Details

sample22.0ms

Algorithm

intervals

Results

9.0ms

256×

body

valid

simplify19.0ms

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* re re) (* im im))
31.2b	(sqrt (+ (* re re) (* im im)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 26

Calls

2 calls:

11.0ms	(+ (* re re) (* im im))
12.0ms	(sqrt (+ (* re re) (* im im)))

series100.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(+ (* re re) (* im im))
58.0ms	(sqrt (+ (* re re) (* im im)))

simplify829.0ms

Counts: 32 → 32

prune96.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 8.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (sqrt (+ (* re re) (* im im))))
0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
31.2b	(sqrt (+ (* re re) (* im im)))
31.2b	(sqrt (+ (* re re) (* im im)))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

82×	`sqrt-prod`
54×	`add-sqr-sqrt`
38×	`sqrt-pow1`
32×	`sqrt-div`
31×	`pow1`
20×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `rem-sqrt-square` `add-log-exp`
2×	`associate-r/` `associate-l/`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 134

Calls

4 calls:

16.0ms	(sqrt (sqrt (+ (* re re) (* im im))))
100.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
13.0ms	(sqrt (+ (* re re) (* im im)))
14.0ms	(sqrt (+ (* re re) (* im im)))

series303.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(sqrt (sqrt (+ (* re re) (* im im))))
59.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
45.0ms	(sqrt (+ (* re re) (* im im)))
63.0ms	(sqrt (+ (* re re) (* im im)))

simplify700.0ms

Counts: 146 → 146

prune407.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 8.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) (sqrt (sqrt (sqrt (+ (* re re) (* im im))))))
31.2b	(sqrt (+ (* re re) (* im im)))
31.2b	(sqrt (+ (* re re) (* im im)))
31.2b	(sqrt (+ (* re re) (* im im)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

165×	`sqrt-prod`
82×	`add-sqr-sqrt`
75×	`sqrt-pow1`
42×	`sqrt-div`
38×	`pow1`
27×	`pow1/2`
24×	`swap-sqr`
23×	`add-cube-cbrt` `*-un-lft-identity`
16×	`unswap-sqr`
13×	`pow-prod-up`
12×	`associate-r` `associate-l`
9×	`flip3-+` `flip-+`
7×	`pow-prod-down` `pow-sqr`
6×	`add-exp-log` `add-cbrt-cube`
4×	`frac-times` `add-log-exp`
3×	`rem-sqrt-square`
2×	`associate-r/` `associate-l/`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 158

Calls

4 calls:

71.0ms	(* (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) (sqrt (sqrt (sqrt (+ (* re re) (* im im))))))
8.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))
13.0ms	(sqrt (+ (* re re) (* im im)))

series287.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(* (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) (sqrt (sqrt (sqrt (+ (* re re) (* im im))))))
51.0ms	(sqrt (+ (* re re) (* im im)))
59.0ms	(sqrt (+ (* re re) (* im im)))
52.0ms	(sqrt (+ (* re re) (* im im)))

simplify793.0ms

Counts: 170 → 170

prune479.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 8.9b

localize1.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify16.0ms

Counts: 0 → 0

prune0.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 8.9b

regimes398.0ms

Accuracy

56.6% (10.7b remaining)

Error of 18.1b against oracle of 7.5b and baseline of 32.0b

bsearch113.0ms

Steps

Iters	Range		Point
5	3.405487938897816e+124	7.120673724870613e+124	3.9375726319446014e+124
10	2.473474062206034e-206	4.167173210830186e-189	2.4469904649327215e-197
9	-2.7933584181899312e-198	-3.0544378147195635e-207	-9.538446928549385e-200
7	-2.1982474146058156e+122	-2.4034702386058127e+120	-1.1991152327731214e+121

simplify23.0ms

end0.0ms

sample667.0ms

Algorithm

intervals

Results

400.0ms

8000×

body

valid