Details

sample32.0ms

Algorithm

intervals

Results

14.0ms

273×

body

valid

simplify15.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.8b

localize22.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* a c) (* b d))
26.3b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite54.0ms

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:

8.0ms	(+ (* a c) (* b d))
45.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series200.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(+ (* a c) (* b d))
154.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify1.4s

Counts: 48 → 48

prune204.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 26.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
15.8b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
31.5b	(sqrt (+ (* c c) (* d d)))
31.5b	(sqrt (+ (* c c) (* d d)))

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
164×	`add-sqr-sqrt`
162×	`add-cube-cbrt` `*-un-lft-identity`
156×	`sqrt-prod`
27×	`associate-/l*`
22×	`sqrt-div`
18×	`associate-/r/`
12×	`flip3-+` `associate-/r*` `flip-+`
11×	`add-exp-log` `add-cbrt-cube`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`associate-/l/`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`

Counts

4 → 264

Calls

4 calls:

99.0ms	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
47.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
8.0ms	(sqrt (+ (* c c) (* d d)))
14.0ms	(sqrt (+ (* c c) (* d d)))

series393.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
157.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
48.0ms	(sqrt (+ (* c c) (* d d)))
52.0ms	(sqrt (+ (* c c) (* d d)))

simplify883.0ms

Counts: 276 → 276

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 23.8b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d))))) (sqrt (+ (* c c) (* d d))))
15.9b	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
31.5b	(sqrt (+ (* c c) (* d d)))
31.5b	(sqrt (+ (* c c) (* d d)))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
28×	`add-exp-log` `times-frac`
26×	`*-un-lft-identity`
24×	`add-cube-cbrt` `associate-r`
23×	`sqrt-prod`
18×	`add-cbrt-cube`
9×	`div-exp`
8×	`pow1` `flip3-+` `sqrt-div` `prod-exp` `flip-+`
6×	`associate-/r*` `associate-/l/`
5×	`cbrt-undiv` `unswap-sqr`
4×	`frac-times` `associate-*l/` `associate-/r/` `cbrt-unprod` `add-log-exp`
3×	`associate-l`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-*r/` `un-div-inv` `div-inv`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `associate-/l`

Counts

4 → 122

Calls

4 calls:

44.0ms	(/ (* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d))))) (sqrt (+ (* c c) (* d d))))
58.0ms	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
14.0ms	(sqrt (+ (* c c) (* d d)))
12.0ms	(sqrt (+ (* c c) (* d d)))

series366.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(/ (* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d))))) (sqrt (+ (* c c) (* d d))))
144.0ms	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
44.0ms	(sqrt (+ (* c c) (* d d)))
46.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.0s

Counts: 134 → 134

prune529.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 23.8b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d))))
15.9b	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
31.5b	(sqrt (+ (* c c) (* d d)))
31.5b	(sqrt (+ (* c c) (* d d)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
100×	`add-sqr-sqrt`
98×	`add-cube-cbrt` `*-un-lft-identity`
54×	`sqrt-prod`
27×	`associate-/r*`
17×	`add-exp-log`
11×	`associate-/r/` `add-cbrt-cube`
9×	`associate-/l*`
8×	`flip3-+` `div-exp` `flip-+`
7×	`pow1`
6×	`sqrt-div` `div-inv`
4×	`cbrt-undiv` `add-log-exp`
2×	`rem-sqrt-square` `rec-exp` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `clear-num` `associate-/l/`
1×	`pow-flip` `inv-pow`

Counts

4 → 193

Calls

4 calls:

32.0ms	(/ 1 (/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d))))
32.0ms	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
8.0ms	(sqrt (+ (* c c) (* d d)))
14.0ms	(sqrt (+ (* c c) (* d d)))

series366.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ 1 (/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d))))
114.0ms	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
51.0ms	(sqrt (+ (* c c) (* d d)))
64.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.1s

Counts: 205 → 205

prune695.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 23.8b

regimes269.0ms

Accuracy

16.7% (2.5b remaining)

Error of 25.8b against oracle of 23.3b and baseline of 26.3b

bsearch4.0ms

simplify4.1s

end0.0ms

sample900.0ms

Algorithm

intervals

Results

543.0ms

8474×

body

valid