Details

Time bar (total: 45.0s)

sample57.0ms

Algorithm
intervals
Results
44.0ms461×body80valid

simplify447.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
447.0ms
(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.7b

localize48.0ms

Local error

Found 4 expressions with local error:

5.8b
(* (- (* x.re x.re) (* x.im x.im)) x.re)
0.2b
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
0.1b
(- (* (- (* 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))

rewrite165.0ms

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
56.0ms
(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
51.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.re)
40.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
17.0ms
(+ (* x.re x.im) (* x.im x.re))

series224.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
81.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.re)
63.0ms
(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
55.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
24.0ms
(+ (* x.re x.im) (* x.im x.re))

simplify9.0s

Counts
48 → 95
Calls
48 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)))
641.0ms
(- (* (* (- (* (* 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)))
472.0ms
(fma (- x.im) (+ (* x.re x.im) (* x.im x.re)) (* x.im (+ (* x.re x.im) (* x.im x.re))))
380.0ms
(* (+ (* (* 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.re x.im)) (- (* (* x.im x.re) (* x.im x.re)) (* (* x.re x.im) (* x.im x.re)))))
379.0ms
(- (pow x.re 3) (* 3 (* (pow x.im 2) x.re)))

prune987.0ms

Pruning

10 alts after pruning (10 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.im x.re)) x.im)
0.2b
(* (+ x.re x.im) (* (- x.re x.im) x.re))
0.1b
(- (* (+ 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))

rewrite179.0ms

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
90.0ms
(- (* (+ x.re x.im) (* (- x.re x.im) x.re)) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
44.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.re))
27.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
15.0ms
(+ (* x.re x.im) (* x.im x.re))

series245.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
91.0ms
(- (* (+ x.re x.im) (* (- x.re x.im) x.re)) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
78.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.re))
53.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
23.0ms
(+ (* x.re x.im) (* x.im x.re))

simplify20.9s

Counts
80 → 113
Calls
80 calls:
Slowest
1.3s
(* (* (- x.re x.im) (+ x.re x.im)) (- (* x.re x.im) (* x.im x.re)))
889.0ms
(- (* (* (- (* 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)))
847.0ms
(- (* (* (+ (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)))
833.0ms
(* (+ (pow x.re 3) (pow x.im 3)) (* (- (pow x.re 3) (pow x.im 3)) x.re))
741.0ms
(* (+ (* x.re x.re) (+ (* x.im x.im) (* x.re x.im))) (- (* x.re x.im) (* x.im x.re)))

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite85.0ms

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
39.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
29.0ms
(* (- 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)))

series238.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
104.0ms
(fma (+ x.re x.im) (* (- x.re x.im) x.re) (- (* (+ (* x.re x.im) (* x.im x.re)) x.im)))
64.0ms
(* (- x.re x.im) x.re)
43.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
27.0ms
(+ (* x.re x.im) (* x.im x.re))

simplify3.6s

Counts
36 → 86
Calls
36 calls:
Slowest
435.0ms
(* (- (pow x.re 3) (pow x.im 3)) x.re)
397.0ms
(- (pow x.re 3) (* 3 (* (pow x.im 2) x.re)))
380.0ms
(- (pow x.re 3) (* 3 (* (pow x.im 2) x.re)))
334.0ms
(- (pow x.re 3) (* 3 (* (pow x.im 2) x.re)))
304.0ms
(* (* (* (- x.re x.im) (- x.re x.im)) (- x.re x.im)) (* (* x.re x.re) x.re))

prune905.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x.im)
0.6b
(cbrt x.im)
0.6b
(cbrt x.im)
0.5b
(* (cbrt x.im) (cbrt x.im))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×pow1/3
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 85
Calls
4 calls:
Slowest
8.0ms
(* (cbrt x.im) (cbrt x.im))
1.0ms
(cbrt x.im)
1.0ms
(cbrt x.im)
1.0ms
(cbrt x.im)

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
379.0ms
(* (cbrt x.im) (cbrt x.im))
315.0ms
(cbrt x.im)
275.0ms
(cbrt x.im)
269.0ms
(cbrt x.im)

simplify1.0s

Counts
63 → 97
Calls
63 calls:
Slowest
157.0ms
(* (pow (* x.im -1) 1/3) (cbrt -1))
135.0ms
(* (pow (* x.im -1) 1/3) (cbrt -1))
132.0ms
(* (pow (* x.im -1) 1/3) (cbrt -1))
100.0ms
(* (* (cbrt (cbrt x.im)) (cbrt (cbrt x.im))) (* (cbrt (cbrt x.im)) (cbrt (cbrt x.im))))
99.0ms
(* (pow (pow x.im 2) 1/3) (pow (cbrt -1) 2))

prune1.7s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes190.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch9.0ms

end0.0ms

sample2.5s

Algorithm
intervals
Results
2.2s14332×body80valid