Details

Time bar (total: 53.1s)

sample79.0ms

Algorithm
intervals
Results
63.0ms461×body80valid

simplify435.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
435.0ms
(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.6b

localize48.0ms

Local error

Found 4 expressions with local error:

7.7b
(* (- (* x.re x.re) (* x.im x.im)) x.re)
0.2b
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
0.2b
(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
0.0b
(+ (* x.re x.im) (* x.im x.re))

rewrite121.0ms

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*
4×expm1-log1p-u flip3-+ flip3-- frac-sub flip-+ insert-posit16 log1p-expm1-u flip--
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative sum-log sub-neg fma-def fma-neg diff-log prod-diff difference-of-squares
Counts
4 → 83
Calls
4 calls:
Slowest
44.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.re)
34.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
30.0ms
(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
13.0ms
(+ (* x.re x.im) (* x.im x.re))

series210.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
70.0ms
(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
68.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.re)
37.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
35.0ms
(+ (* x.re x.im) (* x.im x.re))

simplify8.9s

Counts
48 → 95
Calls
48 calls:
Slowest
1.4s
(* (+ (* (* 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)))
607.0ms
(- (* (* (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))) x.re) (+ (* (* 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.im)))
465.0ms
(fma (- x.im) (+ (* x.re x.im) (* x.im x.re)) (* x.im (+ (* x.re x.im) (* x.im x.re))))
384.0ms
(- (pow x.re 3) (* 3 (* (pow x.im 2) x.re)))
376.0ms
(- (pow x.re 3) (* 3 (* (pow x.im 2) x.re)))

prune931.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite168.0ms

Algorithm
rewrite-expression-head
Rules
42×associate-*l/
19×flip3-+ flip-+
16×frac-sub
12×frac-times
11×pow1 add-cbrt-cube add-exp-log
10×flip3-- flip--
9×add-sqr-sqrt *-un-lft-identity
8×add-log-exp
7×associate-*l* add-cube-cbrt
6×associate-*r/
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u
2×*-commutative
1×+-commutative sum-log sub-neg fma-def fma-neg diff-log prod-diff distribute-lft-out unswap-sqr
Counts
4 → 101
Calls
4 calls:
Slowest
73.0ms
(- (* (+ x.re x.im) (* (- x.re x.im) x.re)) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
46.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.re))
39.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
7.0ms
(+ (* x.re x.im) (* x.im x.re))

series271.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
99.0ms
(- (* (+ x.re x.im) (* (- x.re x.im) x.re)) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
98.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.re))
51.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
23.0ms
(+ (* x.re x.im) (* x.im x.re))

simplify21.0s

Counts
80 → 113
Calls
80 calls:
Slowest
1.4s
(* (* (- x.re x.im) (+ x.re x.im)) (- (* x.re x.im) (* x.im x.re)))
969.0ms
(* (+ (pow x.re 3) (pow x.im 3)) (* (- (* x.re x.re) (* x.im x.im)) x.re))
895.0ms
(- (* (* (- (* x.re x.re) (* x.im x.im)) (* (- (pow x.re 3) (pow x.im 3)) x.re)) (- (* 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.im)))
814.0ms
(* (+ (* x.re x.re) (+ (* x.im x.im) (* x.re x.im))) (- (* x.re x.im) (* x.im x.re)))
728.0ms
(- (* (* (+ (pow x.re 3) (pow x.im 3)) (* (- (pow x.re 3) (pow x.im 3)) x.re)) (- (* 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.im)))

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×*-un-lft-identity
8×pow1 add-cbrt-cube associate-*l* add-exp-log add-cube-cbrt
6×associate-*r* add-log-exp
4×expm1-log1p-u associate-*l/ insert-posit16 log1p-expm1-u
2×flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ unswap-sqr
1×+-commutative sum-log fma-def flip3-- fma-udef flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 74
Calls
4 calls:
Slowest
29.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
26.0ms
(* (- x.re x.im) x.re)
15.0ms
(+ (* x.re x.im) (* x.im x.re))
0.0ms
(fma (+ x.re x.im) (* (- x.re x.im) x.re) (- (* (+ (* x.re x.im) (* x.im x.re)) x.im)))

series225.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
122.0ms
(fma (+ x.re x.im) (* (- x.re x.im) x.re) (- (* (+ (* x.re x.im) (* x.im x.re)) x.im)))
41.0ms
(* (- x.re x.im) x.re)
36.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
27.0ms
(+ (* x.re x.im) (* x.im x.re))

simplify3.5s

Counts
36 → 86
Calls
36 calls:
Slowest
441.0ms
(* (- (pow x.re 3) (pow x.im 3)) x.re)
381.0ms
(- (pow x.re 3) (* 3 (* (pow x.im 2) x.re)))
369.0ms
(- (pow x.re 3) (* 3 (* (pow x.im 2) x.re)))
339.0ms
(- (pow x.re 3) (* 3 (* (pow x.im 2) x.re)))
338.0ms
(* (* (* (- x.re x.im) (- x.re x.im)) (- x.re x.im)) (* (* x.re x.re) x.re))

prune872.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

13.8b
(cbrt (+ (* x.re x.im) (* x.im x.re)))
13.8b
(cbrt (+ (* x.re x.im) (* x.im x.re)))
13.8b
(cbrt (+ (* x.re x.im) (* x.im x.re)))
0.5b
(* (cbrt (+ (* x.re x.im) (* x.im x.re))) (cbrt (+ (* x.re x.im) (* x.im x.re))))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
18×cbrt-div
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×flip3-+ pow1/3 flip-+
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u frac-times add-cbrt-cube insert-posit16 log1p-expm1-u 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
43.0ms
(* (cbrt (+ (* x.re x.im) (* x.im x.re))) (cbrt (+ (* x.re x.im) (* x.im x.re))))
4.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
4.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
4.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))

series604.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
204.0ms
(* (cbrt (+ (* x.re x.im) (* x.im x.re))) (cbrt (+ (* x.re x.im) (* x.im x.re))))
143.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
133.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
124.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))

simplify9.8s

Counts
83 → 111
Calls
83 calls:
Slowest
530.0ms
(* (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))))))
478.0ms
(cbrt (- (* (* x.re x.im) (* x.re x.im)) (* (* x.im x.re) (* x.im x.re))))
441.0ms
(* (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))))
422.0ms
(* (exp (* 1/3 (+ (log x.im) (log x.re)))) (cbrt 2))
413.0ms
(* (exp (* -1/3 (+ (log (/ -1 x.re)) (log (/ -1 x.im))))) (cbrt 2))

prune1.4s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes166.0ms

Accuracy

0% (0.2b remaining)

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

bsearch5.0ms

end0.0ms

sample3.0s

Algorithm
intervals
Results
2.6s14546×body80valid