Details

Time bar (total: 19.1s)

sample200.0ms

Algorithm
intervals
Results
67.0ms25×body2560valid
30.0ms190×body80valid
14.0ms10×body5120valid
13.0ms18×body1280valid
5.0ms9×body640valid
1.0ms2×body320valid
1.0ms2×body160valid

simplify86.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
85.0ms
(* 0.5 (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re))))

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.5b

localize14.0ms

Local error

Found 1 expressions with local error:

0.4b
(- (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
Counts
1 → 29
Calls
1 calls:
Slowest
6.0ms
(- (hypot re im) re)

series217.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
216.0ms
(- (hypot re im) re)

simplify607.0ms

Counts
27 → 32
Calls
27 calls:
Slowest
112.0ms
(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- (* (cbrt re) (* (cbrt re) (cbrt re)))))
54.0ms
(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- (* re 1)))
41.0ms
(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- (* (sqrt re) (sqrt re))))
37.0ms
(fma 1 (hypot re im) (- (* (sqrt re) (sqrt re))))
32.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- (* (cbrt re) (* (cbrt re) (cbrt re)))))

prune352.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 13.3b

localize32.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (cbrt (- (hypot re im) re)) (cbrt (- (hypot re im) re)))
0.4b
(- (hypot re im) re)
0.4b
(- (hypot re im) re)
0.4b
(- (hypot re im) re)

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
55×add-sqr-sqrt
53×*-un-lft-identity
33×add-cube-cbrt
28×cbrt-prod
27×prod-diff
12×cbrt-div
11×pow1
10×swap-sqr add-log-exp
9×flip3-- fma-neg flip-- distribute-lft-out--
8×associate-*r* associate-*l*
7×difference-of-squares
6×pow1/3 add-exp-log
4×expm1-log1p-u frac-times add-cbrt-cube insert-posit16 log1p-expm1-u unswap-sqr
3×sub-neg diff-log
2×pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 146
Calls
4 calls:
Slowest
49.0ms
(* (cbrt (- (hypot re im) re)) (cbrt (- (hypot re im) re)))
10.0ms
(- (hypot re im) re)
10.0ms
(- (hypot re im) re)
10.0ms
(- (hypot re im) re)

series464.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
243.0ms
(* (cbrt (- (hypot re im) re)) (cbrt (- (hypot re im) re)))
80.0ms
(- (hypot re im) re)
73.0ms
(- (hypot re im) re)
68.0ms
(- (hypot re im) re)

simplify5.2s

Counts
152 → 158
Calls
152 calls:
Slowest
422.0ms
(- (+ (pow im 2/3) (* 2/9 (* (pow re 2) (pow (/ 1 (pow im 4)) 1/3)))) (* 2/3 (* re (pow (/ 1 im) 1/3))))
277.0ms
(* (cbrt (- (pow (hypot re im) 3) (pow re 3))) (cbrt (- (* (hypot re im) (hypot re im)) (* re re))))
269.0ms
(* (cbrt (- (* (hypot re im) (hypot re im)) (* re re))) (cbrt (- (pow (hypot re im) 3) (pow re 3))))
269.0ms
(exp (* 1/3 (- (log 4) (* 2 (log (/ -1 re))))))
234.0ms
(* (cbrt (- (pow (hypot re im) 3) (pow re 3))) (cbrt (- (pow (hypot re im) 3) (pow re 3))))

prune2.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 13.3b

localize37.0ms

Local error

Found 4 expressions with local error:

15.7b
(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))
0.6b
(cbrt (hypot re im))
0.6b
(cbrt (hypot re im))
0.6b
(cbrt (hypot re im))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
1×fma-udef
Counts
4 → 53
Calls
4 calls:
Slowest
1.0ms
(cbrt (hypot re im))
1.0ms
(cbrt (hypot re im))
1.0ms
(cbrt (hypot re im))
0.0ms
(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))

series698.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
219.0ms
(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))
178.0ms
(cbrt (hypot re im))
154.0ms
(cbrt (hypot re im))
147.0ms
(cbrt (hypot re im))

simplify941.0ms

Counts
21 → 65
Calls
21 calls:
Slowest
273.0ms
(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
264.0ms
(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
223.0ms
(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
26.0ms
(pow (/ 1 re) -1/3)
23.0ms
(pow (/ -1 re) -1/3)

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 13.3b

localize55.0ms

Local error

Found 4 expressions with local error:

11.8b
(+ (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) (- re))
0.6b
(cbrt (hypot re im))
0.6b
(cbrt (hypot re im))
0.6b
(cbrt (hypot re im))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
8×add-log-exp
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×pow1/3
2×sum-log
1×neg-sub0 +-commutative associate-+r- fma-def flip3-+ unsub-neg neg-log flip-+
Counts
4 → 61
Calls
4 calls:
Slowest
26.0ms
(+ (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) (- re))
1.0ms
(cbrt (hypot re im))
1.0ms
(cbrt (hypot re im))
1.0ms
(cbrt (hypot re im))

series589.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
184.0ms
(cbrt (hypot re im))
173.0ms
(cbrt (hypot re im))
150.0ms
(cbrt (hypot re im))
82.0ms
(+ (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) (- re))

simplify2.0s

Counts
24 → 73
Calls
24 calls:
Slowest
623.0ms
(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
428.0ms
(* (exp (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) (/ 1 (exp re)))
319.0ms
(* (exp (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) (exp (- re)))
223.0ms
(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
190.0ms
(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 13.3b

regimes436.0ms

Accuracy

0% (0.2b remaining)

Error of 12.5b against oracle of 12.3b and baseline of 12.5b

bsearch2.0ms

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.2s6114×body80valid
521.0ms634×body2560valid
336.0ms304×body5120valid
304.0ms473×body1280valid
173.0ms263×body640valid
54.0ms150×body320valid
13.0ms62×body160valid