Details

Time bar (total: 1.4m)

sample68.0ms

Algorithm
intervals
Results
53.0ms450×body80valid

simplify297.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
297.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.5b

localize47.0ms

Local error

Found 4 expressions with local error:

5.5b
(* (- (* 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))

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×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
44.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)
31.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
27.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
15.0ms
(+ (* x.re x.im) (* x.im x.re))

series232.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
83.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
82.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)
36.0ms
(+ (* x.re x.im) (* x.im x.re))
31.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)

simplify20.8s

Counts
97 → 93
Calls
97 calls:
Slowest
1.8s
(* (+ (* (* 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)))
873.0ms
(log1p (* (- (* x.re x.re) (* x.im x.im)) x.im))
641.0ms
(* (* (+ (* x.re x.im) (* x.im x.re)) (+ (* x.re x.im) (* x.im x.re))) (+ (* x.re x.im) (* x.im x.re)))
580.0ms
(* (- (* x.re x.re) (* x.im x.im)) (* (cbrt x.im) (cbrt x.im)))
559.0ms
(+ (* (* (- (* (* 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)))

prune948.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize47.0ms

Local error

Found 4 expressions with local error:

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

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
42×associate-*l/
20×flip3-+ flip-+
16×frac-add
12×frac-times
11×pow1 add-cbrt-cube add-exp-log
9×add-sqr-sqrt *-un-lft-identity flip3-- flip--
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 sum-log fma-def *-commutative
1×distribute-lft-out unswap-sqr
Counts
4 → 99
Calls
4 calls:
Slowest
49.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.im))
40.0ms
(+ (* (+ x.re x.im) (* (- x.re x.im) x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
24.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
7.0ms
(+ (* x.re x.im) (* x.im x.re))

series274.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
106.0ms
(+ (* (+ x.re x.im) (* (- x.re x.im) x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
100.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.im))
38.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
31.0ms
(+ (* x.re x.im) (* x.im x.re))

simplify27.8s

Counts
130 → 111
Calls
130 calls:
Slowest
1.1s
(* (* (- x.re x.im) (+ x.re x.im)) (- (* x.re x.im) (* x.im x.re)))
708.0ms
(* (+ (* x.re x.re) (+ (* x.im x.im) (* x.re x.im))) (- (* x.re x.im) (* x.im x.re)))
616.0ms
(+ (* (* (- (* 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)))
587.0ms
(* (+ (pow x.re 3) (pow x.im 3)) (* (- (* x.re x.re) (* x.im x.im)) x.im))
540.0ms
(* (+ (pow x.re 3) (pow x.im 3)) (* (- (pow x.re 3) (pow x.im 3)) x.im))

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

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

rewrite62.0ms

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
33.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
16.0ms
(* (- x.re x.im) x.im)
11.0ms
(+ (* x.re x.im) (* x.im x.re))
1.0ms
(fma (+ x.re x.im) (* (- x.re x.im) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))

series229.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
116.0ms
(fma (+ x.re x.im) (* (- x.re x.im) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
62.0ms
(* (- x.re x.im) x.im)
27.0ms
(+ (* x.re x.im) (* x.im x.re))
24.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)

simplify11.6s

Counts
86 → 86
Calls
86 calls:
Slowest
702.0ms
(exp (fma (+ x.re x.im) (* (- x.re x.im) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re)))
546.0ms
(* (* (fma (+ x.re x.im) (* (- x.re x.im) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re)) (fma (+ x.re x.im) (* (- x.re x.im) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))) (fma (+ x.re x.im) (* (- x.re x.im) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re)))
535.0ms
(* (* (* (- x.re x.im) x.im) (* (- x.re x.im) x.im)) (* (- x.re x.im) x.im))
509.0ms
(* (* (+ (* x.re x.im) (* x.im x.re)) (+ (* x.re x.im) (* x.im x.re))) (+ (* x.re x.im) (* x.im x.re)))
484.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))

prune805.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

11.8b
(cbrt (+ (* x.re x.im) (* x.im x.re)))
11.8b
(cbrt (+ (* x.re x.im) (* x.im x.re)))
11.8b
(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))))

rewrite74.0ms

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
49.0ms
(* (cbrt (+ (* x.re x.im) (* x.im x.re))) (cbrt (+ (* x.re x.im) (* x.im x.re))))
8.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
8.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
8.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))

series534.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
160.0ms
(* (cbrt (+ (* x.re x.im) (* x.im x.re))) (cbrt (+ (* x.re x.im) (* x.im x.re))))
138.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
118.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
117.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))

simplify12.7s

Counts
135 → 111
Calls
135 calls:
Slowest
483.0ms
(* (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))))
481.0ms
(* (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.re x.im)) (- (* (* x.im x.re) (* x.im x.re)) (* (* x.re x.im) (* x.im x.re))))))
448.0ms
(* (* (* (cbrt (+ (* x.re x.im) (* x.im x.re))) (cbrt (+ (* x.re x.im) (* x.im x.re)))) (* (cbrt (+ (* x.re x.im) (* x.im x.re))) (cbrt (+ (* x.re x.im) (* x.im x.re))))) (* (cbrt (+ (* x.re x.im) (* x.im x.re))) (cbrt (+ (* x.re x.im) (* x.im x.re)))))
441.0ms
(* (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))))))
437.0ms
(* (exp (* -1/3 (+ (log (/ -1 x.re)) (log (/ -1 x.im))))) (cbrt 2))

prune1.3s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

regimes171.0ms

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms

end0.0ms

sample3.0s

Algorithm
intervals
Results
2.6s14185×body80valid