Details

Time bar (total: 1.6m)

sample84.0ms

Algorithm
intervals
Results
72.0ms461×body80valid

simplify254.0ms

Calls
1 calls:
Slowest
254.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.6b

localize22.0ms

Local error

Found 4 expressions with local error:

7.7b
(* (- (* x.re x.re) (* x.im x.im)) x.im)
0.2b
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
0.2b
(+ (* (- (* 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))

rewrite77.0ms

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
Calls
4 calls:
Slowest
23.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
23.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)
21.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
9.0ms
(+ (* x.re x.im) (* x.im x.re))

series266.0ms

Calls
4 calls:
Slowest
121.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
73.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)
36.0ms
(+ (* x.re x.im) (* x.im x.re))
35.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)

simplify8.2s

Calls
46 calls:
Slowest
1.5s
(* (+ (* (* 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)))
543.0ms
(+ (* (* (- (* (* 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)))
477.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)
393.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))
387.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))

prune898.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

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

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
36×prod-diff
35×add-sqr-sqrt
33×*-un-lft-identity
31×add-cube-cbrt
24×associate-*l/ associate-*r/
22×distribute-rgt-in associate-+l+ distribute-lft-in
20×flip3-+ flip-+
16×frac-add
12×frac-times
11×pow1 add-cbrt-cube add-exp-log
9×flip3-- flip--
8×associate-*r* add-log-exp
4×expm1-log1p-u sub-neg associate-*l* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u
2×+-commutative sum-log fma-def *-commutative
1×distribute-lft-out-- difference-of-squares unswap-sqr
Calls
4 calls:
Slowest
42.0ms
(+ (* (* x.im (+ x.re x.im)) (- x.re x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
41.0ms
(* (* x.im (+ x.re x.im)) (- x.re x.im))
38.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
9.0ms
(+ (* x.re x.im) (* x.im x.re))

series244.0ms

Calls
4 calls:
Slowest
99.0ms
(* (* x.im (+ x.re x.im)) (- x.re x.im))
76.0ms
(+ (* (* x.im (+ x.re x.im)) (- x.re x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
39.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
30.0ms
(+ (* x.re x.im) (* x.im x.re))

simplify28.3s

Calls
125 calls:
Slowest
1.3s
(* (* (- x.re x.im) (+ x.re x.im)) (- (* x.re x.im) (* x.im x.re)))
843.0ms
(* (+ (* x.re x.re) (+ (* x.im x.im) (* x.re x.im))) (- (* x.re x.im) (* x.im x.re)))
738.0ms
(* (fma (- (sqrt x.im)) (sqrt x.im) (* (sqrt x.im) (sqrt x.im))) (* x.im (+ x.re x.im)))
632.0ms
(+ (* (* (* x.im (+ x.re x.im)) (- (* x.re 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)))
565.0ms
(+ (* (* (* 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)))

prune1.6s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×*-un-lft-identity
8×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
7×associate-*r*
6×associate-*l* add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×flip3-+ flip-+
2×pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod unswap-sqr
1×distribute-rgt-in +-commutative sum-log fma-def distribute-lft-in fma-udef distribute-lft-out
Calls
4 calls:
Slowest
28.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
20.0ms
(* x.im (+ x.re x.im))
11.0ms
(+ (* x.re x.im) (* x.im x.re))
1.0ms
(fma (* x.im (+ x.re x.im)) (- x.re x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))

series191.0ms

Calls
4 calls:
Slowest
90.0ms
(fma (* 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)
37.0ms
(* x.im (+ x.re x.im))
26.0ms
(+ (* x.re x.im) (* x.im x.re))

simplify2.9s

Calls
39 calls:
Slowest
425.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))
418.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))
398.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))
240.0ms
(* (- (* (* x.re x.im) (* x.re x.im)) (* (* x.im x.re) (* x.im x.re))) x.re)
210.0ms
(* (+ (pow (* x.re x.im) 3) (pow (* x.im x.re) 3)) x.re)

prune845.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0b

localize64.0ms

Local error

Found 4 expressions with local error:

16.7b
(cbrt (* (* x.im (+ x.re x.im)) (- x.re x.im)))
16.7b
(cbrt (* (* x.im (+ x.re x.im)) (- x.re x.im)))
16.7b
(cbrt (* (* x.im (+ x.re x.im)) (- x.re x.im)))
0.3b
(* (cbrt (* (* x.im (+ x.re x.im)) (- x.re x.im))) (cbrt (* (* x.im (+ x.re x.im)) (- x.re x.im))))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
176×associate-*r/
168×cbrt-div
148×frac-times
63×flip3-+ flip3-- flip-+ flip--
50×associate-*l/
11×pow1
10×add-sqr-sqrt
9×pow1/3
8×*-un-lft-identity add-cube-cbrt
7×cbrt-prod
6×add-exp-log
4×expm1-log1p-u add-cbrt-cube swap-sqr associate-*r* associate-*l* insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod unswap-sqr
Calls
4 calls:
Slowest
56.0ms
(* (cbrt (* (* x.im (+ x.re x.im)) (- x.re x.im))) (cbrt (* (* x.im (+ x.re x.im)) (- x.re x.im))))
29.0ms
(cbrt (* (* x.im (+ x.re x.im)) (- x.re x.im)))
26.0ms
(cbrt (* (* x.im (+ x.re x.im)) (- x.re x.im)))
21.0ms
(cbrt (* (* x.im (+ x.re x.im)) (- x.re x.im)))

series743.0ms

Calls
4 calls:
Slowest
213.0ms
(cbrt (* (* x.im (+ x.re x.im)) (- x.re x.im)))
181.0ms
(cbrt (* (* x.im (+ x.re x.im)) (- x.re x.im)))
176.0ms
(* (cbrt (* (* x.im (+ x.re x.im)) (- x.re x.im))) (cbrt (* (* x.im (+ x.re x.im)) (- x.re x.im))))
173.0ms
(cbrt (* (* x.im (+ x.re x.im)) (- x.re x.im)))

simplify46.6s

Calls
213 calls:
Slowest
836.0ms
(* (sqrt (cbrt (* (* x.im (+ x.re x.im)) (- x.re x.im)))) (sqrt (cbrt (* (* x.im (+ x.re x.im)) (- x.re x.im)))))
773.0ms
(cbrt (* (* x.im (+ (pow x.re 3) (pow x.im 3))) (- x.re x.im)))
565.0ms
(* (cbrt (* (* x.im (+ x.re x.im)) (- (pow x.re 3) (pow x.im 3)))) (cbrt (* (* x.im (+ x.re x.im)) (- (pow x.re 3) (pow x.im 3)))))
527.0ms
(cbrt (* (* x.im (- (* x.re x.re) (* x.im x.im))) (- (* x.re x.re) (* x.im x.im))))
507.0ms
(* (cbrt (* (* x.im (- (* x.re x.re) (* x.im x.im))) (- (* x.re x.re) (* x.im x.im)))) (cbrt (* (* x.im (- (* x.re x.re) (* x.im x.im))) (- (* x.re x.re) (* x.im x.im)))))

prune3.0s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0b

regimes217.0ms

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms

end0.0ms

sample2.6s

Algorithm
intervals
Results
2.2s14302×body80valid