Details

Time bar (total: 17.0s)

sample60.0ms

Algorithm
intervals
Results
48.0ms456×body80valid

simplify4.3s

Counts
1 → 1

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.3b

localize34.0ms

Local error

Found 4 expressions with local error:

5.3b
(* (- (* x.re x.re) (* x.im x.im)) x.im)
0.2b
(* (+ (* 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))

rewrite98.0ms

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
31.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
31.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)
19.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
15.0ms
(+ (* x.re x.im) (* x.im x.re))

series226.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
91.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
80.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)
28.0ms
(+ (* x.re x.im) (* x.im x.re))
26.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)

simplify617.0ms

Counts
93 → 93

prune862.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite161.0ms

Algorithm
rewrite-expression-head
Rules
42×associate-*l/
20×flip3-+ flip-+
16×frac-add
12×frac-times
11×pow1 add-cbrt-cube add-exp-log
9×add-sqr-sqrt *-un-lft-identity flip3-- flip--
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 sum-log fma-def *-commutative
1×distribute-lft-out unswap-sqr
Counts
4 → 99
Calls
4 calls:
Slowest
69.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.im))
37.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
37.0ms
(+ (* (+ x.re x.im) (* (- x.re x.im) x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
15.0ms
(+ (* x.re x.im) (* x.im x.re))

series314.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
121.0ms
(+ (* (+ x.re x.im) (* (- x.re x.im) x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
117.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.im))
41.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
35.0ms
(+ (* x.re x.im) (* x.im x.re))

simplify1.4s

Counts
111 → 111

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 3 expressions with local error:

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

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt
5×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt add-log-exp
3×expm1-log1p-u associate-*r* associate-*l* insert-posit16 log1p-expm1-u
2×flip3-+ associate-*l/ flip-+
1×+-commutative sum-log fma-def pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef unswap-sqr
Counts
3 → 49
Calls
3 calls:
Slowest
25.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
16.0ms
(+ (* x.re x.im) (* x.im x.re))
0.0ms
(fma (+ x.re x.im) (* (- x.re x.im) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))

series231.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
156.0ms
(fma (+ x.re x.im) (* (- x.re x.im) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
39.0ms
(+ (* x.re x.im) (* x.im x.re))
37.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)

simplify894.0ms

Counts
58 → 58

prune595.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

12.5b
(cbrt (+ (* x.re x.im) (* x.im x.re)))
12.5b
(cbrt (+ (* x.re x.im) (* x.im x.re)))
12.5b
(cbrt (+ (* x.re x.im) (* x.im x.re)))
0.5b
(* (cbrt (+ (* x.re x.im) (* x.im x.re))) (cbrt (+ (* x.re x.im) (* x.im x.re))))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
18×cbrt-div
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×flip3-+ pow1/3 flip-+
6×swap-sqr associate-*r* associate-*l* 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 → 99
Calls
4 calls:
Slowest
45.0ms
(* (cbrt (+ (* x.re x.im) (* x.im x.re))) (cbrt (+ (* x.re x.im) (* x.im x.re))))
8.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
4.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
4.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))

series616.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
176.0ms
(* (cbrt (+ (* x.re x.im) (* x.im x.re))) (cbrt (+ (* x.re x.im) (* x.im x.re))))
168.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
150.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
122.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))

simplify851.0ms

Counts
111 → 111

prune1.2s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes124.0ms

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms

end0.0ms

sample3.1s

Algorithm
intervals
Results
2.7s14476×body80valid