Details

Time bar (total: 41.0s)

sample60.0ms

Algorithm
intervals
Results
45.0ms473×body80valid

simplify588.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
588.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.3b

localize47.0ms

Local error

Found 4 expressions with local error:

5.3b
(* (- (* 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))

rewrite119.0ms

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.re) (* x.im x.im)) x.im)
39.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
22.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
14.0ms
(+ (* x.re x.im) (* x.im x.re))

series236.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
93.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
86.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)
33.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
24.0ms
(+ (* x.re x.im) (* x.im x.re))

simplify6.7s

Counts
45 → 83
Calls
45 calls:
Slowest
462.0ms
(+ (* (* (- (* (* 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)))
438.0ms
(* (+ (* (* 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)))
416.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))
412.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))
393.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))

prune830.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

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)

rewrite140.0ms

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
72.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.im))
33.0ms
(+ (* (+ x.re x.im) (* (- x.re x.im) x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
18.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
15.0ms
(* (- x.re x.im) x.im)

series277.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
98.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.im))
94.0ms
(+ (* (+ x.re x.im) (* (- x.re x.im) x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
57.0ms
(* (- x.re x.im) x.im)
28.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)

simplify17.0s

Counts
88 → 112
Calls
88 calls:
Slowest
761.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))
662.0ms
(* (* (+ (* 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)))))
572.0ms
(+ (* (* (- (* 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)))
538.0ms
(* (* (- x.re x.im) (+ x.re x.im)) (- (* x.re x.im) (* x.im x.re)))
519.0ms
(* (+ (pow x.re 3) (pow x.im 3)) (* (- (* x.re x.re) (* x.im x.im)) x.im))

prune927.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize72.0ms

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)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
36×cbrt-prod
35×*-un-lft-identity
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt
11×pow1
9×flip3-+ pow1/3 swap-sqr flip-+ distribute-lft-out
7×associate-*r* associate-*l*
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 → 99
Calls
4 calls:
Slowest
45.0ms
(* (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))

series778.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
209.0ms
(* (cbrt (+ x.re x.im)) (cbrt (+ x.re x.im)))
190.0ms
(cbrt (+ x.re x.im))
190.0ms
(cbrt (+ x.re x.im))
189.0ms
(cbrt (+ x.re x.im))

simplify4.7s

Counts
94 → 111
Calls
94 calls:
Slowest
452.0ms
(- (+ (* 1/3 (* (pow (/ 1 (pow x.im 2)) 1/3) x.re)) (pow x.im 1/3)) (* 1/9 (* (pow (/ 1 (pow x.im 5)) 1/3) (pow x.re 2))))
424.0ms
(- (+ (* 1/3 (* (pow (/ 1 (pow x.im 2)) 1/3) x.re)) (pow x.im 1/3)) (* 1/9 (* (pow (/ 1 (pow x.im 5)) 1/3) (pow x.re 2))))
369.0ms
(- (+ (* 1/3 (* (pow (/ 1 (pow x.im 2)) 1/3) x.re)) (pow x.im 1/3)) (* 1/9 (* (pow (/ 1 (pow x.im 5)) 1/3) (pow x.re 2))))
330.0ms
(* (cbrt (+ (pow x.re 3) (pow x.im 3))) (cbrt (+ (pow x.re 3) (pow x.im 3))))
319.0ms
(* (cbrt (+ (pow x.re 3) (pow x.im 3))) (cbrt (+ x.re x.im)))

prune1.5s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 3 expressions with local error:

5.4b
(* (- (* (* x.re x.re) 3) (* x.im x.im)) x.im)
0.2b
(* (* x.re x.re) 3)
0.0b
(- (* (* x.re x.re) 3) (* x.im x.im))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 add-cbrt-cube add-exp-log
9×add-sqr-sqrt
6×*-un-lft-identity associate-*r* add-cube-cbrt
5×add-log-exp
4×associate-*l* pow-prod-down prod-exp cbrt-unprod
3×insert-posit16
2×flip3-- associate-*l/ *-commutative flip-- unswap-sqr
1×sub-neg diff-log
Counts
3 → 54
Calls
3 calls:
Slowest
100.0ms
(* (- (* (* x.re x.re) 3) (* x.im x.im)) x.im)
15.0ms
(- (* (* x.re x.re) 3) (* x.im x.im))
13.0ms
(* (* x.re x.re) 3)

series194.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
88.0ms
(* (- (* (* x.re x.re) 3) (* x.im x.im)) x.im)
74.0ms
(- (* (* x.re x.re) 3) (* x.im x.im))
32.0ms
(* (* x.re x.re) 3)

simplify3.1s

Counts
31 → 63
Calls
31 calls:
Slowest
391.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))
391.0ms
(* (* (* (- (* (* x.re x.re) 3) (* x.im x.im)) (- (* (* x.re x.re) 3) (* x.im x.im))) (- (* (* x.re x.re) 3) (* x.im x.im))) (* (* x.im x.im) x.im))
383.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))
334.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))
322.0ms
(/ (exp (* (* x.re x.re) 3)) (exp (* x.im x.im)))

prune450.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

regimes153.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch2.0ms

end0.0ms

sample2.9s

Algorithm
intervals
Results
2.5s14528×body80valid