Details

Time bar (total: 17.3s)

sample143.0ms

Algorithm
intervals
Results
19.0ms189×body80valid
10.0ms18×body2560valid
6.0ms11×body5120valid
6.0ms14×body1280valid
4.0ms13×body640valid
2.0ms7×body320valid
1.0ms4×body160valid

simplify100.0ms

Counts
1 → 1

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.8b

localize17.0ms

Local error

Found 3 expressions with local error:

1.1b
(- (hypot re im) re)
0.0b
(hypot re im)
0.0b
(sqrt (* (- (hypot re im) re) 2.0))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity
10×add-cube-cbrt
9×prod-diff
6×pow1
5×add-log-exp
3×expm1-log1p-u add-cbrt-cube fma-neg add-exp-log insert-posit16 log1p-expm1-u
2×sqrt-pow1 flip3-- sqrt-div associate-*l/ flip--
1×hypot-udef sub-neg pow1/2 diff-log pow-prod-down sqrt-prod distribute-lft-out-- difference-of-squares
Counts
3 → 56
Calls
3 calls:
Slowest
7.0ms
(sqrt (* (- (hypot re im) re) 2.0))
7.0ms
(- (hypot re im) re)
0.0ms
(hypot re im)

series443.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
295.0ms
(sqrt (* (- (hypot re im) re) 2.0))
78.0ms
(- (hypot re im) re)
69.0ms
(hypot re im)

simplify1.9s

Counts
65 → 65

prune595.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 13.6b

localize16.0ms

Local error

Found 3 expressions with local error:

1.1b
(- (hypot re im) re)
0.3b
(* (sqrt (- (hypot re im) re)) (sqrt 2.0))
0.0b
(hypot re im)

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
18×*-un-lft-identity
14×add-cube-cbrt
12×sqrt-prod
9×prod-diff
8×associate-*l*
7×pow1
6×associate-*r*
5×add-cbrt-cube add-exp-log add-log-exp
4×unswap-sqr
3×expm1-log1p-u fma-neg pow-prod-down insert-posit16 log1p-expm1-u
2×sqrt-pow1 flip3-- pow1/2 sqrt-div associate-*l/ flip-- distribute-lft-out-- difference-of-squares
1×hypot-udef sub-neg sqrt-unprod diff-log prod-exp *-commutative cbrt-unprod
Counts
3 → 77
Calls
3 calls:
Slowest
38.0ms
(* (sqrt (- (hypot re im) re)) (sqrt 2.0))
5.0ms
(- (hypot re im) re)
0.0ms
(hypot re im)

series436.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
253.0ms
(* (sqrt (- (hypot re im) re)) (sqrt 2.0))
97.0ms
(- (hypot re im) re)
86.0ms
(hypot re im)

simplify2.6s

Counts
86 → 86

prune970.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 13.6b

localize20.0ms

Local error

Found 4 expressions with local error:

7.6b
(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
0.5b
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
0.0b
(sqrt (* (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
0.0b
(hypot re im)

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
22×pow1
19×sqrt-prod
13×*-un-lft-identity add-cube-cbrt
10×sqrt-pow1
9×pow1/2
8×swap-sqr
6×add-cbrt-cube associate-*r* associate-*l* add-exp-log add-log-exp
5×pow-prod-up
4×expm1-log1p-u pow-prod-down insert-posit16 log1p-expm1-u unswap-sqr
3×prod-diff pow-sqr
2×flip3-- sqrt-div associate-*l/ flip--
1×pow2 hypot-udef sub-neg rem-square-sqrt pow-plus fma-neg sqrt-unprod diff-log prod-exp *-commutative cbrt-unprod difference-of-squares
Counts
4 → 99
Calls
4 calls:
Slowest
24.0ms
(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
18.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
17.0ms
(sqrt (* (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
0.0ms
(hypot re im)

series533.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
296.0ms
(sqrt (* (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
86.0ms
(hypot re im)
82.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
68.0ms
(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

simplify842.0ms

Counts
111 → 111

prune1.3s

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 13.6b

localize43.0ms

Local error

Found 4 expressions with local error:

7.6b
(- (* (sqrt (hypot re im)) (sqrt (* (sqrt (hypot re im)) (sqrt (hypot re im))))) re)
0.5b
(* (sqrt (hypot re im)) (sqrt (* (sqrt (hypot re im)) (sqrt (hypot re im)))))
0.5b
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
0.0b
(sqrt (* (- (* (sqrt (hypot re im)) (sqrt (* (sqrt (hypot re im)) (sqrt (hypot re im))))) re) 2.0))

rewrite170.0ms

Algorithm
rewrite-expression-head
Rules
56×pow1
48×sqrt-pow1
36×add-sqr-sqrt
30×pow-prod-up sqrt-prod
29×pow1/2
16×*-un-lft-identity add-cube-cbrt
12×associate-*l*
10×swap-sqr associate-*r*
9×pow-prod-down
8×add-cbrt-cube add-exp-log pow-sqr unswap-sqr
6×add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×prod-diff
2×pow2 pow-plus flip3-- sqrt-unprod sqrt-div associate-*l/ prod-exp *-commutative cbrt-unprod flip--
1×sub-neg rem-square-sqrt fma-neg diff-log
Counts
4 → 137
Calls
4 calls:
Slowest
71.0ms
(sqrt (* (- (* (sqrt (hypot re im)) (sqrt (* (sqrt (hypot re im)) (sqrt (hypot re im))))) re) 2.0))
45.0ms
(* (sqrt (hypot re im)) (sqrt (* (sqrt (hypot re im)) (sqrt (hypot re im)))))
32.0ms
(- (* (sqrt (hypot re im)) (sqrt (* (sqrt (hypot re im)) (sqrt (hypot re im))))) re)
17.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))

series473.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
269.0ms
(sqrt (* (- (* (sqrt (hypot re im)) (sqrt (* (sqrt (hypot re im)) (sqrt (hypot re im))))) re) 2.0))
85.0ms
(- (* (sqrt (hypot re im)) (sqrt (* (sqrt (hypot re im)) (sqrt (hypot re im))))) re)
61.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
59.0ms
(* (sqrt (hypot re im)) (sqrt (* (sqrt (hypot re im)) (sqrt (hypot re im)))))

simplify915.0ms

Counts
149 → 149

prune1.6s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 13.6b

regimes789.0ms

Accuracy

0% (0.3b remaining)

Error of 13.6b against oracle of 13.3b and baseline of 13.6b

bsearch8.0ms

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.4s5995×body80valid
599.0ms672×body2560valid
315.0ms514×body1280valid
299.0ms303×body5120valid
210.0ms279×body640valid
95.0ms155×body320valid
20.0ms82×body160valid