Details

Time bar (total: 17.2s)

sample364.0ms

Algorithm
intervals
Results
24.0ms198×body80valid
11.0ms17×body2560valid
11.0ms13×body5120valid
8.0ms14×body1280valid
4.0ms10×body640valid
1.0ms4×body320valid

simplify305.0ms

Counts
1 → 1
Iterations
IterNodes
done44
544
442
335
227
119
012

prune30.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.5b

localize74.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (* (- (hypot re im) re) 2.0))
0.0b
(- (hypot re im) re)

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×prod-diff add-cube-cbrt
5×pow1
4×add-log-exp
3×fma-neg
2×expm1-log1p-u sqrt-pow1 flip3-- add-cbrt-cube sqrt-div associate-*l/ add-exp-log insert-posit16 log1p-expm1-u flip--
1×sub-neg pow1/2 diff-log pow-prod-down sqrt-prod distribute-lft-out-- difference-of-squares
Counts
2 → 45
Calls
2 calls:
15.0ms
(sqrt (* (- (hypot re im) re) 2.0))
13.0ms
(- (hypot re im) re)

series291.0ms

Counts
2 → 6
Calls
2 calls:
201.0ms
(sqrt (* (- (hypot re im) re) 2.0))
90.0ms
(- (hypot re im) re)

simplify2.2s

Counts
51 → 51
Iterations
IterNodes
done5001
31768
2551
1237
0109

prune293.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 11.4b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (hypot re im))
0.0b
(sqrt (hypot re im))
0.0b
(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
14.3b
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1
8×add-sqr-sqrt
7×sqrt-prod
6×*-un-lft-identity add-cube-cbrt
4×expm1-log1p-u sqrt-pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/2
2×rem-sqrt-square
1×pow-prod-down fma-udef
Counts
4 → 57
Calls
4 calls:
2.0ms
(sqrt (hypot re im))
2.0ms
(sqrt (hypot re im))
8.0ms
(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
1.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series814.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(sqrt (hypot re im))
128.0ms
(sqrt (hypot re im))
361.0ms
(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
210.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify2.4s

Counts
69 → 69
Iterations
IterNodes
done5000
32087
2565
1207
097

prune452.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 11.3b

localize55.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))
0.4b
(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))))
14.3b
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
14.3b
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
21×sqrt-prod
20×pow1
13×*-un-lft-identity add-cube-cbrt
9×sqrt-pow1 pow1/2
8×swap-sqr
6×add-cbrt-cube associate-*r* associate-*l* add-exp-log
5×pow-prod-up
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×pow-prod-down pow-sqr
2×fma-udef
1×pow2 rem-sqrt-square rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Counts
4 → 90
Calls
4 calls:
2.0ms
(sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))
18.0ms
(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))))
0.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
1.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series804.0ms

Counts
4 → 12
Calls
4 calls:
243.0ms
(sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))
174.0ms
(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))))
180.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
208.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify1.8s

Counts
102 → 102
Iterations
IterNodes
done5000
31523
2442
1193
096

prune537.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 11.3b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))
0.0b
(- (hypot re im) re)
0.4b
(* (sqrt (- (hypot re im) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))))
14.3b
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
20×*-un-lft-identity
16×add-cube-cbrt
15×sqrt-prod
9×pow1 prod-diff
8×associate-*l*
6×add-cbrt-cube associate-*r* add-exp-log add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u unswap-sqr
3×sqrt-pow1 pow1/2 fma-neg pow-prod-down
2×flip3-- sqrt-div associate-*l/ flip-- distribute-lft-out-- difference-of-squares
1×rem-sqrt-square sub-neg sqrt-unprod diff-log prod-exp *-commutative cbrt-unprod fma-udef
Counts
4 → 93
Calls
4 calls:
1.0ms
(sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))
5.0ms
(- (hypot re im) re)
27.0ms
(* (sqrt (- (hypot re im) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))))
0.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series1.2s

Counts
4 → 12
Calls
4 calls:
227.0ms
(sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))
83.0ms
(- (hypot re im) re)
695.0ms
(* (sqrt (- (hypot re im) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))))
207.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify2.6s

Counts
105 → 105
Iterations
IterNodes
done5000
33669
21150
1431
0184

prune713.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 11.3b

regimes187.0ms

Accuracy

0% (0.3b remaining)

Error of 13.4b against oracle of 13.1b and baseline of 13.4b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done11
111
09

end0.0ms

sample1.9s

Algorithm
intervals
Results
658.0ms6014×body80valid
474.0ms676×body2560valid
228.0ms485×body1280valid
176.0ms282×body640valid
176.0ms293×body5120valid
41.0ms181×body320valid
10.0ms69×body160valid