Details

Time bar (total: 14.4s)

sample185.0ms

Algorithm
intervals
Results
70.0ms197×body80valid
24.0ms27×body2560valid
11.0ms10×body5120valid
6.0ms8×body1280valid
4.0ms6×body640valid
3.0ms8×body320valid

simplify88.0ms

Calls
1 calls:
Slowest
87.0ms
(* 0.5 (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re))))

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.7b

localize16.0ms

Local error

Found 1 expressions with local error:

0.0b
(- (hypot re im) re)

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity
9×prod-diff
8×add-cube-cbrt
3×fma-neg add-log-exp
1×expm1-log1p-u pow1 sub-neg flip3-- add-cbrt-cube diff-log add-exp-log insert-posit16 log1p-expm1-u flip-- distribute-lft-out-- difference-of-squares
Calls
1 calls:
Slowest
6.0ms
(- (hypot re im) re)

series107.0ms

Calls
1 calls:
Slowest
107.0ms
(- (hypot re im) re)

simplify972.0ms

Calls
27 calls:
Slowest
432.0ms
(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- (* re 1)))
87.0ms
(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- (* (cbrt re) (* (cbrt re) (cbrt re)))))
51.0ms
(fma 1 (hypot re im) (- (* (cbrt re) (* (cbrt re) (cbrt re)))))
45.0ms
(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- (* (sqrt re) (sqrt re))))
41.0ms
(fma 1 (hypot re im) (- (* (sqrt re) (sqrt re))))

prune307.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 12.5b

localize30.0ms

Local error

Found 3 expressions with local error:

14.2b
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
0.0b
(sqrt (hypot re im))
0.0b
(sqrt (hypot re im))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt
6×sqrt-prod
5×pow1 *-un-lft-identity add-cube-cbrt
3×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
1×fma-udef
Calls
3 calls:
Slowest
3.0ms
(sqrt (hypot re im))
2.0ms
(sqrt (hypot re im))
1.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series383.0ms

Calls
3 calls:
Slowest
197.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
93.0ms
(sqrt (hypot re im))
92.0ms
(sqrt (hypot re im))

simplify35.0ms

Calls
19 calls:
Slowest
4.0ms
(sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im))))
4.0ms
(sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im))))
3.0ms
(sqrt 1)
3.0ms
(sqrt (sqrt (hypot re im)))
3.0ms
(sqrt (sqrt (hypot re im)))

prune475.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.4b

localize39.0ms

Local error

Found 4 expressions with local error:

7.3b
(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) (- re))
0.5b
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
0.0b
(sqrt (hypot re im))
0.0b
(sqrt (hypot re im))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×sqrt-prod
21×pow1
14×*-un-lft-identity add-cube-cbrt
10×sqrt-pow1 pow1/2
8×swap-sqr add-log-exp
6×add-cbrt-cube associate-*r* associate-*l* add-exp-log
5×pow-prod-up
4×expm1-log1p-u insert-posit16 log1p-expm1-u unswap-sqr
3×pow-prod-down pow-sqr
2×rem-sqrt-square sum-log
1×pow2 neg-sub0 +-commutative associate-+r- rem-square-sqrt fma-def flip3-+ pow-plus sqrt-unprod unsub-neg neg-log prod-exp *-commutative cbrt-unprod flip-+
Calls
4 calls:
Slowest
18.0ms
(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) (- re))
9.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
1.0ms
(sqrt (hypot re im))
1.0ms
(sqrt (hypot re im))

series330.0ms

Calls
4 calls:
Slowest
107.0ms
(sqrt (hypot re im))
92.0ms
(sqrt (hypot re im))
67.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
64.0ms
(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) (- re))

simplify1.1s

Calls
84 calls:
Slowest
275.0ms
(* (exp (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (exp (- re)))
219.0ms
(* (exp (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (/ 1 (exp re)))
143.0ms
(* (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))) (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))))
78.0ms
(* (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))) (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))))
17.0ms
(+ (/ 1 2) 1/2)

prune1.2s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 12.4b

localize49.0ms

Local error

Found 4 expressions with local error:

8.1b
(+ (* (sqrt (hypot re im)) (* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im))))) (- re))
0.6b
(cbrt (hypot re im))
0.6b
(cbrt (hypot re im))
0.5b
(* (sqrt (hypot re im)) (* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 add-cbrt-cube add-exp-log
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt add-log-exp
6×cbrt-prod associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×pow-prod-down prod-exp sqrt-prod cbrt-unprod
2×sum-log pow1/3
1×neg-sub0 +-commutative associate-+r- fma-def flip3-+ associate-*r* unsub-neg neg-log *-commutative flip-+
Calls
4 calls:
Slowest
43.0ms
(* (sqrt (hypot re im)) (* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))))
20.0ms
(+ (* (sqrt (hypot re im)) (* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im))))) (- re))
1.0ms
(cbrt (hypot re im))
1.0ms
(cbrt (hypot re im))

series683.0ms

Calls
4 calls:
Slowest
193.0ms
(* (sqrt (hypot re im)) (* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))))
178.0ms
(cbrt (hypot re im))
160.0ms
(+ (* (sqrt (hypot re im)) (* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im))))) (- re))
153.0ms
(cbrt (hypot re im))

simplify3.8s

Calls
33 calls:
Slowest
517.0ms
(* (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))) (* (* (* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))) (* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im))))) (* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im))))))
460.0ms
(- (+ (* 1/3 (* (* (pow re 2) (fabs (pow (hypot re im) 1/3))) (pow (/ 1 (pow im 4)) 1/3))) (* (fabs (pow (hypot re im) 1/3)) (pow (pow im 2) 1/3))) re)
426.0ms
(* (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))) (* (* (* (fabs (cbrt (hypot re im))) (fabs (cbrt (hypot re im)))) (fabs (cbrt (hypot re im)))) (* (* (sqrt (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))) (sqrt (cbrt (hypot re im))))))
381.0ms
(+ (* 1/3 (* (* (pow re 2) (fabs (pow (hypot re im) 1/3))) (pow (/ 1 (pow im 4)) 1/3))) (* (fabs (pow (hypot re im) 1/3)) (pow (pow im 2) 1/3)))
299.0ms
(* (exp (* (sqrt (hypot re im)) (* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))))) (/ 1 (exp re)))

prune1.2s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 12.4b

regimes222.0ms

Accuracy

0% (0.3b remaining)

Error of 13.5b against oracle of 13.2b and baseline of 13.5b

bsearch3.0ms

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.4s5991×body80valid
624.0ms710×body2560valid
401.0ms490×body1280valid
311.0ms310×body5120valid
153.0ms263×body640valid
61.0ms167×body320valid
17.0ms69×body160valid