Details

Time bar (total: 40.6s)

sample109.0ms

Algorithm
intervals
Results
77.0ms461×body80valid

simplify407.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
407.0ms
(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.7b

localize33.0ms

Local error

Found 4 expressions with local error:

5.8b
(* (- (* x.re x.re) (* x.im x.im)) x.re)
0.2b
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
0.1b
(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
0.0b
(+ (* x.re x.im) (* x.im x.re))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt associate-*l/
8×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt add-log-exp
7×associate-*l*
6×associate-*r*
4×flip3-+ flip3-- frac-sub flip-+ insert-posit16 flip--
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative sum-log sub-neg diff-log difference-of-squares
Counts
4 → 72
Calls
4 calls:
Slowest
46.0ms
(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
32.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
27.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.re)
11.0ms
(+ (* x.re x.im) (* x.im x.re))

series216.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
78.0ms
(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
71.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.re)
34.0ms
(+ (* x.re x.im) (* x.im x.re))
33.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)

simplify7.7s

Counts
45 → 84
Calls
45 calls:
Slowest
578.0ms
(- (* (* (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))) x.re) (+ (* (* x.re x.im) (* x.re x.im)) (- (* (* x.im x.re) (* x.im x.re)) (* (* x.re x.im) (* x.im x.re))))) (* (+ (* x.re x.re) (* x.im x.im)) (* (+ (pow (* x.re x.im) 3) (pow (* x.im x.re) 3)) x.im)))
524.0ms
(* (+ (* (* x.re x.re) (* x.re x.re)) (+ (* (* x.im x.im) (* x.im x.im)) (* (* x.re x.re) (* x.im x.im)))) (- (* x.re x.im) (* x.im x.re)))
513.0ms
(* (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))) x.re)
417.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.re)
393.0ms
(- (* (* (- (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)) x.re) (- (* x.re x.im) (* x.im x.re))) (* (+ (* (* x.re x.re) (* x.re x.re)) (+ (* (* x.im x.im) (* x.im x.im)) (* (* x.re x.re) (* x.im x.im)))) (* (- (* (* x.re x.im) (* x.re x.im)) (* (* x.im x.re) (* x.im x.re))) x.im)))

prune881.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
0.2b
(* (+ x.re x.im) (* (- x.re x.im) x.re))
0.1b
(- (* (+ x.re x.im) (* (- x.re x.im) x.re)) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
0.0b
(+ (* x.re x.im) (* x.im x.re))

rewrite179.0ms

Algorithm
rewrite-expression-head
Rules
42×associate-*l/
19×flip3-+ flip-+
16×frac-sub
12×frac-times
11×pow1 add-cbrt-cube add-exp-log
10×flip3-- flip--
9×add-sqr-sqrt *-un-lft-identity
8×add-log-exp
7×associate-*l* add-cube-cbrt
6×associate-*r/
4×associate-*r* pow-prod-down prod-exp cbrt-unprod insert-posit16
2×*-commutative
1×+-commutative sum-log sub-neg diff-log distribute-lft-out unswap-sqr
Counts
4 → 90
Calls
4 calls:
Slowest
86.0ms
(- (* (+ x.re x.im) (* (- x.re x.im) x.re)) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
55.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.re))
27.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
9.0ms
(+ (* x.re x.im) (* x.im x.re))

series199.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
76.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.re))
66.0ms
(- (* (+ x.re x.im) (* (- x.re x.im) x.re)) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
35.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
23.0ms
(+ (* x.re x.im) (* x.im x.re))

simplify19.3s

Counts
77 → 102
Calls
77 calls:
Slowest
1.0s
(- (* (* (+ (pow x.re 3) (pow x.im 3)) (* (- (pow x.re 3) (pow x.im 3)) x.re)) (- (* x.re x.im) (* x.im x.re))) (* (* (+ (* x.re x.re) (- (* x.im x.im) (* x.re x.im))) (+ (* x.re x.re) (+ (* x.im x.im) (* x.re x.im)))) (* (- (* (* x.re x.im) (* x.re x.im)) (* (* x.im x.re) (* x.im x.re))) x.im)))
826.0ms
(* (* (+ (* x.re x.re) (- (* x.im x.im) (* x.re x.im))) (+ (* x.re x.re) (+ (* x.im x.im) (* x.re x.im)))) (+ (* (* x.re x.im) (* x.re x.im)) (- (* (* x.im x.re) (* x.im x.re)) (* (* x.re x.im) (* x.im x.re)))))
782.0ms
(- (* (* (- (* x.re x.re) (* x.im x.im)) (* (- (pow x.re 3) (pow x.im 3)) x.re)) (- (* x.re x.im) (* x.im x.re))) (* (* (- x.re x.im) (+ (* x.re x.re) (+ (* x.im x.im) (* x.re x.im)))) (* (- (* (* x.re x.im) (* x.re x.im)) (* (* x.im x.re) (* x.im x.re))) x.im)))
648.0ms
(* (+ (pow x.re 3) (pow x.im 3)) (* (- (* x.re x.re) (* x.im x.im)) x.re))
646.0ms
(* (+ (* x.re x.re) (- (* x.im x.im) (* x.re x.im))) (+ (* x.re x.re) (+ (* x.im x.im) (* x.re x.im))))

prune1.5s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize69.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x.im)
0.6b
(cbrt x.im)
0.6b
(cbrt x.im)
0.5b
(* (cbrt x.im) (cbrt x.im))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×pow1/3
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×add-cbrt-cube insert-posit16 add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 77
Calls
4 calls:
Slowest
25.0ms
(* (cbrt x.im) (cbrt x.im))
2.0ms
(cbrt x.im)
1.0ms
(cbrt x.im)
1.0ms
(cbrt x.im)

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
299.0ms
(cbrt x.im)
296.0ms
(cbrt x.im)
291.0ms
(* (cbrt x.im) (cbrt x.im))
251.0ms
(cbrt x.im)

simplify1.0s

Counts
63 → 89
Calls
63 calls:
Slowest
162.0ms
(* (pow (* x.im -1) 1/3) (cbrt -1))
159.0ms
(* (pow (* x.im -1) 1/3) (cbrt -1))
132.0ms
(* (pow (* x.im -1) 1/3) (cbrt -1))
131.0ms
(* (pow (pow x.im 2) 1/3) (pow (cbrt -1) 2))
88.0ms
(* (* (cbrt (cbrt x.im)) (cbrt (cbrt x.im))) (* (cbrt (cbrt x.im)) (cbrt (cbrt x.im))))

prune1.1s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (* (cbrt x.im) (cbrt x.im)))
0.6b
(cbrt (cbrt x.im))
0.6b
(cbrt x.im)
0.6b
(cbrt x.im)

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
16×cbrt-prod
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×pow1 add-cbrt-cube pow1/3 add-exp-log insert-posit16 add-log-exp
Counts
4 → 49
Calls
4 calls:
Slowest
9.0ms
(cbrt (* (cbrt x.im) (cbrt x.im)))
2.0ms
(cbrt (cbrt x.im))
2.0ms
(cbrt x.im)
1.0ms
(cbrt x.im)

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
464.0ms
(cbrt (* (cbrt x.im) (cbrt x.im)))
367.0ms
(cbrt (cbrt x.im))
284.0ms
(cbrt x.im)
264.0ms
(cbrt x.im)

simplify1.4s

Counts
25 → 61
Calls
25 calls:
Slowest
686.0ms
(* (pow (* x.im -1) 1/9) (pow (cbrt -1) 1/3))
183.0ms
(* (pow (pow x.im 2) 1/9) (pow (pow (cbrt -1) 2) 1/3))
165.0ms
(* (pow (* x.im -1) 1/3) (cbrt -1))
150.0ms
(* (pow (* x.im -1) 1/3) (cbrt -1))
23.0ms
(pow (/ 1 x.im) -1/3)

prune896.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes170.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch3.0ms

end0.0ms

sample2.7s

Algorithm
intervals
Results
2.4s14332×body80valid