Details

Time bar (total: 4.0m)

sample7.2s

Algorithm
intervals
Results
6.9s1664×body10240exit
151.0ms256×body80valid

simplify341.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
340.0ms
(* (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))))

prune35.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize51.0ms

Local error

Found 4 expressions with local error:

37.4b
(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.re)
0.2b
(* (atan2 x.im x.re) y.im)
0.2b
(* y.re (log (hypot x.re x.im)))

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

series283.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
149.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
95.0ms
(* y.re (log (hypot x.re x.im)))
22.0ms
(* (atan2 x.im x.re) y.im)
18.0ms
(* (atan2 x.im x.re) y.re)

simplify3.5s

Counts
100 → 93
Calls
100 calls:
Slowest
408.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
388.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.re y.re) y.re))
353.0ms
(* (* (* y.re y.re) y.re) (* (* (log (hypot x.re x.im)) (log (hypot x.re x.im))) (log (hypot x.re x.im))))
245.0ms
(* (* (* (atan2 x.im x.re) y.re) (* (atan2 x.im x.re) y.re)) (* (atan2 x.im x.re) y.re))
217.0ms
(* (* (* (atan2 x.im x.re) y.im) (* (atan2 x.im x.re) y.im)) (* (atan2 x.im x.re) y.im))

prune1.6s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize112.0ms

Local error

Found 4 expressions with local error:

37.4b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
37.4b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
37.4b
(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
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)))
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)))
2.0ms
(cbrt (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))))

series676.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
258.0ms
(cbrt (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)))
138.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
131.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify3.5s

Counts
64 → 59
Calls
64 calls:
Slowest
367.0ms
(pow (sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re))))) 1/3)
340.0ms
(pow (sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ 1 x.re))))) 1/3)
259.0ms
(- (+ (* 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))))))))
151.0ms
(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)))))

prune1.2s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize85.0ms

Local error

Found 4 expressions with local error:

37.4b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
37.4b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
37.4b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
37.4b
(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)))
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)))

series616.0ms

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)))
154.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
143.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
141.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.7s

Counts
60 → 56
Calls
60 calls:
Slowest
142.0ms
(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)))))
114.0ms
(* (* (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))))
113.0ms
(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)))))

prune1.1s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

localize81.0ms

Local error

Found 4 expressions with local error:

37.4b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
37.4b
(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.re)
0.3b
(* (atan2 x.im x.re) y.re)

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r* associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×sin-sum pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef unswap-sqr
Counts
4 → 64
Calls
4 calls:
Slowest
5.0ms
(* (atan2 x.im x.re) y.re)
5.0ms
(* (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)))

series303.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
133.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
128.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
24.0ms
(* (atan2 x.im x.re) y.re)
18.0ms
(* (atan2 x.im x.re) y.re)

simplify3.0s

Counts
78 → 76
Calls
78 calls:
Slowest
434.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.re y.re) y.re))
394.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.re y.re) y.re))
285.0ms
(* (* (* (atan2 x.im x.re) y.re) (* (atan2 x.im x.re) y.re)) (* (atan2 x.im x.re) y.re))
192.0ms
(* (* (* (atan2 x.im x.re) y.re) (* (atan2 x.im x.re) y.re)) (* (atan2 x.im x.re) y.re))
160.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))

prune1.4s

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0.0b

regimes280.0ms

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
3.4m47748×body10240exit
3.7s8000×body80valid