Details

Time bar (total: 21.2s)

sample331.0ms

Algorithm
intervals
Results
66.0ms192×body80valid
19.0ms14×body5120valid
15.0ms19×body1280valid
13.0ms13×body2560valid
5.0ms8×body640valid
2.0ms5×body320valid
1.0ms5×body160valid

simplify109.0ms

Counts
1 → 1
Iterations
IterNodes
644
544
442
335
227
119
012

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.0b

localize31.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (* (- (hypot re im) re) 2.0))
1.3b
(- (hypot re im) re)

rewrite45.0ms

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:
17.0ms
(sqrt (* (- (hypot re im) re) 2.0))
14.0ms
(- (hypot re im) re)

series667.0ms

Counts
2 → 6
Calls
2 calls:
432.0ms
(sqrt (* (- (hypot re im) re) 2.0))
234.0ms
(- (hypot re im) re)

simplify3.5s

Counts
51 → 51
Iterations
IterNodes
45135
31673
2511
1222
0109

prune185.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 12.7b

localize31.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
15.4b
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
5×pow1
2×add-sqr-sqrt expm1-log1p-u *-un-lft-identity sqrt-pow1 add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
1×pow1/2 pow-prod-down sqrt-prod fma-udef
Counts
2 → 25
Calls
2 calls:
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))

series539.0ms

Counts
2 → 6
Calls
2 calls:
333.0ms
(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
207.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify2.5s

Counts
31 → 31
Iterations
IterNodes
44060
31195
2360
1140
067

prune183.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 12.7b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0)))
0.4b
(* (sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))) (sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))))
15.4b
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
15.4b
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
80×sqrt-pow1
65×pow1
31×sqrt-prod
26×add-sqr-sqrt
23×pow-prod-down
20×pow1/2
14×pow-prod-up
13×*-un-lft-identity add-cube-cbrt
9×swap-sqr
8×pow-sqr
7×associate-*r* associate-*l*
6×add-cbrt-cube add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×fma-udef
1×pow2 rem-sqrt-square rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Counts
4 → 116
Calls
4 calls:
7.0ms
(sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0)))
58.0ms
(* (sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))) (sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))))
0.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
0.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series1.0s

Counts
4 → 12
Calls
4 calls:
313.0ms
(sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0)))
343.0ms
(* (sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))) (sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))))
169.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
202.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify1.6s

Counts
128 → 128
Iterations
IterNodes
33733
21153
1418
0177

prune629.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.7b

localize77.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0)))
0.4b
(* (sqrt (sqrt (* (+ (hypot re im) (- re)) 2.0))) (sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))))
1.3b
(+ (hypot re im) (- re))
15.4b
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
26×sqrt-pow1
24×pow1
19×add-sqr-sqrt sqrt-prod
14×*-un-lft-identity
13×pow-prod-down
10×add-cube-cbrt
8×add-log-exp
7×associate-*r* associate-*l*
6×add-cbrt-cube pow1/2 add-exp-log
4×expm1-log1p-u sqrt-div associate-*l/ insert-posit16 log1p-expm1-u unswap-sqr
3×fma-def
2×sum-log flip3-+ flip-+ distribute-lft-out
1×neg-sub0 +-commutative rem-sqrt-square associate-+r- distribute-rgt-neg-in sqrt-unprod unsub-neg neg-log prod-exp *-commutative cbrt-unprod fma-udef
Counts
4 → 96
Calls
4 calls:
8.0ms
(sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0)))
84.0ms
(* (sqrt (sqrt (* (+ (hypot re im) (- re)) 2.0))) (sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))))
12.0ms
(+ (hypot re im) (- re))
1.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series1.4s

Counts
4 → 12
Calls
4 calls:
379.0ms
(sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0)))
642.0ms
(* (sqrt (sqrt (* (+ (hypot re im) (- re)) 2.0))) (sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))))
100.0ms
(+ (hypot re im) (- re))
244.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify3.8s

Counts
108 → 108
Iterations
IterNodes
35201
21631
1543
0225

prune680.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.7b

regimes675.0ms

Accuracy

0% (0.2b remaining)

Error of 13.3b against oracle of 13.1b and baseline of 13.3b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
211
111
09

end0.0ms

sample3.0s

Algorithm
intervals
Results
879.0ms6057×body80valid
819.0ms285×body5120valid
570.0ms652×body2560valid
344.0ms506×body1280valid
158.0ms271×body640valid
52.0ms162×body320valid
14.0ms67×body160valid