Details

sample33.0ms

Algorithm

intervals

Results

15.0ms

271×

body

valid

simplify3.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.1b

localize13.0ms

Local error

Found 2 expressions with local error:

0.5b	(- (* b c) (* a d))
26.6b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow1` `flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

2 → 44

Calls

2 calls:

11.0ms	(- (* b c) (* a d))
47.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series182.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(- (* b c) (* a d))
121.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify103.0ms

Counts: 50 → 50

prune202.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 26.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* b c) (* a d))
17.1b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
28.8b	(sqrt (+ (* c c) (* d d)))
28.8b	(sqrt (+ (* c c) (* d d)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 86

Calls

4 calls:

8.0ms	(- (* b c) (* a d))
34.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
12.0ms	(sqrt (+ (* c c) (* d d)))
12.0ms	(sqrt (+ (* c c) (* d d)))

series304.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b c) (* a d))
166.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
53.0ms	(sqrt (+ (* c c) (* d d)))
38.0ms	(sqrt (+ (* c c) (* d d)))

simplify95.0ms

Counts: 98 → 98

prune432.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 23.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* b c) (* a d))
17.2b	(* (- (* b c) (* a d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
28.8b	(sqrt (+ (* c c) (* d d)))
28.8b	(sqrt (+ (* c c) (* d d)))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
24×	`associate-r`
22×	`*-un-lft-identity` `times-frac`
20×	`add-cube-cbrt`
17×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
6×	`sqrt-div` `add-log-exp`
5×	`unswap-sqr`
4×	`prod-exp`
3×	`flip3--` `flip3-+` `associate-l` `flip--` `flip-+`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `sub-neg` `rec-exp` `diff-log` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 95

Calls

4 calls:

15.0ms	(- (* b c) (* a d))
94.0ms	(* (- (* b c) (* a d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
20.0ms	(sqrt (+ (* c c) (* d d)))
13.0ms	(sqrt (+ (* c c) (* d d)))

series281.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(- (* b c) (* a d))
145.0ms	(* (- (* b c) (* a d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
38.0ms	(sqrt (+ (* c c) (* d d)))
43.0ms	(sqrt (+ (* c c) (* d d)))

simplify67.0ms

Counts: 107 → 107

prune392.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 23.4b

localize32.0ms

Local error

Found 4 expressions with local error:

17.1b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
28.8b	(sqrt (+ (* c c) (* d d)))
29.8b	(cbrt (+ (* c c) (* d d)))
29.8b	(cbrt (+ (* c c) (* d d)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
15×	`sqrt-prod`
6×	`add-exp-log` `cbrt-prod` `associate-/r*` `add-cbrt-cube`
5×	`pow1`
4×	`cbrt-div` `flip3-+` `sqrt-div` `flip-+` `add-log-exp`
3×	`associate-/l*`
2×	`pow1/3` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `clear-num` `flip--` `div-inv`

Counts

4 → 85

Calls

4 calls:

50.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
12.0ms	(sqrt (+ (* c c) (* d d)))
7.0ms	(cbrt (+ (* c c) (* d d)))
7.0ms	(cbrt (+ (* c c) (* d d)))

series484.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
43.0ms	(sqrt (+ (* c c) (* d d)))
123.0ms	(cbrt (+ (* c c) (* d d)))
140.0ms	(cbrt (+ (* c c) (* d d)))

simplify72.0ms

Counts: 97 → 97

prune528.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 23.4b

regimes249.0ms

Accuracy

-2.9% (2.9b remaining)

Error of 26.2b against oracle of 23.3b and baseline of 26.2b

bsearch116.0ms

Steps

Iters	Range		Point
6	7.634858387370288e+142	4.3868455552093375e+143	4.152810026092195e+143
9	6.815249310581322e+103	4.491388250328966e+108	4.454667910693685e+108

simplify39.0ms

end0.0ms

sample1.0s

Algorithm

intervals

Results

609.0ms

8483×

body

valid