Details

Time bar (total: 51.8s)

sample84.0ms

Algorithm
intervals
Results
71.0ms474×body80valid

simplify247.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
246.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.1b

localize41.0ms

Local error

Found 4 expressions with local error:

7.2b
(* (- (* x.re x.re) (* x.im x.im)) x.im)
0.1b
(* (+ (* 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))

rewrite100.0ms

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
33.0ms
(+ (* (- (* 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)
20.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
16.0ms
(+ (* x.re x.im) (* x.im x.re))

series267.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
100.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
84.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)
43.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
40.0ms
(+ (* x.re x.im) (* x.im x.re))

simplify8.5s

Counts
46 → 93
Calls
46 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)))
583.0ms
(+ (* (* (- (* (* 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)))
441.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)
405.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))
402.0ms
(* (- (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)) x.im)

prune828.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite167.0ms

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
65.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.im))
44.0ms
(+ (* (+ x.re x.im) (* (- x.re x.im) x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
38.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
18.0ms
(* (- x.re x.im) x.im)

series249.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
97.0ms
(+ (* (+ x.re x.im) (* (- x.re x.im) x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
86.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.im))
44.0ms
(* (- x.re x.im) x.im)
22.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)

simplify20.1s

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)))
893.0ms
(+ (* (* (+ (pow x.re 3) (pow x.im 3)) (* (- (* x.re x.re) (* x.im x.im)) x.im)) (- (* x.re x.im) (* x.im x.re))) (* (* (+ (* x.re x.re) (- (* x.im x.im) (* x.re x.im))) (+ x.re x.im)) (* (- (* (* x.re x.im) (* x.re x.im)) (* (* x.im x.re) (* x.im x.re))) x.re)))
773.0ms
(* (+ (* x.re x.re) (+ (* x.im x.im) (* x.re x.im))) (- (* x.re x.im) (* x.im x.re)))
600.0ms
(* (+ (pow x.re 3) (pow x.im 3)) (* (- (* x.re x.re) (* x.im x.im)) x.im))
571.0ms
(* (* (+ (* 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

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

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))
0.1b
(* (+ (* 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))

rewrite98.0ms

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
41.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
40.0ms
(* (- x.re x.im) x.im)
15.0ms
(+ (* 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))

series239.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
134.0ms
(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)
34.0ms
(+ (* x.re x.im) (* x.im x.re))
25.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)

simplify3.7s

Counts
36 → 86
Calls
36 calls:
Slowest
438.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))
429.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)
421.0ms
(* (- (pow x.re 3) (pow x.im 3)) x.im)
387.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))
368.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))

prune905.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

12.9b
(cbrt (+ (* x.re x.im) (* x.im x.re)))
12.9b
(cbrt (+ (* x.re x.im) (* x.im x.re)))
12.9b
(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))))

rewrite87.0ms

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
60.0ms
(* (cbrt (+ (* x.re x.im) (* x.im x.re))) (cbrt (+ (* x.re x.im) (* x.im x.re))))
9.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
9.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
8.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))

series598.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
178.0ms
(* (cbrt (+ (* x.re x.im) (* x.im x.re))) (cbrt (+ (* x.re x.im) (* x.im x.re))))
151.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
147.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
122.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))

simplify9.7s

Counts
83 → 111
Calls
83 calls:
Slowest
471.0ms
(* (exp (* 1/3 (+ (log x.im) (log x.re)))) (cbrt 2))
460.0ms
(* (exp (* -1/3 (+ (log (/ -1 x.re)) (log (/ -1 x.im))))) (cbrt 2))
453.0ms
(* (exp (* -1/3 (+ (log (/ -1 x.re)) (log (/ -1 x.im))))) (cbrt 2))
445.0ms
(* (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))))))
436.0ms
(* (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))))

prune1.4s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes516.0ms

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms

end0.0ms

sample2.5s

Algorithm
intervals
Results
2.3s14455×body80valid