Details

Time bar (total: 51.4s)

sample87.0ms

Algorithm
intervals
Results
71.0ms469×body80valid

simplify319.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
318.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.1b

localize39.0ms

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)
0.2b
(+ (* (- (* 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))

rewrite99.0ms

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
32.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)
29.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
22.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
15.0ms
(+ (* x.re x.im) (* x.im x.re))

series261.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
110.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
88.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)
36.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
28.0ms
(+ (* x.re x.im) (* x.im x.re))

simplify8.9s

Counts
46 → 93
Calls
46 calls:
Slowest
2.0s
(* (+ (* (* 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)))
551.0ms
(+ (* (* (- (* (* 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)))
490.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)
412.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))
387.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))

prune870.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize49.0ms

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)
0.2b
(+ (* (+ 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))

rewrite174.0ms

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
77.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.im))
46.0ms
(+ (* (+ 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)
10.0ms
(+ (* x.re x.im) (* x.im x.re))

series268.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
100.0ms
(+ (* (+ x.re x.im) (* (- x.re x.im) x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
96.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.im))
42.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
30.0ms
(+ (* x.re x.im) (* x.im x.re))

simplify18.9s

Counts
78 → 111
Calls
78 calls:
Slowest
1.3s
(* (* (- x.re x.im) (+ x.re x.im)) (- (* x.re x.im) (* x.im x.re)))
789.0ms
(* (+ (* x.re x.re) (+ (* x.im x.im) (* x.re x.im))) (- (* x.re x.im) (* x.im x.re)))
671.0ms
(+ (* (* (+ x.re x.im) (* (- (pow x.re 3) (pow x.im 3)) 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.im x.re) (* x.im x.re))) x.re)))
618.0ms
(+ (* (* (- (* 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)))
558.0ms
(* (+ (pow x.re 3) (pow x.im 3)) (* (- (* x.re x.re) (* x.im x.im)) x.im))

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite61.0ms

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
31.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
15.0ms
(* (- x.re x.im) x.im)
13.0ms
(+ (* 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))

series238.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
121.0ms
(fma (+ x.re x.im) (* (- x.re x.im) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
48.0ms
(* (- x.re x.im) x.im)
36.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
32.0ms
(+ (* x.re x.im) (* x.im x.re))

simplify3.8s

Counts
36 → 86
Calls
36 calls:
Slowest
448.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))
443.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))
407.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)
377.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))
322.0ms
(* (- (pow x.re 3) (pow x.im 3)) x.im)

prune826.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

12.1b
(cbrt (+ (* x.re x.im) (* x.im x.re)))
12.1b
(cbrt (+ (* x.re x.im) (* x.im x.re)))
12.1b
(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))))

rewrite80.0ms

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
58.0ms
(* (cbrt (+ (* x.re x.im) (* x.im x.re))) (cbrt (+ (* x.re x.im) (* x.im x.re))))
7.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
7.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
7.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))

series582.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
200.0ms
(* (cbrt (+ (* x.re x.im) (* x.im x.re))) (cbrt (+ (* x.re x.im) (* x.im x.re))))
128.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
128.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
126.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))

simplify10.3s

Counts
83 → 111
Calls
83 calls:
Slowest
472.0ms
(* (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))))))
464.0ms
(* (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))))
459.0ms
(* (exp (* 1/3 (+ (log x.im) (log x.re)))) (cbrt 2))
455.0ms
(* (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
(* (exp (* 1/3 (+ (log x.im) (log x.re)))) (cbrt 2))

prune1.2s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes142.0ms

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms

end0.0ms

sample2.9s

Algorithm
intervals
Results
2.1s14535×body80valid