Details

Time bar (total: 3.9m)

sample6.8s

Algorithm
intervals
Results
6.5s1489×body10240exit
121.0ms256×body80valid

simplify318.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
317.0ms
(* (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))) (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))))

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize45.0ms

Local error

Found 4 expressions with local error:

35.9b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
0.3b
(* y.re (log (hypot x.re x.im)))
0.2b
(* (atan2 x.im x.re) y.im)
0.2b
(* (atan2 x.im x.re) y.re)

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
12×*-un-lft-identity add-cube-cbrt
11×pow1
10×add-cbrt-cube associate-*r* add-exp-log
9×associate-*l*
6×log-prod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sin-sum log-pow fma-udef
Counts
4 → 81
Calls
4 calls:
Slowest
9.0ms
(* (atan2 x.im x.re) y.re)
7.0ms
(* y.re (log (hypot x.re x.im)))
5.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series317.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
160.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
121.0ms
(* y.re (log (hypot x.re x.im)))
19.0ms
(* (atan2 x.im x.re) y.re)
18.0ms
(* (atan2 x.im x.re) y.im)

simplify1.9s

Counts
48 → 93
Calls
48 calls:
Slowest
405.0ms
(* (* (* y.re y.re) y.re) (* (* (log (hypot x.re x.im)) (log (hypot x.re x.im))) (log (hypot x.re x.im))))
350.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
338.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.re y.re) y.re))
178.0ms
(* -1 (* y.re (log (/ 1 x.re))))
178.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))

prune1.5s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize71.0ms

Local error

Found 4 expressions with local error:

35.9b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
35.9b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
35.9b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
0.6b
(cbrt (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
5×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×cbrt-prod sin-sum fma-udef
1×pow1/3
Counts
4 → 47
Calls
4 calls:
Slowest
2.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
2.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
2.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
1.0ms
(cbrt (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))))

series764.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
255.0ms
(cbrt (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))))
183.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
166.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
159.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.0s

Counts
18 → 59
Calls
18 calls:
Slowest
426.0ms
(pow (sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re))))) 1/3)
313.0ms
(- (+ (* 1/3 (* y.im (* (exp (* 1/3 (- (log (/ 1 (pow (atan2 x.im x.re) 2))) (* 2 (log y.re))))) (log x.im)))) (exp (* 1/3 (+ (log (atan2 x.im x.re)) (log y.re))))) (* 7/81 (* (pow y.im 2) (* (pow (log x.im) 2) (exp (* 1/3 (+ (log (atan2 x.im x.re)) (log y.re))))))))
295.0ms
(pow (sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ 1 x.re))))) 1/3)
154.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
146.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize113.0ms

Local error

Found 4 expressions with local error:

35.9b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
35.9b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
35.9b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
35.9b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube sin-sum add-exp-log add-cube-cbrt fma-udef insert-posit16 log1p-expm1-u add-log-exp
Counts
4 → 44
Calls
4 calls:
Slowest
3.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
2.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
2.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
2.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series673.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
188.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
178.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
165.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
142.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify933.0ms

Counts
16 → 56
Calls
16 calls:
Slowest
143.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
123.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
117.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
115.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
112.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ 1 x.re)))))

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

localize113.0ms

Local error

Found 4 expressions with local error:

35.9b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
35.9b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
35.9b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
35.9b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube sin-sum add-exp-log add-cube-cbrt fma-udef insert-posit16 log1p-expm1-u add-log-exp
Counts
4 → 44
Calls
4 calls:
Slowest
2.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
2.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
2.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
2.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series629.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
194.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
155.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
154.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
125.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.0s

Counts
16 → 56
Calls
16 calls:
Slowest
159.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
148.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
141.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
129.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
91.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ 1 x.re)))))

prune1.3s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.1b

regimes483.0ms

Accuracy

0% (0.0b remaining)

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

bsearch5.0ms

end0.0ms

sample3.5m

Algorithm
intervals
Results
3.4m47587×body10240exit
3.6s8000×body80valid