Details

Time bar (total: 1.2m)

sample92.0ms

Algorithm
intervals
Results
79.0ms442×body80valid

simplify306.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
305.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.1b

localize32.0ms

Local error

Found 2 expressions with local error:

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

rewrite149.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
16×add-sqr-sqrt
15×associate-*r*
9×add-cube-cbrt
8×distribute-rgt-in distribute-lft-in distribute-lft-out
6×pow1 add-cbrt-cube associate-*l* add-exp-log
4×distribute-rgt1-in associate--l+ associate-*r/
3×distribute-rgt-out
2×expm1-log1p-u sub-neg distribute-lft1-in prod-diff pow-prod-down prod-exp *-commutative cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
1×flip3-+ flip3-- flip-+ flip--
Counts
2 → 67
Calls
2 calls:
Slowest
102.0ms
(* x.im (- (* x.re (+ x.re (+ x.re x.re))) (* x.im x.im)))
45.0ms
(* x.re (+ x.re (+ x.re x.re)))

series108.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
74.0ms
(* x.im (- (* x.re (+ x.re (+ x.re x.re))) (* x.im x.im)))
34.0ms
(* x.re (+ x.re (+ x.re x.re)))

simplify4.2s

Counts
49 → 73
Calls
49 calls:
Slowest
432.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))
422.0ms
(+ (* x.re x.re) (- (* (+ x.re x.re) (+ x.re x.re)) (* x.re (+ x.re x.re))))
378.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))
361.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))
288.0ms
(* x.im (- (* x.re (+ x.re (+ x.re x.re))) (* x.im x.im)))

prune553.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.0b

localize24.0ms

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))

rewrite111.0ms

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×expm1-log1p-u frac-add insert-posit16 log1p-expm1-u
3×flip3-- flip--
2×+-commutative sum-log fma-def pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×difference-of-squares
Counts
4 → 81
Calls
4 calls:
Slowest
41.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)
33.0ms
(+ (* (- (* x.re x.re) (* x.im 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)
14.0ms
(+ (* x.re x.im) (* x.im x.re))

series243.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
109.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
79.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)
30.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
26.0ms
(+ (* x.re x.im) (* x.im x.re))

simplify8.4s

Counts
46 → 93
Calls
46 calls:
Slowest
1.6s
(* (+ (* (* 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)))
573.0ms
(+ (* (* (- (* (* 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)))
455.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)
420.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))
377.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))

prune835.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
0.2b
(* (+ 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))
0.0b
(* (- x.re x.im) x.im)

rewrite138.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u
3×*-commutative
2×unswap-sqr
1×+-commutative sum-log fma-def distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 109
Calls
4 calls:
Slowest
56.0ms
(* (+ 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))
27.0ms
(* (- x.re x.im) x.im)
18.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)

series299.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
115.0ms
(+ (* (+ x.re x.im) (* (- x.re x.im) x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
111.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.im))
49.0ms
(* (- x.re x.im) x.im)
23.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)

simplify19.4s

Counts
89 → 121
Calls
89 calls:
Slowest
1.3s
(* (* (- x.re x.im) (+ x.re x.im)) (- (* x.re x.im) (* x.im x.re)))
816.0ms
(* (+ (* x.re x.re) (+ (* x.im x.im) (* x.re x.im))) (- (* x.re x.im) (* x.im x.re)))
737.0ms
(+ (* (* (+ (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)))
615.0ms
(* (+ (pow x.re 3) (pow x.im 3)) (* (- (* x.re x.re) (* x.im x.im)) x.im))
562.0ms
(+ (* (* (+ x.re 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) (* (+ (pow (* x.re x.im) 3) (pow (* x.im x.re) 3)) x.re)))

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* x.im (+ x.re x.im)) (- x.re x.im))
0.2b
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
0.1b
(+ (* (* x.im (+ x.re x.im)) (- x.re x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
0.0b
(* x.im (+ x.re x.im))

rewrite207.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
37×*-un-lft-identity
36×prod-diff
33×add-cube-cbrt
26×associate-*r/
24×associate-*l/
23×distribute-rgt-in distribute-lft-in
22×associate-+l+
20×flip3-+ flip-+
16×frac-add
13×pow1 add-cbrt-cube add-exp-log
12×frac-times associate-*r*
9×flip3-- flip--
7×associate-*l*
6×add-log-exp
5×pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u sub-neg insert-posit16 log1p-expm1-u
3×*-commutative
2×unswap-sqr
1×+-commutative sum-log fma-def distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 155
Calls
4 calls:
Slowest
71.0ms
(* (* x.im (+ x.re x.im)) (- x.re x.im))
66.0ms
(+ (* (* x.im (+ x.re x.im)) (- x.re x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
38.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
26.0ms
(* x.im (+ x.re x.im))

series218.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
85.0ms
(+ (* (* x.im (+ x.re x.im)) (- x.re x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
57.0ms
(* (* x.im (+ x.re x.im)) (- x.re x.im))
49.0ms
(* x.im (+ x.re x.im))
26.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)

simplify28.2s

Counts
139 → 167
Calls
139 calls:
Slowest
1.1s
(* (* (- x.re x.im) (+ x.re x.im)) (- (* x.re x.im) (* x.im x.re)))
702.0ms
(* (+ (* x.re x.re) (+ (* x.im x.im) (* x.re x.im))) (- (* x.re x.im) (* x.im x.re)))
615.0ms
(* (- (* (* x.re x.im) (* x.re x.im)) (* (* x.im x.re) (* x.im x.re))) x.re)
600.0ms
(+ (* (* (* x.im (- (* x.re x.re) (* x.im x.im))) (- (pow x.re 3) (pow x.im 3))) (- (* x.re x.im) (* x.im x.re))) (* (* (- 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)))
585.0ms
(+ (* (* (* 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))))) (* (- x.re x.im) (* (+ (pow (* x.re x.im) 3) (pow (* x.im x.re) 3)) x.re)))

prune1.7s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0b

regimes234.0ms

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms

end0.0ms

sample2.8s

Algorithm
intervals
Results
2.5s14397×body80valid