Details

Time bar (total: 42.8s)

sample82.0ms

Algorithm
intervals
Results
49.0ms476×body80valid

simplify232.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
232.0ms
(+ (* (- (* 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: 6.7b

localize49.0ms

Local error

Found 4 expressions with local error:

6.7b
(* (- (* x.re x.re) (* x.im x.im)) x.im)
0.1b
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
0.1b
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
0.0b
(+ (* x.re x.im) (* x.im x.re))

rewrite76.0ms

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
29.0ms
(+ (* (- (* 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)
19.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
7.0ms
(+ (* x.re x.im) (* x.im x.re))

series234.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
108.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
66.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)
34.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
26.0ms
(+ (* x.re x.im) (* x.im x.re))

simplify7.1s

Counts
45 → 83
Calls
45 calls:
Slowest
507.0ms
(+ (* (* (- (* (* 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)))
486.0ms
(* (+ (* (* 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)))
421.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))
404.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))
360.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))

prune806.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite131.0ms

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
45.0ms
(* (- x.re x.im) (* (+ x.re x.im) x.im))
30.0ms
(+ (* (- x.re x.im) (* (+ x.re x.im) x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
29.0ms
(* (+ x.re x.im) x.im)
24.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)

series267.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
103.0ms
(+ (* (- x.re x.im) (* (+ x.re x.im) x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
93.0ms
(* (- x.re x.im) (* (+ x.re x.im) x.im))
40.0ms
(* (+ x.re x.im) x.im)
30.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)

simplify18.2s

Counts
88 → 112
Calls
88 calls:
Slowest
879.0ms
(+ (* (* (- (* 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)))
749.0ms
(* (* (+ (* x.re x.re) (+ (* x.im x.im) (* x.re 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)))))
729.0ms
(* (* (+ (* 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)))))
607.0ms
(* (* (* (+ x.re x.im) (+ x.re x.im)) (+ x.re x.im)) (* (* x.im x.im) x.im))
588.0ms
(+ (* (* (- (* 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)))

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize48.0ms

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))

rewrite10.0ms

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
7.0ms
(* (cbrt x.im) (cbrt x.im))
1.0ms
(cbrt x.im)
1.0ms
(cbrt x.im)
1.0ms
(cbrt x.im)

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
328.0ms
(* (cbrt x.im) (cbrt x.im))
298.0ms
(cbrt x.im)
291.0ms
(cbrt x.im)
266.0ms
(cbrt x.im)

simplify867.0ms

Counts
63 → 89
Calls
63 calls:
Slowest
127.0ms
(* (pow (* x.im -1) 1/3) (cbrt -1))
124.0ms
(* (pow (* x.im -1) 1/3) (cbrt -1))
108.0ms
(* (pow (pow x.im 2) 1/3) (pow (cbrt -1) 2))
96.0ms
(* (pow (* x.im -1) 1/3) (cbrt -1))
63.0ms
(* (* (cbrt (cbrt x.im)) (cbrt (cbrt x.im))) (* (cbrt (cbrt x.im)) (cbrt (cbrt x.im))))

prune1.0s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
43×cbrt-prod
37×add-sqr-sqrt
35×*-un-lft-identity
18×cbrt-div
15×add-cube-cbrt
11×pow1
10×swap-sqr
9×flip3-- pow1/3 flip-- distribute-lft-out--
8×associate-*r* associate-*l*
7×difference-of-squares
6×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 → 105
Calls
4 calls:
Slowest
30.0ms
(* (cbrt (- x.re x.im)) (cbrt (- x.re x.im)))
5.0ms
(cbrt (- x.re x.im))
5.0ms
(cbrt (- x.re x.im))
5.0ms
(cbrt (- x.re x.im))

series866.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
237.0ms
(cbrt (- x.re x.im))
235.0ms
(cbrt (- x.re x.im))
199.0ms
(* (cbrt (- x.re x.im)) (cbrt (- x.re x.im)))
195.0ms
(cbrt (- x.re x.im))

simplify6.1s

Counts
101 → 117
Calls
101 calls:
Slowest
638.0ms
(exp (* 1/3 (- (log -1) (log (/ -1 x.re)))))
620.0ms
(exp (* 1/3 (- (log -1) (log (/ -1 x.re)))))
585.0ms
(exp (* 1/3 (- (log -1) (log (/ -1 x.re)))))
430.0ms
(- (pow x.im 2/3) (+ (* 1/9 (* (pow (/ 1 (pow x.im 4)) 1/3) (pow x.re 2))) (* 2/3 (* (pow (/ 1 x.im) 1/3) x.re))))
411.0ms
(- (exp (* 1/3 (+ (log x.im) (log -1)))) (+ (* 1/3 (* x.re (exp (* 1/3 (- (log -1) (* 2 (log x.im))))))) (* 1/9 (* (pow x.re 2) (exp (* 1/3 (- (log -1) (* 5 (log x.im)))))))))

prune1.3s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 0b

regimes177.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch4.0ms

end0.0ms

sample2.9s

Algorithm
intervals
Results
2.6s14428×body80valid