Details

Time bar (total: 46.4s)

sample88.0ms

Algorithm
intervals
Results
75.0ms474×body80valid

simplify180.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
180.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.1b

localize37.0ms

Local error

Found 4 expressions with local error:

7.2b
(* (- (* 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))

rewrite107.0ms

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
43.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
35.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
21.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)
7.0ms
(+ (* x.re x.im) (* x.im x.re))

series236.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
94.0ms
(+ (* (- (* 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)
37.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
24.0ms
(+ (* x.re x.im) (* x.im x.re))

simplify6.4s

Counts
45 → 83
Calls
45 calls:
Slowest
551.0ms
(+ (* (* (- (* (* 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)))
415.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))
403.0ms
(* (+ (* (* 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)))
345.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))
337.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)

prune765.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

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)

rewrite153.0ms

Algorithm
rewrite-expression-head
Rules
44×associate-*l/
19×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*
10×flip3-- flip--
9×add-cube-cbrt
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
53.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.im))
34.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
33.0ms
(+ (* (+ x.re x.im) (* (- x.re x.im) x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
30.0ms
(* (- x.re x.im) x.im)

series301.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
110.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.im))
97.0ms
(+ (* (+ x.re x.im) (* (- x.re x.im) x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
58.0ms
(* (- x.re x.im) x.im)
35.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)

simplify17.5s

Counts
88 → 112
Calls
88 calls:
Slowest
700.0ms
(* (- (* x.re x.re) (* x.im x.im)) (* (- x.re x.im) x.im))
678.0ms
(* (* (+ (* 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)))))
648.0ms
(+ (* (* (- (* x.re x.re) (* x.im x.im)) (* (- x.re 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) (* (+ (pow (* x.re x.im) 3) (pow (* x.im x.re) 3)) x.re)))
590.0ms
(* (+ (pow x.re 3) (pow x.im 3)) (* (- (* x.re x.re) (* x.im x.im)) x.im))
562.0ms
(* (- (* x.re x.re) (* x.im x.im)) (* (- (* x.re x.re) (* x.im x.im)) x.im))

prune1.1s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

12.9b
(cbrt (+ (* x.re x.im) (* x.im x.re)))
12.9b
(cbrt (+ (* x.re x.im) (* x.im x.re)))
12.9b
(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))))

rewrite46.0ms

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)))

series660.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
228.0ms
(* (cbrt (+ (* x.re x.im) (* x.im x.re))) (cbrt (+ (* x.re x.im) (* x.im x.re))))
166.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
143.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
123.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))

simplify9.5s

Counts
83 → 103
Calls
83 calls:
Slowest
635.0ms
(* (cbrt (- (* 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))))))
615.0ms
(* (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))))
593.0ms
(* (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))))))
543.0ms
(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)))))
431.0ms
(* (exp (* 1/3 (+ (log x.im) (log x.re)))) (cbrt 2))

prune1.7s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

12.9b
(cbrt (+ (* x.re x.im) (* x.im x.re)))
12.9b
(cbrt (+ (* x.re x.im) (* x.im x.re)))
12.9b
(cbrt (* x.re x.im))
1.0b
(cbrt 2)

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
10×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×pow1 cbrt-div add-cbrt-cube pow1/3 add-exp-log insert-posit16 add-log-exp
2×flip3-+ flip-+
Counts
4 → 50
Calls
4 calls:
Slowest
5.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
4.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
3.0ms
(cbrt (* x.re x.im))
1.0ms
(cbrt 2)

series362.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
141.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
124.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
97.0ms
(cbrt (* x.re x.im))
0.0ms
(cbrt 2)

simplify3.7s

Counts
24 → 60
Calls
24 calls:
Slowest
418.0ms
(* (exp (* 1/3 (+ (log x.im) (log x.re)))) (cbrt 2))
357.0ms
(* (exp (* 1/3 (+ (log x.im) (log x.re)))) (cbrt 2))
342.0ms
(* (exp (* -1/3 (+ (log (/ -1 x.re)) (log (/ -1 x.im))))) (cbrt 2))
333.0ms
(* (exp (* -1/3 (+ (log (/ -1 x.re)) (log (/ -1 x.im))))) (cbrt 2))
323.0ms
(* (exp (* -1/3 (+ (log (/ 1 x.im)) (log (/ 1 x.re))))) (cbrt 2))

prune906.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 0.0b

regimes148.0ms

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms

end0.0ms

sample2.3s

Algorithm
intervals
Results
2.1s14455×body80valid