Details

Time bar (total: 2.4m)

sample4.1s

Algorithm
intervals
Results
3.8s1009×body10240exit
93.0ms256×body80valid

simplify464.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
463.0ms
(* (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))))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.2b

localize68.0ms

Local error

Found 4 expressions with local error:

27.1b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
26.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.3b
(* (atan2 x.im x.re) y.im)

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 *-un-lft-identity add-cube-cbrt
6×add-cbrt-cube add-exp-log sqrt-prod
4×sqrt-div insert-posit16 add-log-exp
3×associate-*r* associate-*l*
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 60
Calls
4 calls:
Slowest
17.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
11.0ms
(* (atan2 x.im x.re) y.im)

series380.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
235.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
60.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
57.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.0ms
(* (atan2 x.im x.re) y.im)

simplify1.6s

Counts
36 → 72
Calls
36 calls:
Slowest
354.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
270.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
257.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
254.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
167.0ms
(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: 13.9b

localize34.0ms

Local error

Found 4 expressions with local error:

26.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.3b
(* (atan2 x.im x.re) y.im)
0.2b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
0.0b
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))

rewrite61.0ms

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
18.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
15.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
15.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
11.0ms
(* (atan2 x.im x.re) y.im)

series382.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
154.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
144.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
62.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms
(* (atan2 x.im x.re) y.im)

simplify2.4s

Counts
39 → 82
Calls
39 calls:
Slowest
526.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
430.0ms
(* (* (* (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))
327.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
263.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
205.0ms
(/ (exp (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)) (exp (* (atan2 x.im x.re) y.im)))

prune1.2s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize34.0ms

Local error

Found 3 expressions with local error:

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

rewrite25.0ms

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
9.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
7.0ms
(* (log (- x.re)) y.re)

series296.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
167.0ms
(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
105.0ms
(* (log (- x.re)) y.re)
24.0ms
(* (atan2 x.im x.re) y.im)

simplify1.4s

Counts
28 → 61
Calls
28 calls:
Slowest
336.0ms
(* (* (* (log (- x.re)) (log (- x.re))) (log (- x.re))) (* (* y.re y.re) y.re))
251.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
191.0ms
(/ (exp (* (log (- x.re)) y.re)) (exp (* (atan2 x.im x.re) y.im)))
154.0ms
(- (* y.re (log -1)) (+ (* y.im (atan2 x.im x.re)) (* y.re (log (/ 1 x.re)))))
123.0ms
(- (+ (* y.re (log (/ -1 x.re))) (* y.im (atan2 x.im x.re))))

prune733.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes258.0ms

Accuracy

98.9% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 7.1b

bsearch1.7s

end0.0ms

sample2.1m

Algorithm
intervals
Results
2.0m30668×body10240exit
2.9s8000×body80valid