Details

Time bar (total: 1.1m)

sample104.0ms

Algorithm
intervals
Results
86.0ms447×body80valid

simplify263.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
263.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.4b

localize35.0ms

Local error

Found 4 expressions with local error:

7.4b
(* (- (* x.re x.re) (* x.im x.im)) x.im)
0.1b
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
0.1b
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
0.0b
(+ (* x.re x.im) (* x.im x.re))

rewrite85.0ms

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*
5×flip3-+ flip-+
4×frac-add insert-posit16
3×flip3-- flip--
2×+-commutative sum-log pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×difference-of-squares
Counts
4 → 71
Calls
4 calls:
Slowest
28.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
27.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)
21.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
9.0ms
(+ (* x.re x.im) (* x.im x.re))

series251.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
104.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
80.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)
34.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
32.0ms
(+ (* x.re x.im) (* x.im x.re))

simplify16.2s

Counts
89 → 83
Calls
89 calls:
Slowest
702.0ms
(* (+ (pow (* x.re x.im) 3) (pow (* x.im x.re) 3)) x.re)
624.0ms
(+ (* (* x.re x.im) (* x.re x.im)) (- (* (* x.im x.re) (* x.im x.re)) (* (* x.re x.im) (* x.im x.re))))
614.0ms
(* (* (+ (* x.re x.im) (* x.im x.re)) (+ (* x.re x.im) (* x.im x.re))) (+ (* x.re x.im) (* x.im x.re)))
520.0ms
(+ (* (* (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))) 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))))) (* (+ (* x.re x.re) (* x.im x.im)) (* (+ (pow (* x.re x.im) 3) (pow (* x.im x.re) 3)) x.re)))
512.0ms
(* (+ (* (* 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)))

prune852.0ms

Pruning

11 alts after pruning (11 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.re x.im) x.im))
0.1b
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
0.1b
(+ (* (- x.re x.im) (* (+ x.re x.im) x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
0.0b
(* (+ x.re x.im) x.im)

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
44×associate-*l/
20×flip3-+ flip-+
16×frac-add
15×add-sqr-sqrt
13×pow1 *-un-lft-identity add-cbrt-cube add-exp-log
12×frac-times associate-*l*
9×flip3-- add-cube-cbrt flip--
7×associate-*r*
6×associate-*r/ add-log-exp
5×pow-prod-down prod-exp cbrt-unprod
4×insert-posit16
3×*-commutative
2×unswap-sqr
1×+-commutative sum-log distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 100
Calls
4 calls:
Slowest
44.0ms
(+ (* (- x.re x.im) (* (+ x.re x.im) x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
35.0ms
(* (- x.re x.im) (* (+ x.re x.im) x.im))
27.0ms
(* (+ x.re x.im) x.im)
27.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)

series262.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
103.0ms
(* (- x.re x.im) (* (+ x.re x.im) x.im))
92.0ms
(+ (* (- x.re x.im) (* (+ x.re x.im) x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
37.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
30.0ms
(* (+ x.re x.im) x.im)

simplify26.0s

Counts
132 → 112
Calls
132 calls:
Slowest
784.0ms
(* (* (+ 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)))))
778.0ms
(+ (* (* (- (* x.re x.re) (* x.im x.im)) (* (- (* x.re x.re) (* x.im x.im)) 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))))) (* (* (+ x.re x.im) (- x.re x.im)) (* (+ (pow (* x.re x.im) 3) (pow (* x.im x.re) 3)) x.re)))
658.0ms
(* (- (pow x.re 3) (pow x.im 3)) (* (- (* x.re x.re) (* x.im x.im)) x.im))
591.0ms
(* (* (* (+ x.re x.im) x.im) (* (+ x.re x.im) x.im)) (* (+ x.re x.im) x.im))
565.0ms
(* (* (+ (* 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)))))

prune1.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize66.0ms

Local error

Found 4 expressions with local error:

13.3b
(cbrt (+ (* x.re x.im) (* x.im x.re)))
13.3b
(cbrt (+ (* x.re x.im) (* x.im x.re)))
13.3b
(cbrt (+ (* x.re x.im) (* x.im x.re)))
0.5b
(* (cbrt (+ (* x.re x.im) (* x.im x.re))) (cbrt (+ (* x.re x.im) (* x.im x.re))))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
18×cbrt-div
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×flip3-+ pow1/3 flip-+
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×frac-times add-cbrt-cube insert-posit16 add-log-exp unswap-sqr
2×pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 91
Calls
4 calls:
Slowest
34.0ms
(* (cbrt (+ (* x.re x.im) (* x.im x.re))) (cbrt (+ (* x.re x.im) (* x.im x.re))))
4.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
4.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
4.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))

series600.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
170.0ms
(* (cbrt (+ (* x.re x.im) (* x.im x.re))) (cbrt (+ (* x.re x.im) (* x.im x.re))))
157.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
140.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
133.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))

simplify13.5s

Counts
127 → 103
Calls
127 calls:
Slowest
750.0ms
(* (exp (* -1/3 (+ (log (/ -1 x.re)) (log (/ -1 x.im))))) (cbrt 2))
689.0ms
(cbrt (+ (* (* x.re x.im) (* x.re x.im)) (- (* (* x.im x.re) (* x.im x.re)) (* (* x.re x.im) (* x.im x.re)))))
675.0ms
(* (cbrt (+ (* (* x.re x.im) (* x.re x.im)) (- (* (* x.im x.re) (* x.im x.re)) (* (* x.re x.im) (* x.im x.re))))) (cbrt (+ (* (* x.re x.im) (* x.re x.im)) (- (* (* x.im x.re) (* x.im x.re)) (* (* x.re x.im) (* x.im x.re))))))
644.0ms
(* (cbrt (+ (* (* x.re x.im) (* x.re x.im)) (- (* (* x.im x.re) (* x.im x.re)) (* (* x.re x.im) (* x.im x.re))))) (cbrt (- (* x.re x.im) (* x.im x.re))))
618.0ms
(cbrt (+ (* (* x.re x.im) (* x.re x.im)) (- (* (* x.im x.re) (* x.im x.re)) (* (* x.re x.im) (* x.im x.re)))))

prune1.2s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

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

rewrite20.0ms

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
15.0ms
(* (cbrt x.re) (cbrt x.re))
2.0ms
(cbrt x.re)
1.0ms
(cbrt x.re)
1.0ms
(cbrt x.re)

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
280.0ms
(* (cbrt x.re) (cbrt x.re))
273.0ms
(cbrt x.re)
265.0ms
(cbrt x.re)
239.0ms
(cbrt x.re)

simplify1.2s

Counts
103 → 89
Calls
103 calls:
Slowest
142.0ms
(* (cbrt -1) (pow (* x.re -1) 1/3))
134.0ms
(* (cbrt -1) (pow (* x.re -1) 1/3))
118.0ms
(* (cbrt -1) (pow (* x.re -1) 1/3))
109.0ms
(* (pow (cbrt -1) 2) (pow (pow x.re 2) 1/3))
94.0ms
(* (* (cbrt (cbrt x.re)) (cbrt (cbrt x.re))) (* (cbrt (cbrt x.re)) (cbrt (cbrt x.re))))

prune1.0s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 0.0b

regimes181.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch5.0ms

end0.0ms

sample2.8s

Algorithm
intervals
Results
2.0s14490×body80valid