Details

Time bar (total: 15.2s)

sample48.0ms

Algorithm
intervals
Results
37.0ms471×body80valid

simplify1.7s

Counts
1 → 1

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.5b

localize46.0ms

Local error

Found 4 expressions with local error:

6.5b
(* (- (* x.re x.re) (* x.im x.im)) x.re)
0.2b
(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
0.1b
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
0.0b
(+ (* x.re x.im) (* x.im x.re))

rewrite95.0ms

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
34.0ms
(- (* (- (* 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.re) (* x.im x.im)) x.re)
22.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
12.0ms
(+ (* x.re x.im) (* x.im x.re))

series193.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
68.0ms
(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
57.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.re)
35.0ms
(+ (* x.re x.im) (* x.im x.re))
33.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)

simplify647.0ms

Counts
95 → 95

prune880.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite182.0ms

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
92.0ms
(- (* (+ 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))
30.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
9.0ms
(+ (* x.re x.im) (* x.im x.re))

series213.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
77.0ms
(- (* (+ 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))
42.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
27.0ms
(+ (* x.re x.im) (* x.im x.re))

simplify1.5s

Counts
113 → 113

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×*-un-lft-identity
8×pow1 add-cbrt-cube associate-*r* associate-*l* add-exp-log add-cube-cbrt
6×add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
2×flip3-+ distribute-rgt-out pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod flip-+ distribute-lft-out unswap-sqr
1×distribute-rgt-in +-commutative sum-log fma-def distribute-lft-in flip3-- fma-udef flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 80
Calls
4 calls:
Slowest
32.0ms
(* x.im (+ (* x.re x.im) (* x.re x.im)))
16.0ms
(* (- x.re x.im) x.re)
7.0ms
(+ (* 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)))))

series263.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
128.0ms
(fma (+ x.re x.im) (* (- x.re x.im) x.re) (- (* x.im (+ (* x.re x.im) (* x.re x.im)))))
49.0ms
(* (- x.re x.im) x.re)
43.0ms
(+ (* x.re x.im) (* x.re x.im))
42.0ms
(* x.im (+ (* x.re x.im) (* x.re x.im)))

simplify1.4s

Counts
92 → 92

prune921.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

22.8b
(cbrt (* x.im (+ (* x.re x.im) (* x.re x.im))))
22.8b
(cbrt (* x.im (+ (* x.re x.im) (* x.re x.im))))
22.8b
(cbrt (* x.im (+ (* x.re x.im) (* x.re x.im))))
0.4b
(* (cbrt (* x.im (+ (* x.re x.im) (* x.re x.im)))) (cbrt (* x.im (+ (* x.re x.im) (* x.re x.im)))))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
20×associate-*r/
18×cbrt-div
11×pow1
10×add-sqr-sqrt
9×flip3-+ pow1/3 flip-+
8×*-un-lft-identity add-cube-cbrt
7×cbrt-prod
6×add-exp-log
4×expm1-log1p-u frac-times add-cbrt-cube swap-sqr associate-*r* associate-*l* insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 84
Calls
4 calls:
Slowest
43.0ms
(* (cbrt (* x.im (+ (* x.re x.im) (* x.re x.im)))) (cbrt (* x.im (+ (* x.re x.im) (* x.re x.im)))))
15.0ms
(cbrt (* x.im (+ (* x.re x.im) (* x.re x.im))))
12.0ms
(cbrt (* x.im (+ (* x.re x.im) (* x.re x.im))))
12.0ms
(cbrt (* x.im (+ (* x.re x.im) (* x.re x.im))))

series679.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
208.0ms
(* (cbrt (* x.im (+ (* x.re x.im) (* x.re x.im)))) (cbrt (* x.im (+ (* x.re x.im) (* x.re x.im)))))
167.0ms
(cbrt (* x.im (+ (* x.re x.im) (* x.re x.im))))
161.0ms
(cbrt (* x.im (+ (* x.re x.im) (* x.re x.im))))
143.0ms
(cbrt (* x.im (+ (* x.re x.im) (* x.re x.im))))

simplify877.0ms

Counts
96 → 96

prune1.1s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes138.0ms

Accuracy

0% (0.2b remaining)

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

bsearch4.0ms

end0.0ms

sample3.0s

Algorithm
intervals
Results
2.6s14524×body80valid