Details

sample72.0ms

Algorithm

intervals

Results

52.0ms

269×

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: 24.9b

localize40.0ms

Local error

Found 2 expressions with local error:

24.9b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
0.7b	(+ (* a c) (* b d))

rewrite75.0ms

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

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

series167.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

121.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
46.0ms	(+ (* a c) (* b d))

simplify1.9s

Counts

36 → 50

Calls

36 calls:

Slowest

332.0ms	(- (* (* a c) (* a c)) (* (* b d) (* b d)))
313.0ms	(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))
264.0ms	(/ (* (* (+ (* a c) (* b d)) (+ (* a c) (* b d))) (+ (* a c) (* b d))) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))))
231.0ms	(+ (pow (* a c) 3) (pow (* b d) 3))
195.0ms	(* (exp (* a c)) (exp (* b d)))

prune621.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 24.5b

localize35.0ms

Local error

Found 4 expressions with local error:

30.8b	(sqrt (+ (* c c) (* d d)))
30.8b	(sqrt (+ (* c c) (* d d)))
16.4b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
0.7b	(+ (* a c) (* b d))

rewrite92.0ms

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

53.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
14.0ms	(+ (* a c) (* b d))
12.0ms	(sqrt (+ (* c c) (* d d)))
11.0ms	(sqrt (+ (* c c) (* d d)))

series305.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

159.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
53.0ms	(sqrt (+ (* c c) (* d d)))
48.0ms	(+ (* a c) (* b d))
45.0ms	(sqrt (+ (* c c) (* d d)))

simplify3.4s

Counts

77 → 100

Calls

77 calls:

Slowest

403.0ms	(- (* (* a c) (* a c)) (* (* b d) (* b d)))
321.0ms	(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
317.0ms	(sqrt (+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d)))))
276.0ms	(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
224.0ms	(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 22.5b

localize43.0ms

Local error

Found 4 expressions with local error:

30.8b	(sqrt (+ (* c c) (* d d)))
30.8b	(sqrt (+ (* c c) (* d d)))
16.5b	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
0.7b	(+ (* a c) (* b d))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
24×	`associate-r`
22×	`*-un-lft-identity` `times-frac`
20×	`add-cube-cbrt`
17×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
6×	`flip3-+` `sqrt-div` `flip-+` `add-log-exp`
5×	`unswap-sqr`
4×	`prod-exp` `insert-posit16`
3×	`associate-l`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `sum-log` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 98

Calls

4 calls:

Slowest

46.0ms	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
16.0ms	(+ (* a c) (* b d))
7.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

series321.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

163.0ms	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
64.0ms	(sqrt (+ (* c c) (* d d)))
48.0ms	(sqrt (+ (* c c) (* d d)))
45.0ms	(+ (* a c) (* b d))

simplify6.2s

Counts

78 → 110

Calls

78 calls:

Slowest

588.0ms	(* (exp (* a c)) (exp (* b d)))
417.0ms	(* (+ (pow (* a c) 3) (pow (* b d) 3)) (/ 1 (sqrt (+ (* c c) (* d d)))))
357.0ms	(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
336.0ms	(* (+ (pow (* a c) 3) (pow (* b d) 3)) 1)
332.0ms	(* (+ (* (* a c) (* a c)) (- (* (* b d) (* b d)) (* (* a c) (* b d)))) (sqrt (+ (* c c) (* d d))))

prune1.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 22.5b

localize26.0ms

Local error

Found 3 expressions with local error:

24.7b	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))
0.7b	(+ (* a c) (* b d))
0.5b	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 129

Calls

3 calls:

Slowest

39.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))
16.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
10.0ms	(+ (* a c) (* b d))

series291.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

172.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
72.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))
48.0ms	(+ (* a c) (* b d))

simplify11.7s

Counts

154 → 138

Calls

154 calls:

Slowest

513.0ms	(/ (sqrt 1) (/ (+ (* c c) (* d d)) (+ (pow (* a c) 3) (pow (* b d) 3))))
447.0ms	(/ (* (cbrt 1) (cbrt 1)) (/ (+ (* c c) (* d d)) (+ (pow (* a c) 3) (pow (* b d) 3))))
436.0ms	(/ (* (* 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)))))
365.0ms	(/ (* (cbrt 1) (cbrt 1)) (/ (+ (* c c) (* d d)) (- (* (* a c) (* a c)) (* (* b d) (* b d)))))
334.0ms	(/ (* (* 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)))))

prune1.4s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 22.5b

regimes478.0ms

Accuracy

0% (2.7b remaining)

Error of 26.2b against oracle of 23.5b and baseline of 26.2b

bsearch3.0ms

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.1s

8453×

body

valid