Details

sample50.0ms

Algorithm

intervals

Results

22.0ms

271×

body

valid

simplify20.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.4b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.0b	(+ (* a c) (* b d))
23.9b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 53

Calls

3 calls:

10.0ms	(+ (* c c) (* d d))
17.0ms	(+ (* a c) (* b d))
74.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series260.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(+ (* c c) (* d d))
65.0ms	(+ (* a c) (* b d))
138.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify1.9s

Counts: 62 → 62

prune236.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 23.7b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
14.4b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
28.9b	(sqrt (+ (* c c) (* d d)))
28.9b	(sqrt (+ (* c c) (* d d)))

rewrite143.0ms

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:

60.0ms	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
37.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
16.0ms	(sqrt (+ (* c c) (* d d)))
14.0ms	(sqrt (+ (* c c) (* d d)))

series314.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
141.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
38.0ms	(sqrt (+ (* c c) (* d d)))
43.0ms	(sqrt (+ (* c c) (* d d)))

simplify951.0ms

Counts: 276 → 276

prune845.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 21.0b

localize17.0ms

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))))
14.5b	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
28.9b	(sqrt (+ (* c c) (* d d)))
28.9b	(sqrt (+ (* c c) (* d d)))

rewrite124.0ms

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:

39.0ms	(/ (* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d))))) (sqrt (+ (* c c) (* d d))))
63.0ms	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
8.0ms	(sqrt (+ (* c c) (* d d)))
9.0ms	(sqrt (+ (* c c) (* d d)))

series349.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(/ (* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d))))) (sqrt (+ (* c c) (* d d))))
145.0ms	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
42.0ms	(sqrt (+ (* c c) (* d d)))
38.0ms	(sqrt (+ (* c c) (* d d)))

simplify987.0ms

Counts: 134 → 134

prune528.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 21.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.0b	(+ (* a c) (* b d))
0.5b	(/ (/ 1 (sqrt 1)) (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
23.7b	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

834×	`times-frac`
381×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
144×	`sqrt-prod`
49×	`associate-/r/`
41×	`div-inv`
28×	`add-exp-log`
27×	`flip3-+` `flip-+`
25×	`associate-/l*`
18×	`associate-/r*` `add-cbrt-cube`
17×	`div-exp`
9×	`cbrt-undiv`
8×	`add-log-exp`
4×	`pow1`
3×	`associate-/l/`
2×	`+-commutative` `rec-exp` `frac-2neg` `1-exp` `clear-num` `sum-log`

Counts

4 → 444

Calls

4 calls:

13.0ms	(+ (* c c) (* d d))
11.0ms	(+ (* a c) (* b d))
47.0ms	(/ (/ 1 (sqrt 1)) (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
50.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

series344.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(+ (* c c) (* d d))
56.0ms	(+ (* a c) (* b d))
180.0ms	(/ (/ 1 (sqrt 1)) (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
61.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

simplify1.1s

Counts: 456 → 456

prune1.7s

Pruning

12 alts after pruning (8 fresh and 4 done)

Merged error: 21.0b

regimes298.0ms

Accuracy

-2.2% (3.1b remaining)

Error of 26.9b against oracle of 23.8b and baseline of 26.8b

bsearch0.0ms

simplify21.0ms

end0.0ms

sample946.0ms

Algorithm

intervals

Results

557.0ms

8479×

body

valid