Details

Time bar (total: 18.1s)

sample58.0ms

Algorithm
intervals
Results
15.0ms188×body80valid
13.0ms26×body2560valid
6.0ms16×body1280valid
4.0ms14×body640valid
3.0ms5×body5120valid
1.0ms6×body320valid
0.0ms1×body160valid

simplify46.0ms

Counts
1 → 1
Iterations
IterNodes
done31
331
229
124
012

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.2b

localize29.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (* (+ (hypot re im) re) 2.0))
0.2b
(+ (hypot re im) re)

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
5×pow1 *-un-lft-identity
4×add-log-exp
3×add-sqr-sqrt fma-def add-cube-cbrt
2×expm1-log1p-u sqrt-pow1 flip3-+ add-cbrt-cube sqrt-div associate-*l/ add-exp-log flip-+ insert-posit16 log1p-expm1-u
1×+-commutative sum-log pow1/2 pow-prod-down sqrt-prod distribute-lft-out
Counts
2 → 34
Calls
2 calls:
13.0ms
(sqrt (* (+ (hypot re im) re) 2.0))
9.0ms
(+ (hypot re im) re)

series308.0ms

Counts
2 → 6
Calls
2 calls:
216.0ms
(sqrt (* (+ (hypot re im) re) 2.0))
91.0ms
(+ (hypot re im) re)

simplify2.9s

Counts
40 → 40
Iterations
IterNodes
done5000
44643
31359
2470
1176
077

prune245.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 15.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (hypot re im))
0.0b
(sqrt (hypot re im))
0.3b
(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
16.6b
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite7.0ms

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:
1.0ms
(sqrt (hypot re im))
1.0ms
(sqrt (hypot re im))
4.0ms
(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)

series789.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(sqrt (hypot re im))
108.0ms
(sqrt (hypot re im))
355.0ms
(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
183.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify2.7s

Counts
69 → 69
Iterations
IterNodes
done5000
31844
2531
1198
093

prune389.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 14.9b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt (hypot re im)))
0.1b
(sqrt (sqrt (hypot re im)))
0.5b
(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
16.6b
(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) re)

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
86×sqrt-prod
54×add-sqr-sqrt
40×sqrt-pow1
31×pow1
20×*-un-lft-identity pow1/2 add-cube-cbrt
15×swap-sqr
9×associate-*r* associate-*l* pow-prod-up unswap-sqr
6×add-cbrt-cube add-exp-log
5×pow-prod-down pow-sqr
4×expm1-log1p-u rem-sqrt-square insert-posit16 log1p-expm1-u add-log-exp
1×pow2 rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod fma-udef
Counts
4 → 133
Calls
4 calls:
2.0ms
(sqrt (sqrt (hypot re im)))
2.0ms
(sqrt (sqrt (hypot re im)))
18.0ms
(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
1.0ms
(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) re)

series947.0ms

Counts
4 → 12
Calls
4 calls:
151.0ms
(sqrt (sqrt (hypot re im)))
142.0ms
(sqrt (sqrt (hypot re im)))
105.0ms
(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
548.0ms
(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) re)

simplify3.1s

Counts
145 → 145
Iterations
IterNodes
done5000
44837
31436
2575
1276
0133

prune678.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 14.9b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im))))
0.5b
(cbrt (* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im)))))
0.5b
(* (sqrt (sqrt (hypot re im))) (cbrt (* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im))))))
16.6b
(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (cbrt (* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im)))))) re)

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt sqrt-prod
17×pow1
15×associate-*l*
13×*-un-lft-identity associate-*r* add-cube-cbrt
11×sqrt-pow1
9×unswap-sqr
8×add-exp-log
7×add-cbrt-cube pow1/2
6×pow-prod-up
4×expm1-log1p-u pow3 pow-prod-down insert-posit16 log1p-expm1-u add-log-exp
2×cbrt-prod prod-exp *-commutative rem-cbrt-cube cbrt-unprod
1×pow1/3 sqrt-unprod fma-udef
Counts
4 → 101
Calls
4 calls:
20.0ms
(* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im))))
12.0ms
(cbrt (* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im)))))
31.0ms
(* (sqrt (sqrt (hypot re im))) (cbrt (* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im))))))
1.0ms
(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (cbrt (* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im)))))) re)

series743.0ms

Counts
4 → 12
Calls
4 calls:
208.0ms
(* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im))))
184.0ms
(cbrt (* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im)))))
116.0ms
(* (sqrt (sqrt (hypot re im))) (cbrt (* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im))))))
234.0ms
(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (cbrt (* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im)))))) re)

simplify2.2s

Counts
113 → 113
Iterations
IterNodes
done5000
32387
2885
1343
0158

prune614.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 14.9b

regimes196.0ms

Accuracy

0% (0.2b remaining)

Error of 12.8b against oracle of 12.6b and baseline of 12.8b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done12
112
09

end0.0ms

sample1.9s

Algorithm
intervals
Results
554.0ms456×body1280valid
550.0ms6092×body80valid
256.0ms657×body2560valid
189.0ms278×body5120valid
162.0ms282×body640valid
59.0ms160×body320valid
9.0ms75×body160valid