Details

Time bar (total: 3.9m)

sample6.3s

Algorithm
intervals
Results
6.1s1539×body10240exit
66.0ms256×body80valid

simplify395.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
394.0ms
(* (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))))

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize51.0ms

Local error

Found 4 expressions with local error:

40.2b
(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)))
0.3b
(* (atan2 x.im x.re) y.re)
0.2b
(* (atan2 x.im x.re) y.im)

rewrite31.0ms

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
11.0ms
(* (atan2 x.im x.re) y.im)
7.0ms
(* y.re (log (hypot x.re x.im)))
6.0ms
(* (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)))

series327.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
170.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
98.0ms
(* y.re (log (hypot x.re x.im)))
34.0ms
(* (atan2 x.im x.re) y.re)
26.0ms
(* (atan2 x.im x.re) y.im)

simplify1.6s

Counts
48 → 93
Calls
48 calls:
Slowest
343.0ms
(* (* (* y.re y.re) y.re) (* (* (log (hypot x.re x.im)) (log (hypot x.re x.im))) (log (hypot x.re x.im))))
340.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.re y.re) y.re))
271.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
151.0ms
(* -1 (* y.re (log (/ -1 x.re))))
107.0ms
(* -1 (* y.re (log (/ 1 x.re))))

prune1.7s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize106.0ms

Local error

Found 4 expressions with local error:

40.2b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
40.2b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
40.2b
(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
Counts
4 → 47
Calls
4 calls:
Slowest
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)))
4.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
2.0ms
(cbrt (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))))

series779.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
256.0ms
(cbrt (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))))
192.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
177.0ms
(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)))

simplify1.7s

Counts
18 → 59
Calls
18 calls:
Slowest
354.0ms
(pow (sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re))))) 1/3)
285.0ms
(pow (sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ 1 x.re))))) 1/3)
249.0ms
(- (+ (* 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))))))))
173.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
165.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))

prune1.3s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize85.0ms

Local error

Found 4 expressions with local error:

40.2b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
40.2b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
40.2b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
40.2b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite20.0ms

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
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)))
4.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series637.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
176.0ms
(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)))
151.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify925.0ms

Counts
16 → 56
Calls
16 calls:
Slowest
155.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
132.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
127.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
103.0ms
(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)))))

prune1.5s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize65.0ms

Local error

Found 4 expressions with local error:

40.2b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
40.2b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
40.2b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
9.3b
(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
Counts
4 → 47
Calls
4 calls:
Slowest
22.0ms
(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)))))
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)))

series615.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
182.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
162.0ms
(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)))
129.0ms
(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)))))

simplify1.1s

Counts
18 → 59
Calls
18 calls:
Slowest
166.0ms
(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)))))
145.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
135.0ms
(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)))))
118.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))

prune1.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes287.0ms

Accuracy

0% (0.0b remaining)

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

bsearch4.0ms

end0.0ms

sample3.5m

Algorithm
intervals
Results
3.4m48305×body10240exit
3.1s8000×body80valid