3-- flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-sub div-exp fma-udef div-inv
Counts
3 → 255
Calls
3 calls:
1.0ms
(fma y.im y.im (* y.re y.re))
90.0ms
(- (* x.im y.re) (* x.re y.im))
175.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

series246.0ms

Counts
3 → 9
Calls
3 calls:
58.0ms
(fma y.im y.im (* y.re y.re))
50.0ms
(- (* x.im y.re) (* x.re y.im))
138.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

simplify1.8s

Counts
264 → 264
Iterations
IterNodes
done5002
21628
1711
0321

prune919.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 22.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* x.im y.re) (* x.re y.im))
11.8b
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
28.6b
(sqrt (fma y.im y.im (* y.re y.re)))
28.6b
(sqrt (fma y.im y.im (* y.re y.re)))

rewrite236.0ms

Algorithm
rewrite-expression-head
Rules
260×add-sqr-sqrt
176×*-un-lft-identity
144×prod-diff
112×add-cube-cbrt
107×associate-*l*
75×associate-*r*
66×times-frac
57×unswap-sqr
42×sqrt-prod
32×distribute-lft-out-- difference-of-squares
25×*-commutative
12×fma-neg
11×associate-/l*
6×pow1 associate-/r* add-cbrt-cube add-exp-log add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
2×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 fma-udef hypot-def flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-sub div-exp div-inv
Counts
4 → 314
Calls
4 calls:
70.0ms
(- (* x.im y.re) (* x.re y.im))
141.0ms
(/ (- (* x.im y.re) (* x.re 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)))

series304.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(- (* x.im y.re) (* x.re y.im))
145.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
50.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
67.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

simplify2.9s

Counts
326 → 326
Iterations
IterNodes
done5000
34986
21576
1756
0351

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 20.8b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* x.im y.re) (* x.re y.im))
12.0b
(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (fma y.im y.im (* y.re y.re)))))
28.6b
(sqrt (fma y.im y.im (* y.re y.re)))
28.6b
(sqrt (fma y.im y.im (* y.re y.re)))

rewrite370.0ms

Algorithm
rewrite-expression-head
Rules
192×add-sqr-sqrt
144×prod-diff
123×*-un-lft-identity
104×add-cube-cbrt
97×associate-*r*
94×associate-*l*
38×unswap-sqr
26×*-commutative sqrt-prod
24×frac-times
22×times-frac
18×associate-/r*
14×flip3-- flip--
13×add-exp-log
12×fma-neg associate-*r/
10×associate-/l*
9×add-cbrt-cube
8×pow1 distribute-lft-out-- difference-of-squares
6×add-log-exp
4×expm1-log1p-u clear-num prod-exp insert-posit16 log1p-expm1-u
3×frac-2neg un-div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2 div-exp associate-*l/ cbrt-unprod fma-udef hypot-def
1×cbrt-undiv rec-exp sub-neg diff-log 1-exp pow-prod-down div-inv
Counts
4 → 310
Calls
4 calls:
100.0ms
(- (* x.im y.re) (* x.re y.im))
243.0ms
(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (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)))

series369.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(- (* x.im y.re) (* x.re y.im))
164.0ms
(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (fma y.im y.im (* y.re y.re)))))
80.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
70.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

simplify2.3s

Counts
322 → 322
Iterations
IterNodes
done5002
22162
1907
0378

prune1.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 20.8b

localize65.0ms

Local error

Found 4 expressions with local error:

6.9b
(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (sqrt (fma y.im y.im (* y.re y.re))))) (sqrt (sqrt (fma y.im y.im (* y.re y.re)))))
28.6b
(sqrt (fma y.im y.im (* y.re y.re)))
28.6b
(sqrt (fma y.im y.im (* y.re y.re)))
28.6b
(sqrt (fma y.im y.im (* y.re y.re)))

rewrite444.0ms

Algorithm
rewrite-expression-head
Rules
1944×sqrt-prod
1917×times-frac
1848×add-sqr-sqrt
1481×*-un-lft-identity
753×add-cube-cbrt
364×associate-*l* distribute-lft-out-- difference-of-squares unswap-sqr
114×associate-/l*
27×associate-/l/
18×associate-/r*
11×div-inv
9×add-cbrt-cube add-exp-log
7×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp fma-udef hypot-def
2×clear-num frac-2neg div-sub
1×flip3-- flip--
Counts
4 → 1133
Calls
4 calls:
261.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (sqrt (fma y.im y.im (* y.re y.re))))) (sqrt (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)))
3.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

series346.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (sqrt (fma y.im y.im (* y.re y.re))))) (sqrt (sqrt (fma y.im y.im (* y.re y.re)))))
62.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
59.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
85.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

simplify3.5s

Counts
1145 → 1145
Iterations
IterNodes
done5000
24194
11769
0801

prune4.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 20.8b

regimes320.0ms

Accuracy

0% (2.5b remaining)

Error of 25.1b against oracle of 22.6b and baseline of 25.1b

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done19
119
014

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.6s8445×body80valid