Details

Time bar (total: 48.0s)

sample65.0ms

Algorithm
intervals
Results
54.0ms442×body80valid

simplify295.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
295.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.1b

localize25.0ms

Local error

Found 4 expressions with local error:

7.1b
(* (- (* x.re x.re) (* x.im x.im)) x.im)
0.2b
(* (+ (* 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))

rewrite71.0ms

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
22.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
21.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)
20.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
7.0ms
(+ (* x.re x.im) (* x.im x.re))

series243.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
112.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
83.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)
26.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
22.0ms
(+ (* x.re x.im) (* x.im x.re))

simplify6.5s

Counts
45 → 83
Calls
45 calls:
Slowest
563.0ms
(+ (* (* (- (* (* 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)))
418.0ms
(* (+ (* (* 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)))
383.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))
370.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))
355.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))

prune790.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite151.0ms

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
68.0ms
(* (- x.re x.im) (* (+ x.re x.im) x.im))
32.0ms
(+ (* (- x.re x.im) (* (+ x.re x.im) x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
24.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
24.0ms
(* (+ x.re x.im) x.im)

series282.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
120.0ms
(+ (* (- x.re x.im) (* (+ x.re x.im) x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
96.0ms
(* (- x.re x.im) (* (+ x.re x.im) x.im))
37.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
30.0ms
(* (+ x.re x.im) x.im)

simplify17.6s

Counts
88 → 112
Calls
88 calls:
Slowest
887.0ms
(+ (* (* (- (pow x.re 3) (pow x.im 3)) (* (+ (pow x.re 3) (pow x.im 3)) x.im)) (- (* 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.re)))
878.0ms
(+ (* (* (- (* 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)))
681.0ms
(* (* (+ (* 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)))))
646.0ms
(* (- (pow x.re 3) (pow x.im 3)) (* (- (* x.re x.re) (* x.im x.im)) x.im))
593.0ms
(* (* (* (+ x.re x.im) (+ x.re x.im)) (+ x.re x.im)) (* (* x.im x.im) x.im))

prune955.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0b

localize68.0ms

Local error

Found 4 expressions with local error:

23.5b
(cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re))
23.5b
(cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re))
23.5b
(cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re))
0.4b
(* (cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re)) (cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re)))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
20×associate-*l/
18×cbrt-div
11×pow1
10×add-sqr-sqrt
9×flip3-+ pow1/3 flip-+
8×*-un-lft-identity add-cube-cbrt
7×cbrt-prod
6×add-exp-log
4×frac-times add-cbrt-cube swap-sqr associate-*r* associate-*l* insert-posit16 add-log-exp
2×pow-prod-down associate-*r/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 76
Calls
4 calls:
Slowest
62.0ms
(* (cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re)) (cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re)))
13.0ms
(cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re))
8.0ms
(cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re))
7.0ms
(cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re))

series603.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
182.0ms
(* (cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re)) (cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re)))
154.0ms
(cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re))
142.0ms
(cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re))
124.0ms
(cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re))

simplify9.9s

Counts
63 → 88
Calls
63 calls:
Slowest
623.0ms
(* (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))))))
576.0ms
(* (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))))
563.0ms
(* (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))))))
539.0ms
(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)))))
451.0ms
(* (exp (* 1/3 (+ (* 2 (log x.im)) (* 4 (log x.re))))) (pow (cbrt 2) 2))

prune1.1s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0b

localize79.0ms

Local error

Found 4 expressions with local error:

23.5b
(cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re))
23.5b
(cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re))
14.5b
(cbrt (+ (* x.re x.im) (* x.im x.re)))
0.6b
(cbrt x.re)

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
8×cbrt-prod
6×add-sqr-sqrt cbrt-div *-un-lft-identity add-cube-cbrt
4×pow1 add-cbrt-cube pow1/3 associate-*l/ add-exp-log insert-posit16 add-log-exp
3×flip3-+ flip-+
Counts
4 → 50
Calls
4 calls:
Slowest
23.0ms
(cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re))
14.0ms
(cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re))
8.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
1.0ms
(cbrt x.re)

series691.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
247.0ms
(cbrt x.re)
164.0ms
(cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re))
142.0ms
(cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re))
138.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))

simplify4.5s

Counts
26 → 62
Calls
26 calls:
Slowest
677.0ms
(cbrt (* (+ (pow (* x.re x.im) 3) (pow (* x.im x.re) 3)) x.re))
443.0ms
(* (cbrt 2) (exp (* -1/3 (+ (log (/ 1 x.im)) (* 2 (log (/ 1 x.re)))))))
386.0ms
(* (cbrt 2) (exp (* -1/3 (+ (log (/ 1 x.im)) (* 2 (log (/ 1 x.re)))))))
367.0ms
(* (exp (* 1/3 (+ (log x.im) (log x.re)))) (cbrt 2))
354.0ms
(* (exp (* -1/3 (+ (log (/ -1 x.re)) (log (/ -1 x.im))))) (cbrt 2))

prune834.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0b

regimes171.0ms

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms

end0.0ms

sample2.7s

Algorithm
intervals
Results
2.4s14397×body80valid