Details

sample39.0ms

Algorithm

intervals

Results

29.0ms

274×

body

valid

simplify17.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

17.0ms

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.6b

localize38.0ms

Local error

Found 3 expressions with local error:

25.6b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
0.2b	(+ (* a c) (* b d))
0.0b	(+ (* c c) (* d d))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-cbrt-cube` `add-exp-log`
4×	`flip3-+` `flip-+`
3×	`pow1` `associate-/r` `insert-posit16` `associate-/l`
2×	`+-commutative` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 56

Calls

3 calls:

Slowest

54.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
7.0ms	(+ (* c c) (* d d))
7.0ms	(+ (* a c) (* b d))

series202.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

109.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
55.0ms	(+ (* a c) (* b d))
38.0ms	(+ (* c c) (* d d))

simplify2.0s

Counts

40 → 65

Calls

40 calls:

Slowest

346.0ms	(- (* (* a c) (* a c)) (* (* b d) (* b d)))
293.0ms	(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))
241.0ms	(* (exp (* a c)) (exp (* b d)))
234.0ms	(/ (* (* (+ (* a c) (* b d)) (+ (* a c) (* b d))) (+ (* a c) (* b d))) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))))
193.0ms	(+ (pow (* a c) 3) (pow (* b d) 3))

prune691.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 25.1b

localize46.0ms

Local error

Found 4 expressions with local error:

29.7b	(sqrt (+ (* c c) (* d d)))
29.7b	(sqrt (+ (* c c) (* d d)))
16.1b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
0.2b	(+ (* a c) (* b d))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `sqrt-div` `add-exp-log` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`insert-posit16`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 88

Calls

4 calls:

Slowest

32.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
7.0ms	(+ (* a c) (* b d))
6.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

series307.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

152.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
59.0ms	(sqrt (+ (* c c) (* d d)))
55.0ms	(sqrt (+ (* c c) (* d d)))
41.0ms	(+ (* a c) (* b d))

simplify3.5s

Counts

77 → 100

Calls

77 calls:

Slowest

340.0ms	(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
322.0ms	(- (* (* a c) (* a c)) (* (* b d) (* b d)))
309.0ms	(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
308.0ms	(sqrt (+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d)))))
274.0ms	(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 23.2b

localize39.0ms

Local error

Found 4 expressions with local error:

25.0b	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))
0.7b	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
0.2b	(+ (* a c) (* b d))
0.0b	(+ (* c c) (* d d))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
56×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`associate-/r*`
17×	`add-exp-log`
11×	`add-cbrt-cube` `associate-/r/`
8×	`flip3-+` `div-exp` `flip-+` `add-log-exp`
6×	`div-inv` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv` `insert-posit16`
2×	`+-commutative` `rec-exp` `clear-num` `sum-log` `frac-2neg` `1-exp` `associate-/l/`
1×	`pow-flip` `inv-pow`

Counts

4 → 141

Calls

4 calls:

Slowest

26.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))
20.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
9.0ms	(+ (* c c) (* d d))
8.0ms	(+ (* a c) (* b d))

series282.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

142.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
61.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))
50.0ms	(+ (* a c) (* b d))
29.0ms	(+ (* c c) (* d d))

simplify11.9s

Counts

158 → 153

Calls

158 calls:

Slowest

444.0ms	(/ (sqrt 1) (/ (+ (* c c) (* d d)) (+ (pow (* a c) 3) (pow (* b d) 3))))
408.0ms	(/ (* (* 1 1) 1) (* (* (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))) (/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))) (/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))))
408.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (pow (* a c) 3) (pow (* b d) 3))))
398.0ms	(/ (* (cbrt 1) (cbrt 1)) (/ (+ (* c c) (* d d)) (+ (pow (* a c) 3) (pow (* b d) 3))))
351.0ms	(/ (* (* 1 1) 1) (/ (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))) (* (* (+ (* a c) (* b d)) (+ (* a c) (* b d))) (+ (* a c) (* b d)))))

prune1.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 23.2b

localize21.0ms

Local error

Found 3 expressions with local error:

25.6b	(/ (+ (* d b) (* a c)) (+ (* c c) (* d d)))
0.2b	(+ (* d b) (* a c))
0.0b	(+ (* c c) (* d d))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-cbrt-cube` `add-exp-log`
4×	`flip3-+` `flip-+`
3×	`pow1` `associate-/r` `insert-posit16` `associate-/l`
2×	`+-commutative` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 56

Calls

3 calls:

Slowest

30.0ms	(/ (+ (* d b) (* a c)) (+ (* c c) (* d d)))
7.0ms	(+ (* c c) (* d d))
7.0ms	(+ (* d b) (* a c))

series129.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

67.0ms	(/ (+ (* d b) (* a c)) (+ (* c c) (* d d)))
34.0ms	(+ (* d b) (* a c))
28.0ms	(+ (* c c) (* d d))

simplify1.5s

Counts

40 → 65

Calls

40 calls:

Slowest

261.0ms	(- (* (* d b) (* d b)) (* (* a c) (* a c)))
214.0ms	(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))
187.0ms	(/ (* (* (+ (* d b) (* a c)) (+ (* d b) (* a c))) (+ (* d b) (* a c))) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))))
155.0ms	(+ (pow (* d b) 3) (pow (* a c) 3))
128.0ms	(* (exp (* d b)) (exp (* a c)))

prune475.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 23.2b

regimes310.0ms

Accuracy

14.7% (1.6b remaining)

Error of 25.6b against oracle of 24.0b and baseline of 25.9b

bsearch5.0ms

end0.0ms

sample1.2s

Algorithm

intervals

Results

1.1s

8459×

body

valid