Details

Time bar (total: 50.7s)

sample76.0ms

Algorithm
intervals
Results
63.0ms461×body80valid

simplify257.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
257.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.7b

localize35.0ms

Local error

Found 4 expressions with local error:

6.8b
(* (- (* 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))

rewrite135.0ms

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
41.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
40.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)
38.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
15.0ms
(+ (* x.re x.im) (* x.im x.re))

series246.0ms

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))
85.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)
38.0ms
(+ (* x.re x.im) (* x.im x.re))
29.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)

simplify8.4s

Counts
46 → 93
Calls
46 calls:
Slowest
1.5s
(* (+ (* (* 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)))
632.0ms
(+ (* (* (- (* (* 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)))
422.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))
418.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)
374.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))

prune821.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize47.0ms

Local error

Found 4 expressions with local error:

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

rewrite132.0ms

Algorithm
rewrite-expression-head
Rules
36×prod-diff
35×add-sqr-sqrt
33×*-un-lft-identity
31×add-cube-cbrt
24×associate-*l/ associate-*r/
22×distribute-rgt-in associate-+l+ distribute-lft-in
20×flip3-+ flip-+
16×frac-add
12×frac-times
11×pow1 add-cbrt-cube add-exp-log
9×flip3-- flip--
8×associate-*r* add-log-exp
4×expm1-log1p-u sub-neg associate-*l* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u
2×+-commutative sum-log fma-def *-commutative
1×distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 144
Calls
4 calls:
Slowest
43.0ms
(+ (* (* x.im (+ x.re x.im)) (- x.re x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
42.0ms
(* (* x.im (+ x.re x.im)) (- x.re x.im))
27.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
15.0ms
(+ (* x.re x.im) (* x.im x.re))

series190.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
76.0ms
(* (* x.im (+ x.re x.im)) (- x.re x.im))
62.0ms
(+ (* (* x.im (+ x.re x.im)) (- x.re x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
28.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
24.0ms
(+ (* x.re x.im) (* x.im x.re))

simplify28.3s

Counts
125 → 156
Calls
125 calls:
Slowest
1.3s
(* (* (- x.re x.im) (+ x.re x.im)) (- (* x.re x.im) (* x.im x.re)))
915.0ms
(* (* (+ (* 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)))))
771.0ms
(* (+ (* x.re x.re) (+ (* x.im x.im) (* x.re x.im))) (- (* x.re x.im) (* x.im x.re)))
573.0ms
(+ (* (* (* 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)))
522.0ms
(+ (* (* (* x.im (+ (pow x.re 3) (pow x.im 3))) (- (* x.re x.re) (* 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)))

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

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

rewrite72.0ms

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
27.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
27.0ms
(* x.im (+ x.re x.im))
16.0ms
(+ (* 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))

series214.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
115.0ms
(fma (* x.im (+ x.re x.im)) (- x.re x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
46.0ms
(* x.im (+ x.re x.im))
30.0ms
(+ (* x.re x.im) (* x.im x.re))
22.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)

simplify2.9s

Counts
39 → 87
Calls
39 calls:
Slowest
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))
370.0ms
(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))
280.0ms
(* (- (* (* x.re x.im) (* x.re x.im)) (* (* x.im x.re) (* x.im x.re))) x.re)
240.0ms
(* (+ (pow (* x.re x.im) 3) (pow (* x.im x.re) 3)) x.re)

prune912.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize67.0ms

Local error

Found 4 expressions with local error:

58.2b
(fma (- (cbrt x.im)) (* (cbrt x.im) (cbrt x.im)) (* (cbrt x.im) (* (cbrt x.im) (cbrt x.im))))
0.6b
(cbrt x.im)
0.6b
(cbrt x.im)
0.6b
(cbrt x.im)

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
1×fma-udef
Counts
4 → 53
Calls
4 calls:
Slowest
1.0ms
(cbrt x.im)
1.0ms
(cbrt x.im)
1.0ms
(cbrt x.im)
1.0ms
(fma (- (cbrt x.im)) (* (cbrt x.im) (cbrt x.im)) (* (cbrt x.im) (* (cbrt x.im) (cbrt x.im))))

series1.8s

Counts
4 → 12
Calls
4 calls:
Slowest
787.0ms
(fma (- (cbrt x.im)) (* (cbrt x.im) (cbrt x.im)) (* (cbrt x.im) (* (cbrt x.im) (cbrt x.im))))
603.0ms
(cbrt x.im)
253.0ms
(cbrt x.im)
205.0ms
(cbrt x.im)

simplify521.0ms

Counts
21 → 65
Calls
21 calls:
Slowest
153.0ms
(* (pow (* x.im -1) 1/3) (cbrt -1))
119.0ms
(* (pow (* x.im -1) 1/3) (cbrt -1))
116.0ms
(* (pow (* x.im -1) 1/3) (cbrt -1))
33.0ms
(pow (/ 1 x.im) -1/3)
31.0ms
(pow (/ 1 x.im) -1/3)

prune923.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes234.0ms

Accuracy

0% (0.1b remaining)

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

bsearch3.0ms

end0.0ms

sample2.8s

Algorithm
intervals
Results
2.4s14563×body80valid