Details

Time bar (total: 18.1s)

sample105.0ms

Algorithm
intervals
Results
87.0ms491×body80valid

simplify2.0s

Counts
1 → 1

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.0b

localize44.0ms

Local error

Found 4 expressions with local error:

6.1b
(* (- (* x.re x.re) (* x.im x.im)) x.re)
0.2b
(* (+ (* 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.im) (* x.im x.re))

rewrite105.0ms

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*
4×expm1-log1p-u flip3-+ flip3-- frac-sub flip-+ insert-posit16 log1p-expm1-u flip--
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative sum-log sub-neg fma-def fma-neg diff-log prod-diff difference-of-squares
Counts
4 → 83
Calls
4 calls:
Slowest
44.0ms
(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
26.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
25.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.re)
9.0ms
(+ (* x.re x.im) (* x.im x.re))

series228.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
77.0ms
(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
63.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.re)
44.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
43.0ms
(+ (* x.re x.im) (* x.im x.re))

simplify648.0ms

Counts
95 → 95

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite176.0ms

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
67.0ms
(- (* (+ x.re x.im) (* (- x.re x.im) x.re)) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
57.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.re))
33.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
15.0ms
(+ (* x.re x.im) (* x.im x.re))

series246.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
96.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.re))
77.0ms
(- (* (+ x.re x.im) (* (- x.re x.im) x.re)) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
42.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
32.0ms
(+ (* x.re x.im) (* x.im x.re))

simplify1.3s

Counts
113 → 113

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize93.0ms

Local error

Found 4 expressions with local error:

35.4b
(fma (- x.im) (+ (* x.re x.im) (* x.im x.re)) (* x.im (+ (* x.re x.im) (* x.im x.re))))
0.2b
(* x.im (+ (* x.re x.im) (* x.im x.re)))
0.2b
(* x.im (+ (* x.re x.im) (* x.im x.re)))
0.2b
(fma (+ x.re x.im) (* (- x.re x.im) x.re) (- (* x.im (+ (* x.re x.im) (* x.im x.re)))))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r* associate-*l*
4×expm1-log1p-u associate-*r/ insert-posit16 log1p-expm1-u add-log-exp
2×distribute-rgt-in distribute-lft-in flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ fma-udef unswap-sqr
Counts
4 → 72
Calls
4 calls:
Slowest
44.0ms
(* x.im (+ (* x.re x.im) (* x.im x.re)))
19.0ms
(* x.im (+ (* x.re x.im) (* x.im x.re)))
1.0ms
(fma (- x.im) (+ (* x.re x.im) (* x.im x.re)) (* x.im (+ (* x.re x.im) (* x.im x.re))))
0.0ms
(fma (+ x.re x.im) (* (- x.re x.im) x.re) (- (* x.im (+ (* x.re x.im) (* x.im x.re)))))

series250.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
121.0ms
(fma (+ x.re x.im) (* (- x.re x.im) x.re) (- (* x.im (+ (* x.re x.im) (* x.im x.re)))))
55.0ms
(fma (- x.im) (+ (* x.re x.im) (* x.im x.re)) (* x.im (+ (* x.re x.im) (* x.im x.re))))
47.0ms
(* x.im (+ (* x.re x.im) (* x.im x.re)))
26.0ms
(* x.im (+ (* x.re x.im) (* x.im x.re)))

simplify1.1s

Counts
84 → 84

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize84.0ms

Local error

Found 4 expressions with local error:

34.8b
(fma (- x.im) (+ (* x.re x.im) (* x.im x.re)) (* (* (cbrt x.im) (cbrt x.im)) (* (cbrt x.im) (+ (* x.re x.im) (* x.im x.re)))))
0.6b
(cbrt x.im)
0.6b
(cbrt x.im)
0.6b
(cbrt x.im)

rewrite5.0ms

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 (- x.im) (+ (* x.re x.im) (* x.im x.re)) (* (* (cbrt x.im) (cbrt x.im)) (* (cbrt x.im) (+ (* x.re x.im) (* x.im x.re)))))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
315.0ms
(cbrt x.im)
302.0ms
(cbrt x.im)
286.0ms
(cbrt x.im)
114.0ms
(fma (- x.im) (+ (* x.re x.im) (* x.im x.re)) (* (* (cbrt x.im) (cbrt x.im)) (* (cbrt x.im) (+ (* x.re x.im) (* x.im x.re)))))

simplify2.7s

Counts
65 → 65

prune1.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes214.0ms

Accuracy

0% (0.2b remaining)

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

bsearch5.0ms

end0.0ms

sample2.8s

Algorithm
intervals
Results
2.4s14353×body80valid