Details

sample25.0ms

Algorithm

intervals

Results

11.0ms

271×

body

valid

simplify1.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize15.0ms

Local error

Found 2 expressions with local error:

0.7b	(+ (* a c) (* b d))
27.9b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite66.0ms

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×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`pow1` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 42

Calls

2 calls:

13.0ms	(+ (* a c) (* b d))
51.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series172.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(+ (* a c) (* b d))
125.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify78.0ms

Counts: 48 → 48

prune186.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 27.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (* a c) (* b d))
17.2b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
30.4b	(sqrt (+ (* c c) (* d d)))
30.4b	(sqrt (+ (* c c) (* d d)))

rewrite76.0ms

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`
5×	`flip3-+` `flip-+`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 84

Calls

4 calls:

8.0ms	(+ (* a c) (* b d))
47.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
9.0ms	(sqrt (+ (* c c) (* d d)))
10.0ms	(sqrt (+ (* c c) (* d d)))

series613.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(+ (* a c) (* b d))
174.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
357.0ms	(sqrt (+ (* c c) (* d d)))
42.0ms	(sqrt (+ (* c c) (* d d)))

simplify72.0ms

Counts: 96 → 96

prune379.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 25.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (* a c) (* b d))
17.3b	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
30.4b	(sqrt (+ (* c c) (* d d)))
30.4b	(sqrt (+ (* c c) (* d d)))

rewrite71.0ms

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` `add-cbrt-cube` `associate-/l*` `add-log-exp`
5×	`flip3-+` `flip-+`
3×	`associate-/r*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 84

Calls

4 calls:

13.0ms	(+ (* a c) (* b d))
23.0ms	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
18.0ms	(sqrt (+ (* c c) (* d d)))
13.0ms	(sqrt (+ (* c c) (* d d)))

series277.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(+ (* a c) (* b d))
105.0ms	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
57.0ms	(sqrt (+ (* c c) (* d d)))
60.0ms	(sqrt (+ (* c c) (* d d)))

simplify83.0ms

Counts: 96 → 96

prune416.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 25.2b

localize21.0ms

Local error

Found 3 expressions with local error:

0.5b	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
0.7b	(+ (* a c) (* b d))
27.5b	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
55×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`associate-/r*`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp`
7×	`flip3-+` `flip-+`
6×	`div-inv` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `associate-/l/`
1×	`+-commutative` `pow-flip` `sum-log` `inv-pow`

Counts

3 → 126

Calls

3 calls:

37.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
8.0ms	(+ (* a c) (* b d))
40.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

series289.0ms

Counts

3 → 9

Calls

3 calls:

162.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
38.0ms	(+ (* a c) (* b d))
88.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

simplify57.0ms

Counts: 135 → 135

prune446.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 25.2b

regimes334.0ms

Accuracy

25% (2.2b remaining)

Error of 25.4b against oracle of 23.2b and baseline of 26.1b

bsearch2.0ms

simplify226.0ms

end0.0ms

sample1.0s

Algorithm

intervals

Results

606.0ms

8500×

body

valid