Details

Time bar (total: 20.2s)

sample178.0ms

Algorithm
intervals
Results
29.0ms196×body80valid
13.0ms19×body1280valid
12.0ms16×body2560valid
11.0ms13×body5120valid
3.0ms6×body640valid
2.0ms4×body320valid
0.0ms2×body160valid

simplify135.0ms

Counts
1 → 1

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.1b

localize56.0ms

Local error

Found 3 expressions with local error:

0.6b
(- (hypot re im) re)
0.2b
(sqrt (* (- (hypot re im) re) 2.0))
0.0b
(hypot re im)

rewrite32.0ms

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
16.0ms
(sqrt (* (- (hypot re im) re) 2.0))
13.0ms
(- (hypot re im) re)
0.0ms
(hypot re im)

series537.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
311.0ms
(sqrt (* (- (hypot re im) re) 2.0))
142.0ms
(- (hypot re im) re)
84.0ms
(hypot re im)

simplify2.1s

Counts
65 → 65

prune902.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.0b

localize49.0ms

Local error

Found 4 expressions with local error:

6.7b
(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
0.5b
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
0.2b
(sqrt (* (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
0.0b
(hypot re im)

rewrite49.0ms

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
17.0ms
(sqrt (* (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
17.0ms
(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
13.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
0.0ms
(hypot re im)

series529.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
292.0ms
(sqrt (* (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
91.0ms
(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
79.0ms
(hypot re im)
67.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))

simplify897.0ms

Counts
111 → 111

prune2.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 11.9b

localize43.0ms

Local error

Found 4 expressions with local error:

6.7b
(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
6.7b
(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
0.5b
(* (sqrt (sqrt (* (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))) (sqrt (sqrt (* (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))))
0.5b
(* (sqrt (hypot re im)) (sqrt (hypot re im)))

rewrite208.0ms

Algorithm
rewrite-expression-head
Rules
82×sqrt-pow1
76×pow1
48×add-sqr-sqrt
44×sqrt-prod
26×pow1/2
25×pow-prod-down
24×sqrt-div
22×*-un-lft-identity add-cube-cbrt
19×pow-prod-up
17×swap-sqr
14×associate-*l/
13×associate-*r* associate-*l*
11×pow-sqr
8×flip3-- add-cbrt-cube add-exp-log flip-- add-log-exp unswap-sqr
6×prod-diff
4×expm1-log1p-u frac-times insert-posit16 log1p-expm1-u
2×pow2 sub-neg rem-square-sqrt pow-plus fma-neg sqrt-unprod diff-log prod-exp associate-*r/ *-commutative cbrt-unprod difference-of-squares
Counts
4 → 174
Calls
4 calls:
Slowest
168.0ms
(* (sqrt (sqrt (* (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))) (sqrt (sqrt (* (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))))
15.0ms
(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
12.0ms
(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
9.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))

series559.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
279.0ms
(* (sqrt (sqrt (* (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))) (sqrt (sqrt (* (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))))
113.0ms
(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
101.0ms
(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
66.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))

simplify1.3s

Counts
186 → 186

prune3.4s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 11.9b

localize127.0ms

Local error

Found 4 expressions with local error:

7.5b
(- (* (* (fabs (cbrt (hypot re im))) (sqrt (hypot re im))) (sqrt (cbrt (hypot re im)))) re)
6.7b
(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
0.5b
(cbrt (hypot re im))
0.5b
(cbrt (hypot re im))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt add-log-exp
6×cbrt-prod prod-diff
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
2×sub-neg flip3-- fma-neg pow1/3 diff-log flip--
1×difference-of-squares
Counts
4 → 67
Calls
4 calls:
Slowest
53.0ms
(- (* (* (fabs (cbrt (hypot re im))) (sqrt (hypot re im))) (sqrt (cbrt (hypot re im)))) re)
22.0ms
(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
1.0ms
(cbrt (hypot re im))
1.0ms
(cbrt (hypot re im))

series571.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
167.0ms
(- (* (* (fabs (cbrt (hypot re im))) (sqrt (hypot re im))) (sqrt (cbrt (hypot re im)))) re)
164.0ms
(cbrt (hypot re im))
157.0ms
(cbrt (hypot re im))
82.0ms
(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

simplify972.0ms

Counts
79 → 79

prune1.8s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 11.9b

regimes343.0ms

Accuracy

0% (0.2b remaining)

Error of 12.6b against oracle of 12.4b and baseline of 12.6b

bsearch2.0ms

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.0s6096×body80valid
968.0ms698×body2560valid
392.0ms479×body1280valid
302.0ms301×body5120valid
138.0ms221×body640valid
47.0ms128×body320valid
18.0ms77×body160valid