Details

Time bar (total: 3.7m)

sample6.0s

Algorithm
intervals
Results
5.7s1354×body10240exit
69.0ms256×body80valid

simplify210.0ms

Calls
1 calls:
Slowest
201.0ms
(* (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))))

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize51.0ms

Local error

Found 4 expressions with local error:

36.4b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
0.3b
(* (atan2 x.im x.re) y.im)
0.3b
(* y.re (log (hypot x.re x.im)))
0.3b
(* (atan2 x.im x.re) y.re)

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×log-prod associate-*l*
5×pow1
4×expm1-log1p-u add-cbrt-cube associate-*r* add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in *-commutative
1×sin-sum log-pow fma-udef
Calls
4 calls:
Slowest
4.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
3.0ms
(* (atan2 x.im x.re) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)
2.0ms
(* y.re (log (hypot x.re x.im)))

series315.0ms

Calls
4 calls:
Slowest
184.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
89.0ms
(* y.re (log (hypot x.re x.im)))
22.0ms
(* (atan2 x.im x.re) y.re)
21.0ms
(* (atan2 x.im x.re) y.im)

simplify501.0ms

Calls
27 calls:
Slowest
122.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
109.0ms
(* -1 (* y.re (log (/ -1 x.re))))
83.0ms
(* -1 (* y.re (log (/ 1 x.re))))
51.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ 1 x.re)))))
19.0ms
(+ (* (atan2 x.im x.re) y.re) (* y.im (log x.im)))

prune1.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

36.4b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
36.4b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
36.4b
(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))))

rewrite17.0ms

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
Calls
4 calls:
Slowest
5.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
5.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
5.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
3.0ms
(cbrt (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))))

series719.0ms

Calls
4 calls:
Slowest
239.0ms
(cbrt (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))))
179.0ms
(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)))
148.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.1s

Calls
18 calls:
Slowest
178.0ms
(- (+ (* 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))))))))
146.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
134.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
132.0ms
(pow (sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re))))) 1/3)
120.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))

prune1.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

36.4b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
36.4b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
36.4b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
36.4b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite12.0ms

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
Calls
4 calls:
Slowest
4.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
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)))

series711.0ms

Calls
4 calls:
Slowest
188.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
184.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
171.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
168.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify930.0ms

Calls
16 calls:
Slowest
158.0ms
(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)))))
140.0ms
(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)))))
80.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ 1 x.re)))))

prune1.4s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

36.4b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
36.4b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
36.4b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
9.6b
(cbrt (* (* (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))) (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))) (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
3×sin-sum fma-udef
1×cbrt-prod cbrt-div pow1/3 pow3 associate-*l/ rem-cbrt-cube sin-mult
Calls
4 calls:
Slowest
15.0ms
(cbrt (* (* (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))) (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))) (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
5.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
5.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
4.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series619.0ms

Calls
4 calls:
Slowest
170.0ms
(cbrt (* (* (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))) (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))) (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
160.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
150.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
140.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.1s

Calls
18 calls:
Slowest
177.0ms
(cbrt (* (- (cos (- (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)) (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))) (cos (+ (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)) (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))))) (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
154.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
145.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
131.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
131.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))

prune1.1s

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 0.0b

regimes381.0ms

Accuracy

0% (0.0b remaining)

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

bsearch3.0ms

end0.0ms

sample3.4m

Algorithm
intervals
Results
3.3m47125×body10240exit
3.5s8000×body80valid