Details

Time bar (total: 3.4s)

sample29.0ms

Algorithm
intervals
Results
16.0ms272×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0177
1217
2217

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 26.5b

Counts
2 → 1

localize12.0ms

Local error

Found 2 expressions with local error:

0.5b
(+ (* x.re y.re) (* x.im y.im))
26.2b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×flip3-+ associate-/r* flip-+ associate-/l*
2×pow1 expm1-log1p-u associate-/r/ log1p-expm1-u associate-/l/
1×cbrt-undiv +-commutative fma-def frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 47
Calls
2 calls:
4.0ms
(+ (* x.re y.re) (* x.im y.im))
8.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series163.0ms

Counts
2 → 6
Calls
2 calls:
45.0ms
(+ (* x.re y.re) (* x.im y.im))
118.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify98.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0244458
1872411
23164403
35001403

prune145.0ms

Filtered
53 candidates to 44 candidates (83.0%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New44953
Fresh000
Picked011
Done000
Total441054

Merged error: 15.8b

Counts
54 → 10

localize10.0ms

Local error

Found 2 expressions with local error:

0.3b
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
15.4b
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
153×add-exp-log
86×prod-exp
57×div-exp
43×add-cbrt-cube
35×1-exp
16×cbrt-unprod
14×cbrt-undiv
12×rec-exp
10×add-sqr-sqrt
9×times-frac
8×add-cube-cbrt *-un-lft-identity
7×associate-*r* associate-*l*
4×pow1
3×div-inv associate-/l*
2×expm1-log1p-u log1p-expm1-u add-log-exp
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num associate-/r* *-commutative unswap-sqr
Counts
2 → 102
Calls
2 calls:
11.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
4.0ms
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

series288.0ms

Counts
2 → 6
Calls
2 calls:
178.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
111.0ms
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

simplify47.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
04651038
11570760
25001758

prune177.0ms

Filtered
108 candidates to 48 candidates (44.4%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New999108
Fresh718
Picked101
Done011
Total10711118

Merged error: 6.4b

Counts
118 → 11

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
15.4b
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
40×times-frac
24×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
21×add-exp-log
16×add-cbrt-cube associate-/l*
10×div-exp
7×cbrt-undiv
4×prod-exp associate-/r* div-inv
2×pow1 expm1-log1p-u frac-2neg 1-exp clear-num cbrt-unprod log1p-expm1-u add-log-exp
1×associate-/l/
Counts
2 → 79
Calls
2 calls:
10.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
3.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series227.0ms

Counts
2 → 6
Calls
2 calls:
114.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
113.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify75.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 3 (66.0ms)

IterNodesCost
0290726
11060641
23129641
35001634

prune206.0ms

Filtered
85 candidates to 64 candidates (75.3%)
Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New79685
Fresh459
Picked011
Done011
Total831396

Merged error: 6.4b

Counts
96 → 13

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))) (* (hypot y.re y.im) 1))
0.2b
(/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im))))
15.5b
(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
260×times-frac
123×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
80×add-exp-log
50×div-exp associate-/l*
31×add-cbrt-cube
17×associate-/r*
16×cbrt-undiv
15×1-exp div-inv
14×prod-exp
8×rec-exp
4×pow1
3×expm1-log1p-u frac-2neg clear-num associate-/r/ cbrt-unprod log1p-expm1-u add-log-exp
1×pow-flip associate-/l/ inv-pow
Counts
3 → 236
Calls
3 calls:
13.0ms
(/ (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))) (* (hypot y.re y.im) 1))
6.0ms
(/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im))))
3.0ms
(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))

series385.0ms

Counts
3 → 9
Calls
3 calls:
180.0ms
(/ (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))) (* (hypot y.re y.im) 1))
115.0ms
(/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im))))
90.0ms
(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))

simplify80.0ms

Algorithm
egg-herbie
Counts
245 → 245
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
07882549
136412224
250012062

prune381.0ms

Filtered
245 candidates to 130 candidates (53.1%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New2441245
Fresh1910
Picked011
Done112
Total24612258

Merged error: 6.4b

Counts
258 → 12

regimes259.0ms

Accuracy

35.5% (7.3b remaining)

Error of 13.1b against oracle of 5.8b and baseline of 17.1b

bsearch79.0ms

Steps
ItersRangePoint
6
2.785836946022763e+173
3.318950338713399e+174
3.952297659823982e+173
10
-1.3123487377944479e+153
-4.2328545580813956e+142
-3.148568769446241e+146

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02815
13115
23115

end0.0ms

sample580.0ms

Algorithm
intervals
Results
374.0ms8447×body80valid