Details

Time bar (total: 3.8m)

sample6.1s

Algorithm
intervals
Results
5.8s1339×body10240exit
97.0ms256×body80valid

simplify351.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
350.0ms
(* (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))))

prune36.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.9b

localize79.0ms

Local error

Found 4 expressions with local error:

36.1b
(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)))
0.2b
(* (atan2 x.im x.re) y.re)

rewrite24.0ms

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
7.0ms
(* y.re (log (hypot x.re x.im)))
5.0ms
(* (atan2 x.im x.re) y.im)
5.0ms
(* (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)))

series336.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
159.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
125.0ms
(* y.re (log (hypot x.re x.im)))
32.0ms
(* (atan2 x.im x.re) y.re)
20.0ms
(* (atan2 x.im x.re) y.im)

simplify1.6s

Counts
48 → 93
Calls
48 calls:
Slowest
344.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
315.0ms
(* (* (* y.re y.re) y.re) (* (* (log (hypot x.re x.im)) (log (hypot x.re x.im))) (log (hypot x.re x.im))))
280.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.re y.re) y.re))
125.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
116.0ms
(* -1 (* y.re (log (/ -1 x.re))))

prune1.5s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.8b

localize59.0ms

Local error

Found 4 expressions with local error:

36.1b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
36.1b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
36.1b
(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))))

rewrite10.0ms

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
4.0ms
(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))))

series631.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
227.0ms
(cbrt (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))))
145.0ms
(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)))
119.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.6s

Counts
18 → 59
Calls
18 calls:
Slowest
336.0ms
(pow (sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re))))) 1/3)
279.0ms
(pow (sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ 1 x.re))))) 1/3)
217.0ms
(- (+ (* 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))))))))
171.0ms
(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)))))

prune1.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.8b

localize103.0ms

Local error

Found 4 expressions with local error:

36.1b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
36.1b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
36.1b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
36.1b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite22.0ms

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
9.0ms
(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)))
4.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series659.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
190.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
163.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
153.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
152.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify945.0ms

Counts
16 → 56
Calls
16 calls:
Slowest
157.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
149.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
144.0ms
(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)))))
78.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ 1 x.re)))))

prune1.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.8b

localize110.0ms

Local error

Found 4 expressions with local error:

36.1b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
36.1b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
36.1b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
36.1b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite11.0ms

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)))

series662.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
178.0ms
(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)))
166.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
146.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify853.0ms

Counts
16 → 56
Calls
16 calls:
Slowest
138.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
119.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
113.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
90.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
81.0ms
(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: 0.8b

regimes383.0ms

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
3.3m47643×body10240exit
4.4s8000×body80valid