Details

sample59.0ms

Algorithm

intervals

Results

40.0ms

270×

body

valid

simplify118.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

118.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.2b

localize24.0ms

Local error

Found 2 expressions with local error:

23.2b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
0.5b	(- (* b c) (* a d))

rewrite30.0ms

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`

Counts

2 → 46

Calls

2 calls:

Slowest

22.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
8.0ms	(- (* b c) (* a d))

series174.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

120.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
53.0ms	(- (* b c) (* a d))

simplify5.3s

Counts

65 → 52

Calls

65 calls:

Slowest

490.0ms	(* (* (/ (- (* b c) (* a d)) (+ (* c c) (* d d))) (/ (- (* b c) (* a d)) (+ (* c c) (* d d)))) (/ (- (* b c) (* a d)) (+ (* c c) (* d d))))
321.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
303.0ms	(- (* (* b c) (* b c)) (* (* a d) (* a d)))
231.0ms	(/ (- (* b c) (* a d)) (* (cbrt (+ (* c c) (* d d))) (cbrt (+ (* c c) (* d d)))))
209.0ms	(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))))

prune486.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 22.8b

localize28.0ms

Local error

Found 4 expressions with local error:

24.7b	(sqrt (+ (* c c) (* d d)))
24.7b	(sqrt (+ (* c c) (* d d)))
16.2b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
0.5b	(- (* b c) (* a d))

rewrite51.0ms

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`

Counts

4 → 90

Calls

4 calls:

Slowest

30.0ms	(/ (- (* 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)))

series291.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

154.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
50.0ms	(- (* b c) (* a d))
44.0ms	(sqrt (+ (* c c) (* d d)))
42.0ms	(sqrt (+ (* c c) (* d d)))

simplify8.4s

Counts

130 → 102

Calls

130 calls:

Slowest

367.0ms	(* (* (/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d)))) (/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))) (/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d)))))
337.0ms	(/ (* (* (- (* 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)))))
332.0ms	(* (sqrt (+ (* c c) (* d d))) (+ (* (* b c) (* b c)) (+ (* (* a d) (* a d)) (* (* b c) (* a d)))))
321.0ms	(- (* (* b c) (* b c)) (* (* a d) (* a d)))
314.0ms	(- (pow (* b c) 3) (pow (* a d) 3))

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 20.6b

localize28.0ms

Local error

Found 4 expressions with local error:

24.7b	(sqrt (+ (* c c) (* d d)))
24.7b	(sqrt (+ (* c c) (* d d)))
16.2b	(/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d)))
0.5b	(- (* b c) (* a d))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-cbrt-cube` `sqrt-div` `add-exp-log` `associate-/l*` `add-log-exp`
4×	`insert-posit16`
3×	`associate-/r*` `flip3-+` `flip-+`
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-exp` `div-inv`

Counts

4 → 89

Calls

4 calls:

Slowest

26.0ms	(/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d)))
7.0ms	(- (* b c) (* a d))
6.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

series207.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

82.0ms	(/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d)))
46.0ms	(- (* b c) (* a d))
42.0ms	(sqrt (+ (* c c) (* d d)))
38.0ms	(sqrt (+ (* c c) (* d d)))

simplify6.5s

Counts

128 → 101

Calls

128 calls:

Slowest

341.0ms	(* (* (sqrt (+ (* c c) (* d d))) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
294.0ms	(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
278.0ms	(* (- (* b c) (* a d)) (sqrt (+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))))
276.0ms	(sqrt (+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d)))))
271.0ms	(/ (sqrt (+ (* c c) (* d d))) (- (pow (* b c) 3) (pow (* a d) 3)))

prune878.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 20.6b

localize23.0ms

Local error

Found 3 expressions with local error:

23.1b	(* (- (* b c) (* a d)) (/ 1 (+ (* c c) (* d d))))
0.5b	(/ 1 (+ (* c c) (* d d)))
0.5b	(- (* b c) (* a d))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `times-frac`
19×	`add-cube-cbrt`
16×	`add-exp-log`
15×	`associate-r`
10×	`add-cbrt-cube`
6×	`pow1`
5×	`add-log-exp`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`associate-/r` `flip3--` `associate-l` `insert-posit16` `flip--` `associate-/l` `unswap-sqr`
2×	`frac-times` `cbrt-undiv` `rec-exp` `flip3-+` `1-exp` `associate-*l/` `cbrt-unprod` `flip-+` `div-inv`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Counts

3 → 90

Calls

3 calls:

Slowest

38.0ms	(* (- (* b c) (* a d)) (/ 1 (+ (* c c) (* d d))))
13.0ms	(/ 1 (+ (* c c) (* d d)))
7.0ms	(- (* b c) (* a d))

series168.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

85.0ms	(* (- (* b c) (* a d)) (/ 1 (+ (* c c) (* d d))))
44.0ms	(- (* b c) (* a d))
38.0ms	(/ 1 (+ (* c c) (* d d)))

simplify8.5s

Counts

113 → 99

Calls

113 calls:

Slowest

601.0ms	(* (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (/ 1 (+ (* c c) (* d d))) (/ 1 (+ (* c c) (* d d)))) (/ 1 (+ (* c c) (* d d)))))
373.0ms	(/ (* (* 1 1) 1) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))))
260.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
254.0ms	(- (* (* b c) (* b c)) (* (* a d) (* a d)))
241.0ms	(* (- (* b c) (* a d)) (/ 1 (* (cbrt (+ (* c c) (* d d))) (cbrt (+ (* c c) (* d d))))))

prune694.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 20.6b

regimes279.0ms

Accuracy

0% (2.8b remaining)

Error of 25.5b against oracle of 22.8b and baseline of 25.5b

bsearch2.0ms

end0.0ms

sample1.3s

Algorithm

intervals

Results

1.0s

8522×

body

valid