Details

Time bar (total: 53.3s)

sample84.0ms

Algorithm
intervals
Results
68.0ms487×body80valid

simplify452.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
452.0ms
(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize37.0ms

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))))

rewrite145.0ms

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
76.0ms
(* (* x.re x.im) (+ x.im (+ x.im x.im)))
37.0ms
(- (* x.re (* x.re x.re)) (* (* x.re x.im) (+ x.im (+ x.im x.im))))
30.0ms
(* x.re (* x.re x.re))

series182.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
64.0ms
(- (* x.re (* x.re x.re)) (* (* x.re x.im) (+ x.im (+ x.im x.im))))
62.0ms
(* x.re (* x.re x.re))
55.0ms
(* (* x.re x.im) (+ x.im (+ x.im x.im)))

simplify4.9s

Counts
48 → 89
Calls
48 calls:
Slowest
682.0ms
(* (* (* x.re x.re) x.re) (* (* (* x.re x.re) x.re) (* (* x.re x.re) x.re)))
536.0ms
(* (* (* x.re x.re) x.re) (* (* (* x.re x.re) (* x.re x.re)) (* x.re x.re)))
464.0ms
(- (pow x.re 3) (* 3 (* (pow x.im 2) x.re)))
367.0ms
(- (pow x.re 3) (* 3 (* (pow x.im 2) x.re)))
365.0ms
(- (pow x.re 3) (* 3 (* (pow x.im 2) x.re)))

prune748.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

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))))

rewrite109.0ms

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
57.0ms
(* (* x.re x.im) (+ x.im (+ x.im x.im)))
51.0ms
(- (pow x.re 3) (* (* x.re x.im) (+ x.im (+ x.im x.im))))

series129.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
77.0ms
(- (pow x.re 3) (* (* x.re x.im) (+ x.im (+ x.im x.im))))
52.0ms
(* (* x.re x.im) (+ x.im (+ x.im x.im)))

simplify8.6s

Counts
63 → 81
Calls
63 calls:
Slowest
655.0ms
(fma (pow (* (cbrt x.re) (cbrt x.re)) 3) (pow (cbrt x.re) 3) (- (* (+ x.im (+ x.im x.im)) (* x.re x.im))))
393.0ms
(- (pow x.re 3) (* 3 (* (pow x.im 2) x.re)))
381.0ms
(+ (* x.im x.im) (- (* (+ x.im x.im) (+ x.im x.im)) (* x.im (+ x.im x.im))))
378.0ms
(fma (* x.re x.re) x.re (- (* (+ x.im (+ x.im x.im)) (* x.re x.im))))
378.0ms
(- (pow x.re 3) (* 3 (* (pow x.im 2) x.re)))

prune752.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (* x.re x.im) (+ (+ 1 1) 1))
0.2b
(* (* (* x.re x.im) (+ (+ 1 1) 1)) x.im)
0.0b
(- (pow x.re 3) (* (* (* x.re x.im) (+ (+ 1 1) 1)) x.im))

rewrite322.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
17×add-sqr-sqrt pow1 add-cbrt-cube add-exp-log
16×associate-*r*
14×add-cube-cbrt
12×fma-neg prod-diff
9×pow-prod-down prod-exp cbrt-unprod distribute-lft-out
6×unpow-prod-down cube-prod
5×add-log-exp
4×distribute-lft1-in distribute-rgt-out associate-*r/
3×expm1-log1p-u insert-posit16 log1p-expm1-u
2×cube-mult flip3-+ unpow3 associate-*l* associate-*l/ distribute-rgt1-in *-commutative flip-+ sqr-pow
1×distribute-rgt-in sub-neg distribute-lft-in flip3-- diff-log flip--
Counts
3 → 100
Calls
3 calls:
Slowest
140.0ms
(* (* (* x.re x.im) (+ (+ 1 1) 1)) x.im)
101.0ms
(- (pow x.re 3) (* (* (* x.re x.im) (+ (+ 1 1) 1)) x.im))
79.0ms
(* (* x.re x.im) (+ (+ 1 1) 1))

series174.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
99.0ms
(- (pow x.re 3) (* (* (* x.re x.im) (+ (+ 1 1) 1)) x.im))
53.0ms
(* (* (* x.re x.im) (+ (+ 1 1) 1)) x.im)
22.0ms
(* (* x.re x.im) (+ (+ 1 1) 1))

simplify11.4s

Counts
79 → 109
Calls
79 calls:
Slowest
648.0ms
(* (* (* (* (* x.re x.im) (+ (+ 1 1) 1)) (* (* x.re x.im) (+ (+ 1 1) 1))) (* (* x.re x.im) (+ (+ 1 1) 1))) (* (* x.im x.im) x.im))
598.0ms
(* (* (* (* (* x.re x.re) x.re) (* (* x.im x.im) x.im)) (* (* (+ (+ 1 1) 1) (+ (+ 1 1) 1)) (+ (+ 1 1) 1))) (* (* x.im x.im) x.im))
476.0ms
(* (* (* x.re x.im) (+ (+ 1 1) 1)) x.im)
440.0ms
(* (* (* x.re x.im) (+ (+ 1 1) 1)) x.im)
427.0ms
(* (* (* x.re x.im) (+ (pow (+ 1 1) 3) (pow 1 3))) x.im)

prune1.0s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* x.re x.im) (sqrt (+ (+ 1 1) 1)))
0.3b
(* (* (* x.re x.im) (sqrt (+ (+ 1 1) 1))) (sqrt (+ (+ 1 1) 1)))
0.2b
(* (* (* (* x.re x.im) (sqrt (+ (+ 1 1) 1))) (sqrt (+ (+ 1 1) 1))) x.im)
0.0b
(- (pow x.re 3) (* (* (* (* x.re x.im) (sqrt (+ (+ 1 1) 1))) (sqrt (+ (+ 1 1) 1))) x.im))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
43×*-un-lft-identity
35×associate-*r*
32×pow1 add-cbrt-cube add-exp-log
27×add-sqr-sqrt
26×sqrt-div sqrt-prod
21×add-cube-cbrt
19×pow-prod-down prod-exp cbrt-unprod
18×associate-*r/ distribute-lft-out
13×flip3-+ flip-+
12×fma-neg prod-diff associate-*l/
8×frac-times distribute-lft1-in distribute-rgt-out
6×unpow-prod-down cube-prod add-log-exp
4×expm1-log1p-u distribute-rgt1-in insert-posit16 log1p-expm1-u
3×associate-*l* *-commutative
2×cube-mult unpow3 sqr-pow
1×sub-neg flip3-- diff-log flip--
Counts
4 → 155
Calls
4 calls:
Slowest
599.0ms
(* (* (* (* x.re x.im) (sqrt (+ (+ 1 1) 1))) (sqrt (+ (+ 1 1) 1))) x.im)
518.0ms
(- (pow x.re 3) (* (* (* (* x.re x.im) (sqrt (+ (+ 1 1) 1))) (sqrt (+ (+ 1 1) 1))) x.im))
138.0ms
(* (* (* x.re x.im) (sqrt (+ (+ 1 1) 1))) (sqrt (+ (+ 1 1) 1)))
51.0ms
(* (* x.re x.im) (sqrt (+ (+ 1 1) 1)))

series475.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
140.0ms
(* (* (* x.re x.im) (sqrt (+ (+ 1 1) 1))) (sqrt (+ (+ 1 1) 1)))
140.0ms
(- (pow x.re 3) (* (* (* (* x.re x.im) (sqrt (+ (+ 1 1) 1))) (sqrt (+ (+ 1 1) 1))) x.im))
131.0ms
(* (* (* (* x.re x.im) (sqrt (+ (+ 1 1) 1))) (sqrt (+ (+ 1 1) 1))) x.im)
65.0ms
(* (* x.re x.im) (sqrt (+ (+ 1 1) 1)))

simplify17.3s

Counts
132 → 167
Calls
132 calls:
Slowest
553.0ms
(* (* (* (* x.re x.im) (sqrt (- (* (+ 1 1) (+ 1 1)) (* 1 1)))) (sqrt (- (* (+ 1 1) (+ 1 1)) (* 1 1)))) x.im)
525.0ms
(* (* (* (* x.re x.re) x.re) (* (* x.im x.im) x.im)) (* (* (sqrt (+ (+ 1 1) 1)) (sqrt (+ (+ 1 1) 1))) (sqrt (+ (+ 1 1) 1))))
520.0ms
(* (* (* (* x.re x.im) (* x.re x.im)) (* x.re x.im)) (* (* (sqrt (+ (+ 1 1) 1)) (sqrt (+ (+ 1 1) 1))) (sqrt (+ (+ 1 1) 1))))
417.0ms
(* (* (* x.re x.im) (sqrt (- (* (+ 1 1) (+ 1 1)) (* 1 1)))) (sqrt (+ (pow (+ 1 1) 3) (pow 1 3))))
415.0ms
(* (* (* (* x.re x.im) (sqrt (+ (pow (+ 1 1) 3) (pow 1 3)))) (sqrt (+ (pow (+ 1 1) 3) (pow 1 3)))) x.im)

prune1.9s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes127.0ms

Accuracy

0% (0.1b remaining)

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

bsearch5.0ms

end0.0ms

sample3.0s

Algorithm
intervals
Results
2.6s14508×body80valid