Details

sample59.0ms

Algorithm

intervals

Results

40.0ms

271×

body

valid

simplify16.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

16.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.3b

localize28.0ms

Local error

Found 2 expressions with local error:

24.3b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
0.5b	(+ (* a c) (* b d))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 44

Calls

2 calls:

Slowest

52.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
14.0ms	(+ (* a c) (* b d))

series157.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

112.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
45.0ms	(+ (* a c) (* b d))

simplify1.8s

Counts

36 → 50

Calls

36 calls:

Slowest

372.0ms	(- (* (* a c) (* a c)) (* (* b d) (* b d)))
329.0ms	(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))
278.0ms	(/ (* (* (+ (* a c) (* b d)) (+ (* a c) (* b d))) (+ (* a c) (* b d))) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))))
214.0ms	(* (exp (* a c)) (exp (* b d)))
200.0ms	(+ (pow (* a c) 3) (pow (* b d) 3))

prune580.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 23.9b

localize47.0ms

Local error

Found 4 expressions with local error:

28.3b	(sqrt (+ (* c c) (* d d)))
28.3b	(sqrt (+ (* c c) (* d d)))
14.9b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
0.5b	(+ (* a c) (* b d))

rewrite71.0ms

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

29.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
20.0ms	(sqrt (+ (* c c) (* d d)))
14.0ms	(+ (* a c) (* b d))
6.0ms	(sqrt (+ (* c c) (* d d)))

series308.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

164.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
54.0ms	(+ (* a c) (* b d))
52.0ms	(sqrt (+ (* c c) (* d d)))
37.0ms	(sqrt (+ (* c c) (* d d)))

simplify3.3s

Counts

77 → 100

Calls

77 calls:

Slowest

394.0ms	(- (* (* a c) (* a c)) (* (* b d) (* b d)))
316.0ms	(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
307.0ms	(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
302.0ms	(sqrt (+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d)))))
222.0ms	(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 20.8b

localize18.0ms

Local error

Found 2 expressions with local error:

24.3b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
0.5b	(+ (* a c) (* b d))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 44

Calls

2 calls:

Slowest

49.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
8.0ms	(+ (* a c) (* b d))

series184.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

122.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
62.0ms	(+ (* a c) (* b d))

simplify1.8s

Counts

36 → 50

Calls

36 calls:

Slowest

409.0ms	(- (* (* a c) (* a c)) (* (* b d) (* b d)))
329.0ms	(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))
255.0ms	(/ (* (* (+ (* a c) (* b d)) (+ (* a c) (* b d))) (+ (* a c) (* b d))) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))))
197.0ms	(+ (pow (* a c) 3) (pow (* b d) 3))
186.0ms	(* (exp (* a c)) (exp (* b d)))

prune581.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 20.8b

localize40.0ms

Local error

Found 4 expressions with local error:

28.3b	(sqrt (+ (* c c) (* d d)))
28.3b	(sqrt (+ (* c c) (* d d)))
28.3b	(sqrt (+ (* c c) (* d d)))
14.9b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

Slowest

28.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
17.0ms	(sqrt (+ (* c c) (* d d)))
13.0ms	(sqrt (+ (* c c) (* d d)))
12.0ms	(sqrt (+ (* c c) (* d d)))

series355.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

184.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
61.0ms	(sqrt (+ (* c c) (* d d)))
55.0ms	(sqrt (+ (* c c) (* d d)))
54.0ms	(sqrt (+ (* c c) (* d d)))

simplify4.1s

Counts

83 → 104

Calls

83 calls:

Slowest

647.0ms	(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
357.0ms	(- (* (* a c) (* a c)) (* (* b d) (* b d)))
342.0ms	(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
301.0ms	(sqrt (+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d)))))
291.0ms	(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))

prune1.6s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 20.8b

regimes441.0ms

Accuracy

0% (2.4b remaining)

Error of 25.9b against oracle of 23.5b and baseline of 25.9b

bsearch2.0ms

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.3s

8456×

body

valid