Details

Time bar (total: 44.3s)

sample53.0ms

Algorithm
intervals
Results
44.0ms462×body80valid

simplify308.0ms

Calls
1 calls:
Slowest
308.0ms
(+ (* (- (* 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: 8.3b

localize24.0ms

Local error

Found 4 expressions with local error:

8.3b
(* (- (* 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))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
12×associate-*l/
8×add-log-exp
7×associate-*l*
6×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
5×flip3-+ flip-+
4×expm1-log1p-u pow1 add-cbrt-cube frac-add add-exp-log insert-posit16 log1p-expm1-u
3×flip3-- flip--
2×+-commutative sum-log fma-def *-commutative
1×difference-of-squares
Calls
4 calls:
Slowest
16.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)
8.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
5.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
3.0ms
(+ (* x.re x.im) (* x.im x.re))

series107.0ms

Calls
4 calls:
Slowest
45.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
30.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)
19.0ms
(+ (* x.re x.im) (* x.im x.re))
12.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)

simplify5.8s

Calls
32 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)))
481.0ms
(* (+ (pow (* x.re x.im) 3) (pow (* x.im x.re) 3)) x.re)
444.0ms
(+ (* (* (- (* (* 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)))
439.0ms
(+ (* (* (- (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)) 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.re x.re)) (+ (* (* x.im x.im) (* x.im x.im)) (* (* x.re x.re) (* x.im x.im)))) (* (+ (pow (* x.re x.im) 3) (pow (* x.im x.re) 3)) x.re)))
328.0ms
(* (exp (* (- (* x.re x.re) (* x.im x.im)) x.im)) (exp (* (+ (* x.re x.im) (* x.im x.re)) x.re)))

prune758.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

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)

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
44×associate-*l/
19×flip3-+ flip-+
16×frac-add
12×frac-times
10×flip3-- flip--
9×associate-*l*
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow1 add-cbrt-cube associate-*r/ add-exp-log add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×*-commutative
1×+-commutative sum-log fma-def associate-*r* pow-prod-down prod-exp cbrt-unprod
Calls
4 calls:
Slowest
24.0ms
(+ (* (+ x.re x.im) (* (- x.re x.im) x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
19.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.im))
10.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
10.0ms
(* (- x.re x.im) x.im)

series144.0ms

Calls
4 calls:
Slowest
56.0ms
(+ (* (+ x.re x.im) (* (- x.re x.im) x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
36.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.im))
33.0ms
(* (- x.re x.im) x.im)
18.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)

simplify16.5s

Calls
71 calls:
Slowest
1.3s
(* (* (- x.re x.im) (+ x.re x.im)) (- (* x.re x.im) (* x.im x.re)))
746.0ms
(* (+ (* x.re x.re) (+ (* x.im x.im) (* x.re x.im))) (- (* x.re x.im) (* x.im x.re)))
617.0ms
(+ (* (* (+ x.re x.im) (* (- (pow x.re 3) (pow x.im 3)) 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) (* x.re x.im))) (* (+ (pow (* x.re x.im) 3) (pow (* x.im x.re) 3)) x.re)))
605.0ms
(+ (* (* (+ (pow x.re 3) (pow x.im 3)) (* (- 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.re) (- (* x.im x.im) (* x.re x.im))) (* (+ (pow (* x.re x.im) 3) (pow (* x.im x.re) 3)) x.re)))
562.0ms
(* (+ (pow x.re 3) (pow x.im 3)) (* (- (* x.re x.re) (* x.im x.im)) x.im))

prune1.0s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

24.1b
(cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re))
24.1b
(cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re))
24.1b
(cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re))
0.4b
(* (cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re)) (cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
20×associate-*l/
18×cbrt-div
9×pow1 flip3-+ flip-+
7×pow1/3
6×add-sqr-sqrt *-un-lft-identity add-exp-log add-cube-cbrt
5×cbrt-prod
4×expm1-log1p-u frac-times add-cbrt-cube associate-*r* associate-*l* insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down associate-*r/ pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
12.0ms
(* (cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re)) (cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re)))
6.0ms
(cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re))
5.0ms
(cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re))
5.0ms
(cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re))

series580.0ms

Calls
4 calls:
Slowest
165.0ms
(* (cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re)) (cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re)))
159.0ms
(cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re))
135.0ms
(cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re))
121.0ms
(cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re))

simplify9.2s

Calls
49 calls:
Slowest
735.0ms
(cbrt (* (+ (pow (* x.re x.im) 3) (pow (* x.im x.re) 3)) x.re))
473.0ms
(* (cbrt (* (+ (pow (* x.re x.im) 3) (pow (* x.im x.re) 3)) x.re)) (cbrt (* (+ (pow (* x.re x.im) 3) (pow (* x.im x.re) 3)) x.re)))
460.0ms
(cbrt (* (+ (pow (* x.re x.im) 3) (pow (* x.im x.re) 3)) x.re))
408.0ms
(cbrt (* (+ (pow (* x.re x.im) 3) (pow (* x.im x.re) 3)) x.re))
388.0ms
(* (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))))

prune1.0s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

24.1b
(cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re))
24.1b
(cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re))
12.7b
(cbrt (+ (* x.re x.im) (* x.im x.re)))
0.6b
(cbrt x.re)

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
6×cbrt-div
5×cbrt-prod add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube pow1/3 associate-*l/ add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×flip3-+ flip-+
Calls
4 calls:
Slowest
3.0ms
(cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re))
3.0ms
(cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re))
1.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
0.0ms
(cbrt x.re)

series671.0ms

Calls
4 calls:
Slowest
283.0ms
(cbrt x.re)
147.0ms
(cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re))
130.0ms
(cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re))
111.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))

simplify4.1s

Calls
23 calls:
Slowest
480.0ms
(cbrt (* (+ (pow (* x.re x.im) 3) (pow (* x.im x.re) 3)) x.re))
419.0ms
(cbrt (* (+ (pow (* x.re x.im) 3) (pow (* x.im x.re) 3)) x.re))
417.0ms
(cbrt (+ (pow (* x.re x.im) 3) (pow (* x.im x.re) 3)))
358.0ms
(* (exp (* -1/3 (+ (* 2 (log (/ -1 x.re))) (log (/ -1 x.im))))) (cbrt -2))
314.0ms
(* (exp (* -1/3 (+ (log (/ 1 x.im)) (log (/ 1 x.re))))) (cbrt 2))

prune886.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 0.0b

regimes238.0ms

Accuracy

0% (0.2b remaining)

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

bsearch4.0ms

end0.0ms

sample2.7s

Algorithm
intervals
Results
2.5s14461×body80valid