Details

Time bar (total: 17.2s)

sample53.0ms

Algorithm
intervals
Results
42.0ms455×body80valid

simplify1.8s

Counts
1 → 1

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.8b

localize48.0ms

Local error

Found 4 expressions with local error:

4.8b
(* (- (* x.re x.re) (* x.im x.im)) x.re)
0.1b
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
0.1b
(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
0.0b
(- (* x.re x.re) (* x.im x.im))

rewrite132.0ms

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-sub insert-posit16 log1p-expm1-u
3×flip3-+ flip-+
2×sub-neg fma-neg diff-log prod-diff pow-prod-down prod-exp *-commutative cbrt-unprod difference-of-squares unswap-sqr
Counts
4 → 86
Calls
4 calls:
Slowest
48.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.re)
44.0ms
(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
23.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
15.0ms
(- (* x.re x.re) (* x.im x.im))

series228.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
80.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.re)
73.0ms
(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
37.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
37.0ms
(- (* x.re x.re) (* x.im x.im))

simplify593.0ms

Counts
98 → 98

prune921.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite165.0ms

Algorithm
rewrite-expression-head
Rules
42×associate-*l/
19×flip3-+ flip-+
16×frac-sub
12×frac-times
11×pow1 add-cbrt-cube add-exp-log
10×flip3-- flip--
9×add-sqr-sqrt *-un-lft-identity
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
1×+-commutative sum-log sub-neg fma-def fma-neg diff-log prod-diff distribute-lft-out unswap-sqr
Counts
4 → 101
Calls
4 calls:
Slowest
80.0ms
(- (* (+ x.re x.im) (* (- x.re x.im) x.re)) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
50.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.re))
26.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
7.0ms
(+ (* x.re x.im) (* x.im x.re))

series244.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
96.0ms
(- (* (+ x.re x.im) (* (- x.re x.im) x.re)) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
67.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.re))
50.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
31.0ms
(+ (* x.re x.im) (* x.im x.re))

simplify1.3s

Counts
113 → 113

prune988.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
17×associate-*r*
16×add-sqr-sqrt
12×*-un-lft-identity
10×add-cube-cbrt
8×pow1 add-cbrt-cube associate-*l* add-exp-log
6×add-log-exp
5×distribute-lft-neg-in distribute-rgt-neg-in
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×distribute-rgt-out distribute-lft-out
2×distribute-neg-in flip3-+ pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod flip-+ distribute-neg-frac unswap-sqr
1×distribute-rgt-in +-commutative neg-mul-1 sum-log fma-def distribute-lft-in flip3-- distribute-rgt-neg-out fma-udef flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 90
Calls
4 calls:
Slowest
48.0ms
(* x.im (- (+ (* x.re x.im) (* x.re x.im))))
16.0ms
(* (- x.re x.im) x.re)
14.0ms
(+ (* x.re x.im) (* x.re x.im))
0.0ms
(fma (+ x.re x.im) (* (- x.re x.im) x.re) (* x.im (- (+ (* x.re x.im) (* x.re x.im)))))

series231.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
120.0ms
(fma (+ x.re x.im) (* (- x.re x.im) x.re) (* x.im (- (+ (* x.re x.im) (* x.re x.im)))))
48.0ms
(* (- x.re x.im) x.re)
33.0ms
(+ (* x.re x.im) (* x.re x.im))
30.0ms
(* x.im (- (+ (* x.re x.im) (* x.re x.im))))

simplify1.6s

Counts
102 → 102

prune985.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
36×cbrt-prod
35×*-un-lft-identity
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt
11×pow1
9×flip3-+ pow1/3 swap-sqr flip-+ distribute-lft-out
7×associate-*r* associate-*l*
6×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 → 107
Calls
4 calls:
Slowest
48.0ms
(* (cbrt (+ x.re x.im)) (cbrt (+ x.re x.im)))
6.0ms
(cbrt (+ x.re x.im))
6.0ms
(cbrt (+ x.re x.im))
5.0ms
(cbrt (+ x.re x.im))

series874.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
268.0ms
(* (cbrt (+ x.re x.im)) (cbrt (+ x.re x.im)))
210.0ms
(cbrt (+ x.re x.im))
208.0ms
(cbrt (+ x.re x.im))
188.0ms
(cbrt (+ x.re x.im))

simplify2.2s

Counts
119 → 119

prune1.7s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes147.0ms

Accuracy

0% (0.1b remaining)

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

bsearch4.0ms

end0.0ms

sample2.7s

Algorithm
intervals
Results
2.3s14530×body80valid