Details

Time bar (total: 2.6m)

sample4.5s

Algorithm
intervals
Results
4.2s1008×body10240exit
78.0ms256×body80valid

simplify441.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
440.0ms
(* (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))) (cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))))

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize109.0ms

Local error

Found 4 expressions with local error:

27.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
21.4b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
0.3b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im)

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×pow1
8×*-un-lft-identity add-cube-cbrt
6×add-cbrt-cube associate-*l* add-exp-log sqrt-prod
4×sqrt-div insert-posit16 add-log-exp
3×sqrt-pow1 pow1/2 associate-*r* log-pow
2×rem-sqrt-square flip3-+ flip-+
1×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 63
Calls
4 calls:
Slowest
16.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im)
15.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
7.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series485.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
239.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
118.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im)
64.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
63.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.5s

Counts
37 → 75
Calls
37 calls:
Slowest
570.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
428.0ms
(* (* (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) (log (sqrt (+ (* x.re x.re) (* x.im x.im))))) (log (sqrt (+ (* x.re x.re) (* x.im x.im))))) (* (* y.im y.im) y.im))
301.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
274.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
247.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))

prune1.3s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.2b

localize37.0ms

Local error

Found 4 expressions with local error:

27.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.3b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
0.2b
(* (atan2 x.im x.re) y.im)
0.0b
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×pow1
9×*-un-lft-identity associate-*l* add-cube-cbrt
8×add-cbrt-cube add-exp-log
6×associate-*r* add-log-exp
4×insert-posit16
3×log-pow sqrt-prod
2×sqrt-pow1 pow1/2 sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×rem-sqrt-square sub-neg flip3-+ flip3-- diff-log flip-+ flip--
Counts
4 → 70
Calls
4 calls:
Slowest
9.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
8.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
5.0ms
(* (atan2 x.im x.re) y.im)

series408.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
187.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
139.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
55.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.0ms
(* (atan2 x.im x.re) y.im)

simplify2.3s

Counts
39 → 82
Calls
39 calls:
Slowest
415.0ms
(* (* (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) (log (sqrt (+ (* x.re x.re) (* x.im x.im))))) (log (sqrt (+ (* x.re x.re) (* x.im x.im))))) (* (* y.re y.re) y.re))
331.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
276.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
270.0ms
(/ (exp (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)) (exp (* (atan2 x.im x.re) y.im)))
213.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))

prune1.3s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (log (- x.re)) y.re)
0.2b
(* (atan2 x.im x.re) y.im)
0.0b
(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
8×pow1
7×*-un-lft-identity add-cbrt-cube associate-*l* add-exp-log add-cube-cbrt
6×associate-*r*
5×add-log-exp
3×insert-posit16
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sub-neg flip3-- diff-log log-pow flip--
Counts
3 → 52
Calls
3 calls:
Slowest
7.0ms
(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
6.0ms
(* (log (- x.re)) y.re)
5.0ms
(* (atan2 x.im x.re) y.im)

series324.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
188.0ms
(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
112.0ms
(* (log (- x.re)) y.re)
24.0ms
(* (atan2 x.im x.re) y.im)

simplify1.5s

Counts
28 → 61
Calls
28 calls:
Slowest
352.0ms
(* (* (* (log (- x.re)) (log (- x.re))) (log (- x.re))) (* (* y.re y.re) y.re))
272.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
165.0ms
(/ (exp (* (log (- x.re)) y.re)) (exp (* (atan2 x.im x.re) y.im)))
147.0ms
(- (+ (* y.re (log (/ -1 x.re))) (* y.im (atan2 x.im x.re))))
135.0ms
(- (* y.re (log -1)) (+ (* y.im (atan2 x.im x.re)) (* y.re (log (/ 1 x.re)))))

prune883.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (atan2 x.im x.re) y.im)
0.1b
(* (log x.im) y.re)
0.0b
(- (* (log x.im) y.re) (* (atan2 x.im x.re) y.im))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
8×pow1
7×*-un-lft-identity add-cbrt-cube associate-*l* add-exp-log add-cube-cbrt
6×associate-*r*
5×add-log-exp
3×insert-posit16
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sub-neg flip3-- diff-log log-pow flip--
Counts
3 → 52
Calls
3 calls:
Slowest
8.0ms
(- (* (log x.im) y.re) (* (atan2 x.im x.re) y.im))
6.0ms
(* (log x.im) y.re)
6.0ms
(* (atan2 x.im x.re) y.im)

series247.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
138.0ms
(- (* (log x.im) y.re) (* (atan2 x.im x.re) y.im))
90.0ms
(* (log x.im) y.re)
20.0ms
(* (atan2 x.im x.re) y.im)

simplify1.4s

Counts
28 → 61
Calls
28 calls:
Slowest
309.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
293.0ms
(- (* y.re (log -1)) (+ (* y.re (log (/ -1 x.im))) (* y.im (atan2 x.im x.re))))
293.0ms
(* (* (* (log x.im) (log x.im)) (log x.im)) (* (* y.re y.re) y.re))
163.0ms
(/ (exp (* (log x.im) y.re)) (exp (* (atan2 x.im x.re) y.im)))
109.0ms
(* y.re (- (log -1) (log (/ -1 x.im))))

prune728.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.1b

regimes205.0ms

Accuracy

98.3% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 6.7b

bsearch3.2s

end0.0ms

sample2.2m

Algorithm
intervals
Results
2.1m30118×body10240exit
3.4s8000×body80valid