Details

Time bar (total: 46.2s)

sample71.0ms

Algorithm
intervals
Results
55.0ms471×body80valid

simplify279.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
279.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.1b

localize28.0ms

Local error

Found 4 expressions with local error:

7.2b
(* (- (* 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.re) (* x.im x.im))

rewrite102.0ms

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-add flip-+ insert-posit16 log1p-expm1-u flip--
2×pow-prod-down prod-exp *-commutative cbrt-unprod difference-of-squares unswap-sqr
1×+-commutative sum-log sub-neg fma-def fma-neg diff-log prod-diff
Counts
4 → 84
Calls
4 calls:
Slowest
32.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)
28.0ms
(+ (* (- (* x.re x.re) (* x.im 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)
15.0ms
(- (* x.re x.re) (* x.im x.im))

series238.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
95.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
77.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)
39.0ms
(- (* x.re x.re) (* x.im x.im))
26.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)

simplify8.6s

Counts
50 → 96
Calls
50 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)))
552.0ms
(+ (* (* (- (* (* 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)))
449.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))
412.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)
403.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))

prune763.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

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)

rewrite132.0ms

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
63.0ms
(* (+ 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))
18.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
16.0ms
(* (- x.re x.im) x.im)

series295.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
107.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.im))
105.0ms
(+ (* (+ x.re x.im) (* (- x.re x.im) x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
57.0ms
(* (- x.re x.im) x.im)
26.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)

simplify19.7s

Counts
89 → 121
Calls
89 calls:
Slowest
1.2s
(* (* (- x.re x.im) (+ x.re x.im)) (- (* x.re x.im) (* x.im x.re)))
885.0ms
(* (+ (* x.re x.re) (+ (* x.im x.im) (* x.re x.im))) (- (* x.re x.im) (* x.im x.re)))
823.0ms
(* (* (- 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 x.im) (* x.im x.re)))))
608.0ms
(* (+ (pow x.re 3) (pow x.im 3)) (* (- (pow x.re 3) (pow x.im 3)) x.im))
605.0ms
(* (* (+ (* 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 x.im) (* x.im x.re)))))

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

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

rewrite89.0ms

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
38.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
35.0ms
(* (- x.re x.im) x.im)
14.0ms
(+ (* x.re x.im) (* x.im x.re))
0.0ms
(fma (+ x.re x.im) (* (- x.re x.im) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))

series250.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
132.0ms
(fma (+ x.re x.im) (* (- x.re x.im) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
46.0ms
(* (- x.re x.im) x.im)
40.0ms
(+ (* x.re x.im) (* x.im x.re))
32.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)

simplify3.8s

Counts
36 → 86
Calls
36 calls:
Slowest
492.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)
400.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))
390.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))
383.0ms
(* (- (pow x.re 3) (pow x.im 3)) x.im)
342.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))

prune841.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

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

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
36×cbrt-prod
35×*-un-lft-identity
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt
11×pow1
9×flip3-+ pow1/3 swap-sqr flip-+ distribute-lft-out
7×associate-*r* associate-*l*
6×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 → 107
Calls
4 calls:
Slowest
49.0ms
(* (cbrt (+ x.re x.im)) (cbrt (+ x.re x.im)))
3.0ms
(cbrt (+ x.re x.im))
3.0ms
(cbrt (+ x.re x.im))
2.0ms
(cbrt (+ x.re x.im))

series758.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
234.0ms
(* (cbrt (+ x.re x.im)) (cbrt (+ x.re x.im)))
186.0ms
(cbrt (+ x.re x.im))
180.0ms
(cbrt (+ x.re x.im))
158.0ms
(cbrt (+ x.re x.im))

simplify4.4s

Counts
94 → 119
Calls
94 calls:
Slowest
416.0ms
(- (+ (pow x.im 2/3) (* 2/3 (* (pow (/ 1 x.im) 1/3) x.re))) (* 1/9 (* (pow (/ 1 (pow x.im 4)) 1/3) (pow x.re 2))))
345.0ms
(* (cbrt (+ (pow x.re 3) (pow x.im 3))) (cbrt (+ (pow x.re 3) (pow x.im 3))))
295.0ms
(* (cbrt (+ (pow x.re 3) (pow x.im 3))) (cbrt (+ x.re x.im)))
270.0ms
(* (cbrt (- (* x.re x.re) (* x.im x.im))) (cbrt (+ (pow x.re 3) (pow x.im 3))))
180.0ms
(- (+ (* 1/3 (* (pow (/ 1 (pow x.im 2)) 1/3) x.re)) (pow x.im 1/3)) (* 1/9 (* (pow (/ 1 (pow x.im 5)) 1/3) (pow x.re 2))))

prune1.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

regimes142.0ms

Accuracy

0% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 0.7b

bsearch4.0ms

end0.0ms

sample2.9s

Algorithm
intervals
Results
2.1s14353×body80valid