Details

sample17.0ms

Algorithm

intervals

Results

7.0ms

256×

body

valid

simplify1.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.2b

localize7.0ms

Local error

Found 1 expressions with local error:

31.2b

(sqrt (+ (* re re) (* im im)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `sqrt-prod`
2×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
1×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

1 → 15

Calls

1 calls:

11.0ms

(sqrt (+ (* re re) (* im im)))

series49.0ms

Counts

1 → 3

Calls

1 calls:

49.0ms

(sqrt (+ (* re re) (* im im)))

simplify115.0ms

Counts: 18 → 18

prune55.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 10.0b

localize17.0ms

Local error

Found 2 expressions with local error:

5.8b	(exp (log (sqrt (+ (* re re) (* im im)))))
31.2b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `log-prod` `exp-prod` `*-un-lft-identity` `exp-sum` `sqrt-prod`
5×	`pow1`
4×	`sqrt-div`
3×	`log-pow`
2×	`add-exp-log` `log-div` `sqrt-pow1` `flip3-+` `pow1/2` `exp-diff` `add-cbrt-cube` `flip-+` `add-log-exp`
1×	`rem-sqrt-square` `rem-exp-log`

Counts

2 → 37

Calls

2 calls:

13.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
9.0ms	(sqrt (+ (* re re) (* im im)))

series86.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify117.0ms

Counts: 43 → 43

prune94.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 10.0b

localize18.0ms

Local error

Found 2 expressions with local error:

6.4b	(pow (exp 1/2) (log (+ (* re re) (* im im))))
32.4b	(log (+ (* re re) (* im im)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`log-prod`
5×	`pow1`
4×	`log-div` `pow-unpow` `pow-pow`
3×	`unpow-prod-up` `add-exp-log` `unpow-prod-down` `exp-prod`
2×	`flip3-+` `log-pow` `add-cbrt-cube` `flip-+` `pow-sub` `add-log-exp`
1×	`pow-to-exp` `rem-log-exp` `pow-exp` `sqr-pow`

Counts

2 → 40

Calls

2 calls:

16.0ms	(pow (exp 1/2) (log (+ (* re re) (* im im))))
8.0ms	(log (+ (* re re) (* im im)))

series223.0ms

Counts

2 → 6

Calls

2 calls:

154.0ms	(pow (exp 1/2) (log (+ (* re re) (* im im))))
68.0ms	(log (+ (* re re) (* im im)))

simplify112.0ms

Counts: 46 → 46

prune181.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 10.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt 1/2) (log (+ (* re re) (* im im))))
1.0b	(* (cbrt 1/2) (cbrt 1/2))
6.5b	(pow (exp (* (cbrt 1/2) (cbrt 1/2))) (* (cbrt 1/2) (log (+ (* re re) (* im im)))))
32.4b	(log (+ (* re re) (* im im)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
20×	`cbrt-prod`
16×	`pow1`
15×	`log-prod`
12×	`associate-l`
10×	`associate-r`
9×	`add-exp-log`
6×	`unpow-prod-up` `distribute-rgt-in` `distribute-lft-in` `pow1/3` `swap-sqr` `unswap-sqr`
5×	`add-cbrt-cube` `add-log-exp`
3×	`unpow-prod-down` `pow-pow` `pow-prod-down`
2×	`log-div` `prod-exp` `pow-sqr` `log-pow` `*-commutative` `pow-prod-up` `cbrt-unprod`
1×	`pow2` `pow-to-exp` `pow-unpow` `exp-prod` `exp-to-pow` `flip3-+` `pow-plus` `rem-log-exp` `pow-exp` `flip-+` `sqr-pow`

Counts

4 → 106

Calls

4 calls:

26.0ms	(* (cbrt 1/2) (log (+ (* re re) (* im im))))
17.0ms	(* (cbrt 1/2) (cbrt 1/2))
26.0ms	(pow (exp (* (cbrt 1/2) (cbrt 1/2))) (* (cbrt 1/2) (log (+ (* re re) (* im im)))))
10.0ms	(log (+ (* re re) (* im im)))

series430.0ms

Counts

4 → 10

Calls

4 calls:

93.0ms	(* (cbrt 1/2) (log (+ (* re re) (* im im))))
0.0ms	(* (cbrt 1/2) (cbrt 1/2))
260.0ms	(pow (exp (* (cbrt 1/2) (cbrt 1/2))) (* (cbrt 1/2) (log (+ (* re re) (* im im)))))
76.0ms	(log (+ (* re re) (* im im)))

simplify64.0ms

Counts: 116 → 116

prune305.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 10.0b

regimes446.0ms

Accuracy

58.7% (9.8b remaining)

Error of 17.9b against oracle of 8.1b and baseline of 31.7b

bsearch52.0ms

Steps

Iters	Range		Point
6	4.200512674035927e+74	5.041755508587056e+75	4.342031878168628e+75
9	-3.705252492998041e+114	-1.4290697573002828e+105	-1.4917404615387262e+111

simplify1.0ms

end0.0ms

sample720.0ms

Algorithm

intervals

Results

430.0ms

8000×

body

valid