Details

Time bar (total: 4.2m)

sample6.1s

Algorithm
intervals
Results
5.9s1444×body10240exit
67.0ms256×body80valid

simplify390.0ms

Calls
1 calls:
Slowest
389.0ms
(* (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))))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize60.0ms

Local error

Found 4 expressions with local error:

37.1b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
27.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.3b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
32×*-un-lft-identity
16×sqrt-prod
14×associate-*l*
12×add-sqr-sqrt
10×pow1 distribute-lft-out
8×add-cube-cbrt
6×add-cbrt-cube add-exp-log
4×sqrt-div swap-sqr insert-posit16 add-log-exp
3×sqrt-pow1 pow1/2 associate-*r* log-pow
2×rem-sqrt-square flip3-+ sin-sum flip-+
1×+-commutative pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Calls
4 calls:
Slowest
74.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
23.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
22.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
14.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)

series450.0ms

Calls
4 calls:
Slowest
237.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
110.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
55.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
47.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.2s

Calls
48 calls:
Slowest
399.0ms
(* (* (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) (log (sqrt (+ (* x.re x.re) (* x.im x.im))))) (log (sqrt (+ (* x.re x.re) (* x.im x.im))))) (* (* y.re y.re) y.re))
284.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
279.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
264.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
251.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))

prune1.5s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 8.3b

localize23.0ms

Local error

Found 4 expressions with local error:

37.0b
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
27.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.3b
(* (log (- x.re)) y.im)
0.3b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity
14×add-sqr-sqrt associate-*l*
12×pow1
9×add-cube-cbrt
8×add-cbrt-cube add-exp-log sqrt-prod
6×associate-*r*
5×distribute-lft-out
4×log-pow insert-posit16 add-log-exp
2×sqrt-pow1 pow1/2 sin-sum sqrt-div swap-sqr pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative rem-sqrt-square flip3-+ flip-+
Calls
4 calls:
Slowest
58.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
49.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
7.0ms
(* (log (- x.re)) y.im)

series471.0ms

Calls
4 calls:
Slowest
192.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
123.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
104.0ms
(* (log (- x.re)) y.im)
52.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.4s

Calls
45 calls:
Slowest
464.0ms
(* (* (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) (log (sqrt (+ (* x.re x.re) (* x.im x.im))))) (log (sqrt (+ (* x.re x.re) (* x.im x.im))))) (* (* y.re y.re) y.re))
370.0ms
(* (* (* (log (- x.re)) (log (- x.re))) (log (- x.re))) (* (* y.im y.im) y.im))
311.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
232.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
137.0ms
(sin (- (+ (* (atan2 x.im x.re) y.re) (* y.im (log -1))) (* y.im (log (/ 1 x.re)))))

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.2b

localize20.0ms

Local error

Found 4 expressions with local error:

37.0b
(sin (+ (* (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))
27.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.5b
(* (cbrt (log (- x.re))) (cbrt (log (- x.re))))
0.5b
(cbrt (log (- x.re)))

rewrite481.0ms

Algorithm
rewrite-expression-head
Rules
28×cbrt-prod *-un-lft-identity
23×add-sqr-sqrt
19×pow1
14×add-cube-cbrt
11×swap-sqr associate-*l*
8×add-cbrt-cube sqrt-prod
7×pow1/3 associate-*r* log-pow
6×add-exp-log
5×distribute-lft-out
4×cbrt-unprod insert-posit16 add-log-exp unswap-sqr
2×sin-sum sqrt-div pow-prod-down pow-sqr pow-prod-up
1×pow2 +-commutative rem-sqrt-square sqrt-pow1 flip3-+ pow-plus pow1/2 prod-exp *-commutative flip-+
Calls
4 calls:
Slowest
412.0ms
(sin (+ (* (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))
47.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
18.0ms
(* (cbrt (log (- x.re))) (cbrt (log (- x.re))))
2.0ms
(cbrt (log (- x.re)))

series1.1s

Calls
4 calls:
Slowest
461.0ms
(* (cbrt (log (- x.re))) (cbrt (log (- x.re))))
432.0ms
(cbrt (log (- x.re)))
169.0ms
(sin (+ (* (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))
61.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify3.7s

Calls
85 calls:
Slowest
450.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
330.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
285.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
284.0ms
(pow (- (log -1) (log (/ 1 x.re))) 1/3)
273.0ms
(pow (pow (- (log -1) (log (/ 1 x.re))) 2) 1/3)

prune2.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.2b

localize33.0ms

Local error

Found 4 expressions with local error:

37.0b
(sin (+ (* (cbrt (* (* (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))) (* (cbrt (log (- x.re))) (cbrt (log (- x.re))))) (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))
27.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.5b
(* (cbrt (log (- x.re))) (cbrt (log (- x.re))))
0.5b
(* (cbrt (log (- x.re))) (cbrt (log (- x.re))))

rewrite5.1s

Algorithm
rewrite-expression-head
Rules
48×cbrt-prod
38×add-sqr-sqrt
37×*-un-lft-identity
31×pow1
21×add-cube-cbrt
20×swap-sqr
18×associate-*l*
14×associate-*r*
12×add-cbrt-cube pow1/3 log-pow
8×add-exp-log sqrt-prod cbrt-unprod unswap-sqr
5×distribute-lft-out
4×pow-prod-down pow-sqr pow-prod-up insert-posit16 add-log-exp
2×pow2 pow-plus sin-sum sqrt-div prod-exp *-commutative
1×+-commutative rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Calls
4 calls:
Slowest
5.1s
(sin (+ (* (cbrt (* (* (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))) (* (cbrt (log (- x.re))) (cbrt (log (- x.re))))) (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))
25.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
19.0ms
(* (cbrt (log (- x.re))) (cbrt (log (- x.re))))
17.0ms
(* (cbrt (log (- x.re))) (cbrt (log (- x.re))))

series1.6s

Calls
4 calls:
Slowest
863.0ms
(* (cbrt (log (- x.re))) (cbrt (log (- x.re))))
454.0ms
(* (cbrt (log (- x.re))) (cbrt (log (- x.re))))
179.0ms
(sin (+ (* (cbrt (* (* (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))) (* (cbrt (log (- x.re))) (cbrt (log (- x.re))))) (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))
66.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify4.6s

Calls
136 calls:
Slowest
282.0ms
(* (sin (* (cbrt (* (* (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))) (* (cbrt (log (- x.re))) (cbrt (log (- x.re))))) (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))))) (* (cbrt (log (- x.re))) y.im))) (cos (* (atan2 x.im x.re) y.re)))
271.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
265.0ms
(* (sin (* (atan2 x.im x.re) y.re)) (cos (* (cbrt (* (* (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))) (* (cbrt (log (- x.re))) (cbrt (log (- x.re))))) (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))))) (* (cbrt (log (- x.re))) y.im))))
250.0ms
(pow (pow (- (log -1) (log (/ 1 x.re))) 2) 1/3)
236.0ms
(pow (pow (- (log -1) (log (/ 1 x.re))) 2) 1/3)

prune3.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.2b

regimes651.0ms

Accuracy

46.8% (6.0b remaining)

Error of 11.0b against oracle of 5.0b and baseline of 16.3b

bsearch12.3s

end0.0ms

sample3.4m

Algorithm
intervals
Results
3.3m47062×body10240exit
3.8s8000×body80valid