Details

Time bar (total: 51.4s)

sample100.0ms

Algorithm
intervals
Results
81.0ms483×body80valid

simplify347.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
347.0ms
(+ (* (- (* 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

localize53.0ms

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))

rewrite85.0ms

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
28.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
26.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
22.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)
7.0ms
(+ (* x.re x.im) (* x.im x.re))

series215.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
94.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
60.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)
37.0ms
(+ (* x.re x.im) (* x.im x.re))
23.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)

simplify8.3s

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)))
573.0ms
(+ (* (* (- (* (* 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)))
454.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))
434.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)
429.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))

prune943.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite179.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
37×*-un-lft-identity
36×prod-diff
33×add-cube-cbrt
26×associate-*r/
24×associate-*l/
23×distribute-rgt-in distribute-lft-in
22×associate-+l+
20×flip3-+ flip-+
16×frac-add
13×pow1 add-cbrt-cube add-exp-log
12×frac-times associate-*r*
9×flip3-- flip--
7×associate-*l*
6×add-log-exp
5×pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u sub-neg 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 → 155
Calls
4 calls:
Slowest
67.0ms
(+ (* (* x.im (+ x.re x.im)) (- x.re x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
41.0ms
(* (* x.im (+ x.re x.im)) (- x.re x.im))
40.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
29.0ms
(* x.im (+ x.re x.im))

series197.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
69.0ms
(* (* x.im (+ x.re x.im)) (- x.re x.im))
66.0ms
(+ (* (* x.im (+ x.re x.im)) (- x.re x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
38.0ms
(* x.im (+ x.re x.im))
25.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)

simplify28.9s

Counts
139 → 167
Calls
139 calls:
Slowest
1.1s
(* (* (- x.re x.im) (+ x.re x.im)) (- (* x.re x.im) (* x.im x.re)))
872.0ms
(* (+ (* x.re x.re) (+ (* x.im x.im) (* x.re x.im))) (- (* x.re x.im) (* x.im x.re)))
848.0ms
(+ (* (* (* x.im (- (* x.re x.re) (* x.im x.im))) (- (pow x.re 3) (pow x.im 3))) (- (* x.re x.im) (* x.im x.re))) (* (* (- 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)))
599.0ms
(* (* (+ (* 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)))))
544.0ms
(+ (* (* (* x.im (+ x.re x.im)) (- (* x.re 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)))

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×*-un-lft-identity
8×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
7×associate-*r*
6×associate-*l* add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×flip3-+ flip-+
2×pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod unswap-sqr
1×distribute-rgt-in +-commutative sum-log fma-def distribute-lft-in fma-udef distribute-lft-out
Counts
4 → 75
Calls
4 calls:
Slowest
45.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
28.0ms
(* x.im (+ x.re x.im))
15.0ms
(+ (* x.re x.im) (* x.im x.re))
1.0ms
(fma (* x.im (+ x.re x.im)) (- x.re x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))

series238.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
110.0ms
(fma (* x.im (+ x.re x.im)) (- x.re x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
53.0ms
(* x.im (+ x.re x.im))
37.0ms
(+ (* x.re x.im) (* x.im x.re))
37.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)

simplify2.8s

Counts
39 → 87
Calls
39 calls:
Slowest
390.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))
379.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))
353.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))
255.0ms
(* (+ (pow (* x.re x.im) 3) (pow (* x.im x.re) 3)) x.re)
234.0ms
(* (- (* (* x.re x.im) (* x.re x.im)) (* (* x.im x.re) (* x.im x.re))) x.re)

prune863.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize63.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x.re)
0.6b
(cbrt x.re)
0.6b
(cbrt x.re)
0.5b
(* (cbrt x.re) (cbrt x.re))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×pow1/3
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 85
Calls
4 calls:
Slowest
16.0ms
(* (cbrt x.re) (cbrt x.re))
2.0ms
(cbrt x.re)
1.0ms
(cbrt x.re)
1.0ms
(cbrt x.re)

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
307.0ms
(* (cbrt x.re) (cbrt x.re))
301.0ms
(cbrt x.re)
266.0ms
(cbrt x.re)
248.0ms
(cbrt x.re)

simplify972.0ms

Counts
63 → 97
Calls
63 calls:
Slowest
159.0ms
(* (cbrt -1) (pow (* x.re -1) 1/3))
153.0ms
(* (cbrt -1) (pow (* x.re -1) 1/3))
134.0ms
(* (cbrt -1) (pow (* x.re -1) 1/3))
119.0ms
(* (pow (cbrt -1) 2) (pow (pow x.re 2) 1/3))
103.0ms
(* (* (cbrt (cbrt x.re)) (cbrt (cbrt x.re))) (* (cbrt (cbrt x.re)) (cbrt (cbrt x.re))))

prune1.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes144.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch2.0ms

end0.0ms

sample2.9s

Algorithm
intervals
Results
2.5s14344×body80valid