Details

sample35.0ms

Algorithm

intervals

Results

23.0ms

271×

body

valid

simplify133.0ms

Calls

1 calls:

Slowest

132.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize24.0ms

Local error

Found 2 expressions with local error:

28.6b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
1.0b	(- (* b c) (* a d))

rewrite43.0ms

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` `associate-/l`
2×	`pow1` `flip3--` `associate-/r/` `insert-posit16` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `flip-+` `div-inv`

Calls

2 calls:

Slowest

35.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
7.0ms	(- (* b c) (* a d))

series184.0ms

Calls

2 calls:

Slowest

109.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
74.0ms	(- (* b c) (* a d))

simplify2.5s

Calls

37 calls:

Slowest

425.0ms	(- (* (* b c) (* b c)) (* (* a d) (* a d)))
282.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
282.0ms	(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))
192.0ms	(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))))
182.0ms	(/ (exp (* b c)) (exp (* a d)))

prune691.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 28.1b

localize27.0ms

Local error

Found 4 expressions with local error:

32.2b	(sqrt (+ (* c c) (* d d)))
32.2b	(sqrt (+ (* c c) (* d d)))
18.4b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
1.0b	(- (* b c) (* a d))

rewrite58.0ms

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`
4×	`insert-posit16`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Calls

4 calls:

Slowest

38.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
7.0ms	(- (* b c) (* a d))
6.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

series279.0ms

Calls

4 calls:

Slowest

125.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
53.0ms	(- (* b c) (* a d))
52.0ms	(sqrt (+ (* c c) (* d d)))
49.0ms	(sqrt (+ (* c c) (* d d)))

simplify4.1s

Calls

78 calls:

Slowest

339.0ms	(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (sqrt (+ (* c c) (* d d))) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d)))))
298.0ms	(- (* (* b c) (* b c)) (* (* a d) (* a d)))
296.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
248.0ms	(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
226.0ms	(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))

prune1.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 26.4b

localize33.0ms

Local error

Found 4 expressions with local error:

32.2b	(sqrt (+ (* c c) (* d d)))
32.2b	(sqrt (+ (* c c) (* d d)))
18.4b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
1.0b	(- (* b c) (* a d))

rewrite50.0ms

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`
4×	`insert-posit16`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Calls

4 calls:

Slowest

21.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
11.0ms	(sqrt (+ (* c c) (* d d)))
11.0ms	(- (* b c) (* a d))
6.0ms	(sqrt (+ (* c c) (* d d)))

series290.0ms

Calls

4 calls:

Slowest

156.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
52.0ms	(- (* b c) (* a d))
42.0ms	(sqrt (+ (* c c) (* d d)))
40.0ms	(sqrt (+ (* c c) (* d d)))

simplify4.1s

Calls

78 calls:

Slowest

343.0ms	(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (sqrt (+ (* c c) (* d d))) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d)))))
315.0ms	(sqrt (+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d)))))
280.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
279.0ms	(- (* (* b c) (* b c)) (* (* a d) (* a d)))
277.0ms	(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))

prune1.2s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 26.4b

localize57.0ms

Local error

Found 4 expressions with local error:

32.2b	(sqrt (+ (* c c) (* d d)))
32.2b	(sqrt (+ (* c c) (* d d)))
32.2b	(sqrt (+ (* c c) (* d d)))
18.4b	(/ (- (* b c) (* a d)) (* (sqrt (sqrt (+ (* c c) (* d d)))) (sqrt (sqrt (+ (* c c) (* d d))))))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

30×	`sqrt-div`
12×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `flip3-+` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `sqrt-prod` `flip-+`
8×	`associate-/r/`
7×	`pow1`
4×	`frac-times` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `times-frac` `pow1/2` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `associate-l/` `associate-r/` `associate-/l/`
1×	`clear-num` `associate-/r*` `frac-2neg` `flip3--` `div-sub` `prod-exp` `cbrt-unprod` `div-inv` `flip--`

Calls

4 calls:

Slowest

54.0ms	(/ (- (* b c) (* a d)) (* (sqrt (sqrt (+ (* c c) (* d d)))) (sqrt (sqrt (+ (* c c) (* d d))))))
10.0ms	(sqrt (+ (* c c) (* d d)))
10.0ms	(sqrt (+ (* c c) (* d d)))
9.0ms	(sqrt (+ (* c c) (* d d)))

series320.0ms

Calls

4 calls:

Slowest

152.0ms	(/ (- (* b c) (* a d)) (* (sqrt (sqrt (+ (* c c) (* d d)))) (sqrt (sqrt (+ (* c c) (* d d))))))
57.0ms	(sqrt (+ (* c c) (* d d)))
56.0ms	(sqrt (+ (* c c) (* d d)))
55.0ms	(sqrt (+ (* c c) (* d d)))

simplify3.4s

Calls

57 calls:

Slowest

232.0ms	(- (* (* b c) (* b c)) (* (* a d) (* a d)))
220.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
216.0ms	(* (sqrt (sqrt (- (* c c) (* d d)))) (sqrt (sqrt (+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d)))))))
214.0ms	(* (sqrt (sqrt (+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d)))))) (sqrt (sqrt (- (* c c) (* d d)))))
203.0ms	(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))

prune887.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 26.4b

regimes363.0ms

Accuracy

0% (2.7b remaining)

Error of 25.7b against oracle of 22.9b and baseline of 25.7b

bsearch2.0ms

end0.0ms

sample1.2s

Algorithm

intervals

Results

775.0ms

8474×

body

valid