Details

Time bar (total: 1.3m)

sample67.0ms

Algorithm
intervals
Results
55.0ms468×body80valid

simplify415.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
415.0ms
(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 3 expressions with local error:

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

rewrite139.0ms

Algorithm
rewrite-expression-head
Rules
22×pow1
16×*-un-lft-identity
13×add-cbrt-cube associate-*r* add-exp-log
12×add-sqr-sqrt
8×add-cube-cbrt distribute-lft-out
6×pow-prod-down prod-exp cbrt-unprod
5×pow-prod-up add-log-exp
4×associate-*l* distribute-rgt1-in
3×expm1-log1p-u distribute-rgt-out insert-posit16 log1p-expm1-u
2×distribute-rgt-in distribute-lft-in distribute-lft1-in associate-*r/ *-commutative associate--r+
1×pow2 sub-neg flip3-+ pow-plus flip3-- fma-neg diff-log cube-unmult prod-diff pow-sqr flip-+ flip-- unswap-sqr
Counts
3 → 80
Calls
3 calls:
Slowest
67.0ms
(* (* x.re x.im) (+ x.im (+ x.im x.im)))
54.0ms
(- (* x.re (* x.re x.re)) (* (* x.re x.im) (+ x.im (+ x.im x.im))))
16.0ms
(* x.re (* x.re x.re))

series162.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
73.0ms
(- (* x.re (* x.re x.re)) (* (* x.re x.im) (+ x.im (+ x.im x.im))))
49.0ms
(* x.re (* x.re x.re))
40.0ms
(* (* x.re x.im) (+ x.im (+ x.im x.im)))

simplify13.1s

Counts
92 → 89
Calls
92 calls:
Slowest
939.0ms
(* (* (- (* x.re (* x.re x.re)) (* (* x.re x.im) (+ x.im (+ x.im x.im)))) (- (* x.re (* x.re x.re)) (* (* x.re x.im) (+ x.im (+ x.im x.im))))) (- (* x.re (* x.re x.re)) (* (* x.re x.im) (+ x.im (+ x.im x.im)))))
555.0ms
(* (* (* x.re x.re) x.re) (* (* (* x.re x.re) x.re) (* (* x.re x.re) x.re)))
429.0ms
(+ (* (* x.re (* x.re x.re)) (* x.re (* x.re x.re))) (+ (* (* (* x.re x.im) (+ x.im (+ x.im x.im))) (* (* x.re x.im) (+ x.im (+ x.im x.im)))) (* (* x.re (* x.re x.re)) (* (* x.re x.im) (+ x.im (+ x.im x.im))))))
427.0ms
(- (pow x.re 3) (* 3 (* (pow x.im 2) x.re)))
399.0ms
(- (* (* x.re x.im) (+ x.im (+ x.im x.im))))

prune834.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize32.0ms

Local error

Found 2 expressions with local error:

0.2b
(* (* x.re x.im) (+ x.im (+ x.im x.im)))
0.0b
(- (pow x.re 3) (* (* x.re x.im) (+ x.im (+ x.im x.im))))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
15×add-sqr-sqrt
12×fma-neg associate-*r* prod-diff add-cube-cbrt
8×distribute-lft-out
7×pow1 add-cbrt-cube add-exp-log
6×unpow-prod-down cube-prod
4×distribute-rgt1-in add-log-exp
3×distribute-rgt-out pow-prod-down prod-exp cbrt-unprod
2×distribute-rgt-in expm1-log1p-u cube-mult distribute-lft-in distribute-lft1-in unpow3 associate-*r/ insert-posit16 log1p-expm1-u associate--r+ sqr-pow
1×sub-neg flip3-+ flip3-- diff-log associate-*l* *-commutative flip-+ flip--
Counts
2 → 75
Calls
2 calls:
Slowest
81.0ms
(* (* x.re x.im) (+ x.im (+ x.im x.im)))
52.0ms
(- (pow x.re 3) (* (* x.re x.im) (+ x.im (+ x.im x.im))))

series122.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
85.0ms
(- (pow x.re 3) (* (* x.re x.im) (+ x.im (+ x.im x.im))))
37.0ms
(* (* x.re x.im) (+ x.im (+ x.im x.im)))

simplify20.5s

Counts
96 → 81
Calls
96 calls:
Slowest
472.0ms
(- (* (* x.re x.im) (+ x.im (+ x.im x.im))))
469.0ms
(- (* (* x.re x.im) (+ x.im (+ x.im x.im))))
455.0ms
(* (cbrt (* (* x.re x.im) (+ x.im (+ x.im x.im)))) (cbrt (* (* x.re x.im) (+ x.im (+ x.im x.im)))))
443.0ms
(- (* (* x.re x.im) (+ x.im (+ x.im x.im))))
435.0ms
(+ (* (pow x.re 3) (pow x.re 3)) (+ (* (* (* x.re x.im) (+ x.im (+ x.im x.im))) (* (* x.re x.im) (+ x.im (+ x.im x.im)))) (* (pow x.re 3) (* (* x.re x.im) (+ x.im (+ x.im x.im))))))

prune878.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.2b
(* 3 (* x.re x.im))
0.1b
(* (* 3 (* x.re x.im)) x.im)
0.0b
(- (pow x.re 3) (* (* 3 (* x.re x.im)) x.im))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
17×pow1 add-cbrt-cube add-exp-log
12×fma-neg prod-diff
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×pow-prod-down prod-exp cbrt-unprod
6×unpow-prod-down cube-prod
5×add-log-exp
4×associate-*r* associate-*l*
3×expm1-log1p-u insert-posit16 log1p-expm1-u
2×cube-mult unpow3 *-commutative sqr-pow
1×sub-neg flip3-- diff-log flip--
Counts
3 → 84
Calls
3 calls:
Slowest
74.0ms
(* (* 3 (* x.re x.im)) x.im)
45.0ms
(- (pow x.re 3) (* (* 3 (* x.re x.im)) x.im))
14.0ms
(* 3 (* x.re x.im))

series156.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
73.0ms
(- (pow x.re 3) (* (* 3 (* x.re x.im)) x.im))
54.0ms
(* (* 3 (* x.re x.im)) x.im)
29.0ms
(* 3 (* x.re x.im))

simplify18.3s

Counts
105 → 93
Calls
105 calls:
Slowest
547.0ms
(* (* (* 3 3) 3) (* (* (* x.re x.im) (* x.re x.im)) (* x.re x.im)))
537.0ms
(* (* (- (pow x.re 3) (* (* 3 (* x.re x.im)) x.im)) (- (pow x.re 3) (* (* 3 (* x.re x.im)) x.im))) (- (pow x.re 3) (* (* 3 (* x.re x.im)) x.im)))
529.0ms
(fma (- x.im) (* 3 (* x.re x.im)) (* x.im (* 3 (* x.re x.im))))
521.0ms
(* (* (* 3 (* x.re x.im)) (* 3 (* x.re x.im))) (* 3 (* x.re x.im)))
499.0ms
(fma (pow 1 3) (pow x.re 3) (- (* x.im (* 3 (* x.re x.im)))))

prune775.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (* 3 x.re) x.im)
0.1b
(* (* (* 3 x.re) x.im) x.im)
0.0b
(- (pow x.re 3) (* (* (* 3 x.re) x.im) x.im))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
17×pow1 add-cbrt-cube add-exp-log
12×fma-neg prod-diff
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×pow-prod-down prod-exp cbrt-unprod
6×unpow-prod-down cube-prod associate-*r*
5×add-log-exp
3×expm1-log1p-u insert-posit16 log1p-expm1-u
2×cube-mult unpow3 associate-*l* *-commutative sqr-pow
1×sub-neg flip3-- diff-log flip--
Counts
3 → 84
Calls
3 calls:
Slowest
63.0ms
(* (* (* 3 x.re) x.im) x.im)
51.0ms
(- (pow x.re 3) (* (* (* 3 x.re) x.im) x.im))
19.0ms
(* (* 3 x.re) x.im)

series132.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
69.0ms
(- (pow x.re 3) (* (* (* 3 x.re) x.im) x.im))
43.0ms
(* (* (* 3 x.re) x.im) x.im)
20.0ms
(* (* 3 x.re) x.im)

simplify19.2s

Counts
105 → 93
Calls
105 calls:
Slowest
693.0ms
(* (* (- (pow x.re 3) (* (* (* 3 x.re) x.im) x.im)) (- (pow x.re 3) (* (* (* 3 x.re) x.im) x.im))) (- (pow x.re 3) (* (* (* 3 x.re) x.im) x.im)))
610.0ms
(* (* (* (* 3 x.re) x.im) (* (* 3 x.re) x.im)) (* (* 3 x.re) x.im))
491.0ms
(* (* (* (* 3 3) 3) (* (* x.re x.re) x.re)) (* (* x.im x.im) x.im))
460.0ms
(log (- (pow x.re 3) (* (* (* 3 x.re) x.im) x.im)))
452.0ms
(* (* (* (* 3 x.re) (* 3 x.re)) (* 3 x.re)) (* (* x.im x.im) x.im))

prune850.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes86.0ms

Accuracy

0% (0.1b remaining)

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

bsearch3.0ms

end0.0ms

sample3.2s

Algorithm
intervals
Results
2.9s14526×body80valid