Details

Time bar (total: 3.9m)

sample6.1s

Algorithm
intervals
Results
5.9s1457×body10240exit
68.0ms256×body80valid

simplify425.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
424.0ms
(* (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: 31.6b

localize80.0ms

Local error

Found 4 expressions with local error:

34.7b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
29.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.3b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×pow1
8×*-un-lft-identity add-cube-cbrt
6×add-cbrt-cube associate-*l* add-exp-log sqrt-prod
4×sqrt-div insert-posit16 add-log-exp
3×sqrt-pow1 pow1/2 associate-*r* log-pow
2×rem-sqrt-square flip3-+ flip-+
1×sin-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 63
Calls
4 calls:
Slowest
33.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
22.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series438.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
217.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
112.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
63.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
45.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.3s

Counts
37 → 75
Calls
37 calls:
Slowest
451.0ms
(* (* (* (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))
318.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
310.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
298.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
279.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 10.7b

localize85.0ms

Local error

Found 4 expressions with local error:

34.7b
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
29.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.3b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
0.3b
(* (log (- x.re)) y.im)

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×pow1
10×associate-*l*
9×*-un-lft-identity add-cube-cbrt
8×add-cbrt-cube add-exp-log
6×associate-*r*
4×log-pow insert-posit16 add-log-exp
3×sqrt-prod
2×sqrt-pow1 pow1/2 sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×rem-sqrt-square flip3-+ sin-sum flip-+
Counts
4 → 67
Calls
4 calls:
Slowest
24.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
14.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
13.0ms
(* (log (- x.re)) y.im)
11.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series483.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
185.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))
125.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
108.0ms
(* (log (- x.re)) y.im)
64.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.2s

Counts
39 → 79
Calls
39 calls:
Slowest
379.0ms
(* (* (* (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))
342.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
285.0ms
(* (* (* (log (- x.re)) (log (- x.re))) (log (- x.re))) (* (* y.im y.im) y.im))
244.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
170.0ms
(sin (- (+ (* (atan2 x.im x.re) y.re) (* y.im (log -1))) (* y.im (log (/ 1 x.re)))))

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.0b

localize64.0ms

Local error

Found 4 expressions with local error:

34.7b
(sin (+ (* (* (cbrt (* (log (- x.re)) y.im)) (cbrt (* (log (- x.re)) y.im))) (cbrt (* (log (- x.re)) y.im))) (* (atan2 x.im x.re) y.re)))
29.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.6b
(cbrt (* (log (- x.re)) y.im))
0.6b
(cbrt (* (log (- x.re)) y.im))

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
5×pow1 *-un-lft-identity add-cube-cbrt
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×sqrt-prod
2×cbrt-prod pow1/3 sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 sin-sum flip-+
Counts
4 → 45
Calls
4 calls:
Slowest
126.0ms
(sin (+ (* (* (cbrt (* (log (- x.re)) y.im)) (cbrt (* (log (- x.re)) y.im))) (cbrt (* (log (- x.re)) y.im))) (* (atan2 x.im x.re) y.re)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms
(cbrt (* (log (- x.re)) y.im))
3.0ms
(cbrt (* (log (- x.re)) y.im))

series667.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
227.0ms
(sin (+ (* (* (cbrt (* (log (- x.re)) y.im)) (cbrt (* (log (- x.re)) y.im))) (cbrt (* (log (- x.re)) y.im))) (* (atan2 x.im x.re) y.re)))
205.0ms
(cbrt (* (log (- x.re)) y.im))
175.0ms
(cbrt (* (log (- x.re)) y.im))
60.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify3.3s

Counts
22 → 57
Calls
22 calls:
Slowest
701.0ms
(exp (* 1/3 (- (log (- (log -1) (log (/ 1 x.re)))) (log (/ 1 y.im)))))
371.0ms
(* (exp (* 1/3 (- (log (* -1 (log (/ -1 x.re)))) (log (/ -1 y.im))))) (cbrt -1))
350.0ms
(* (exp (* 1/3 (- (log (* -1 (log (/ -1 x.re)))) (log (/ -1 y.im))))) (cbrt -1))
324.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
322.0ms
(exp (* 1/3 (- (log (- (log -1) (log (/ 1 x.re)))) (log (/ 1 y.im)))))

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.0b

localize123.0ms

Local error

Found 4 expressions with local error:

34.7b
(sin (+ (* (* (cbrt (* (log (- x.re)) y.im)) (* (cbrt (log (- x.re))) (cbrt y.im))) (cbrt (* (log (- x.re)) y.im))) (* (atan2 x.im x.re) y.re)))
29.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.6b
(cbrt (* (log (- x.re)) y.im))
0.6b
(cbrt (* (log (- x.re)) y.im))

rewrite256.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
5×pow1 *-un-lft-identity add-cube-cbrt
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×sqrt-prod
2×cbrt-prod pow1/3 sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 sin-sum flip-+
Counts
4 → 45
Calls
4 calls:
Slowest
244.0ms
(sin (+ (* (* (cbrt (* (log (- x.re)) y.im)) (* (cbrt (log (- x.re))) (cbrt y.im))) (cbrt (* (log (- x.re)) y.im))) (* (atan2 x.im x.re) y.re)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms
(cbrt (* (log (- x.re)) y.im))
3.0ms
(cbrt (* (log (- x.re)) y.im))

series690.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
217.0ms
(cbrt (* (log (- x.re)) y.im))
208.0ms
(cbrt (* (log (- x.re)) y.im))
198.0ms
(sin (+ (* (* (cbrt (* (log (- x.re)) y.im)) (* (cbrt (log (- x.re))) (cbrt y.im))) (cbrt (* (log (- x.re)) y.im))) (* (atan2 x.im x.re) y.re)))
67.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify3.0s

Counts
22 → 57
Calls
22 calls:
Slowest
429.0ms
(* (exp (* 1/3 (- (log (* -1 (log (/ -1 x.re)))) (log (/ -1 y.im))))) (cbrt -1))
399.0ms
(* (exp (* 1/3 (- (log (* -1 (log (/ -1 x.re)))) (log (/ -1 y.im))))) (cbrt -1))
339.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
308.0ms
(exp (* 1/3 (- (log (- (log -1) (log (/ 1 x.re)))) (log (/ 1 y.im)))))
303.0ms
(exp (* 1/3 (- (log (- (log -1) (log (/ 1 x.re)))) (log (/ 1 y.im)))))

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.0b

regimes559.0ms

Accuracy

51% (5.7b remaining)

Error of 10.9b against oracle of 5.2b and baseline of 16.9b

bsearch2.8s

end0.0ms

sample3.4m

Algorithm
intervals
Results
3.3m46760×body10240exit
3.6s8000×body80valid