Details

sample117.0ms

Algorithm

intervals

Results

97.0ms

477×

body

valid

simplify2.0s

Counts

1 → 1

Iterations

Iter	Nodes
7	2992
6	1223
5	597
4	245
3	121
2	51
1	20
0	11

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.4b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* (* x.re x.re) 3) (* x.im x.im))
0.1b	(* (* x.re x.re) 3)
7.4b	(* x.im (- (* (* x.re x.re) 3) (* x.im x.im)))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt`
6×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
5×	`add-log-exp`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3--` `associate-r/` `-commutative` `flip--` `unswap-sqr`
1×	`diff-log`

Counts

3 → 55

Calls

3 calls:

14.0ms	(- (* (* x.re x.re) 3) (* x.im x.im))
12.0ms	(* (* x.re x.re) 3)
75.0ms	(* x.im (- (* (* x.re x.re) 3) (* x.im x.im)))

series167.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(- (* (* x.re x.re) 3) (* x.im x.im))
48.0ms	(* (* x.re x.re) 3)
64.0ms	(* x.im (- (* (* x.re x.re) 3) (* x.im x.im)))

simplify1.1s

Counts

64 → 64

Iterations

Iter	Nodes
3	2638
2	697
1	241
0	91

prune426.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.3b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* (* 3 x.re) x.re) (* x.im x.im))
0.2b	(* (* 3 x.re) x.re)
7.4b	(* x.im (- (* (* 3 x.re) x.re) (* x.im x.im)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt`
6×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
5×	`add-log-exp`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3--` `associate-r/` `-commutative` `flip--`
1×	`diff-log` `unswap-sqr`

Counts

3 → 54

Calls

3 calls:

14.0ms	(- (* (* 3 x.re) x.re) (* x.im x.im))
12.0ms	(* (* 3 x.re) x.re)
64.0ms	(* x.im (- (* (* 3 x.re) x.re) (* x.im x.im)))

series204.0ms

Counts

3 → 9

Calls

3 calls:

70.0ms	(- (* (* 3 x.re) x.re) (* x.im x.im))
48.0ms	(* (* 3 x.re) x.re)
86.0ms	(* x.im (- (* (* 3 x.re) x.re) (* x.im x.im)))

simplify2.0s

Counts

63 → 63

Iterations

Iter	Nodes
3	3388
2	783
1	238
0	90

prune562.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 7.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt x.im)
0.7b	(cbrt x.im)
2.8b	(* (cbrt x.im) (- (* (* 3 x.re) x.re) (* x.im x.im)))
4.9b	(* (* (cbrt x.im) (cbrt x.im)) (* (cbrt x.im) (- (* (* 3 x.re) x.re) (* x.im x.im))))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1` `add-exp-log`
13×	`add-sqr-sqrt`
11×	`add-cbrt-cube`
10×	`cbrt-prod` `distribute-rgt-in` `distribute-lft-in`
9×	`*-un-lft-identity` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
7×	`associate-l`
6×	`sub-neg` `associate-*r/`
4×	`associate-r` `add-log-exp`
2×	`flip3--` `pow1/3` `*-commutative` `flip--` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

1.0ms	(cbrt x.im)
1.0ms	(cbrt x.im)
47.0ms	(* (cbrt x.im) (- (* (* 3 x.re) x.re) (* x.im x.im)))
105.0ms	(* (* (cbrt x.im) (cbrt x.im)) (* (cbrt x.im) (- (* (* 3 x.re) x.re) (* x.im x.im))))

series857.0ms

Counts

4 → 12

Calls

4 calls:

295.0ms	(cbrt x.im)
260.0ms	(cbrt x.im)
206.0ms	(* (cbrt x.im) (- (* (* 3 x.re) x.re) (* x.im x.im)))
96.0ms	(* (* (cbrt x.im) (cbrt x.im)) (* (cbrt x.im) (- (* (* 3 x.re) x.re) (* x.im x.im))))

simplify3.7s

Counts

94 → 94

Iterations

Iter	Nodes
3	5783
2	1300
1	351
0	117

prune917.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x.re (* (* 3 x.re) x.im)) (* x.im (* (- x.im) x.im)))
0.1b	(* x.re (* (* 3 x.re) x.im))
0.1b	(* x.im (* (- x.im) x.im))
0.2b	(* (* 3 x.re) x.im)

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1` `add-cbrt-cube` `add-exp-log`
12×	`pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`add-sqr-sqrt` `-un-lft-identity` `associate-l*` `add-cube-cbrt`
6×	`add-log-exp`
5×	`associate-r`
3×	`distribute-lft-neg-out` `*-commutative` `distribute-rgt-neg-out`
1×	`+-commutative` `sum-log` `flip3-+` `unsub-neg` `flip-+`

Counts

4 → 71

Calls

4 calls:

34.0ms	(+ (* x.re (* (* 3 x.re) x.im)) (* x.im (* (- x.im) x.im)))
44.0ms	(* x.re (* (* 3 x.re) x.im))
13.0ms	(* x.im (* (- x.im) x.im))
22.0ms	(* (* 3 x.re) x.im)

series209.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(+ (* x.re (* (* 3 x.re) x.im)) (* x.im (* (- x.im) x.im)))
33.0ms	(* x.re (* (* 3 x.re) x.im))
52.0ms	(* x.im (* (- x.im) x.im))
32.0ms	(* (* 3 x.re) x.im)

simplify5.0s

Counts

83 → 83

Iterations

Iter	Nodes
3	7091
2	1208
1	303
0	110

prune678.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

regimes180.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
4	24
3	24
2	22
1	18
0	10

end0.0ms

sample2.9s

Algorithm

intervals

Results

2.5s

14575×

body

valid