Details

sample34.0ms

Algorithm

intervals

Results

21.0ms

267×

body

valid

simplify17.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

17.0ms

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.8b

localize34.0ms

Local error

Found 2 expressions with local error:

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

rewrite60.0ms

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

46.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
13.0ms	(+ (* a c) (* b d))

series152.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

102.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
50.0ms	(+ (* a c) (* b d))

simplify1.7s

Counts

36 → 50

Calls

36 calls:

Slowest

362.0ms	(- (* (* a c) (* a c)) (* (* b d) (* b d)))
252.0ms	(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))
240.0ms	(/ (* (* (+ (* a c) (* b d)) (+ (* a c) (* b d))) (+ (* a c) (* b d))) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))))
210.0ms	(+ (pow (* a c) 3) (pow (* b d) 3))
165.0ms	(* (exp (* a c)) (exp (* b d)))

prune528.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 24.3b

localize52.0ms

Local error

Found 4 expressions with local error:

25.6b	(sqrt (+ (* c c) (* d d)))
25.6b	(sqrt (+ (* c c) (* d d)))
16.3b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
0.5b	(+ (* a c) (* b d))

rewrite83.0ms

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

51.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
12.0ms	(sqrt (+ (* c c) (* d d)))
12.0ms	(sqrt (+ (* c c) (* d d)))
7.0ms	(+ (* a c) (* b d))

series321.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

158.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
62.0ms	(+ (* a c) (* b d))
51.0ms	(sqrt (+ (* c c) (* d d)))
50.0ms	(sqrt (+ (* c c) (* d d)))

simplify3.3s

Counts

77 → 100

Calls

77 calls:

Slowest

362.0ms	(- (* (* a c) (* a c)) (* (* b d) (* b d)))
287.0ms	(sqrt (+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d)))))
269.0ms	(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
259.0ms	(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
252.0ms	(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))

prune1.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 21.0b

localize54.0ms

Local error

Found 4 expressions with local error:

25.6b	(sqrt (+ (* c c) (* d d)))
25.6b	(sqrt (+ (* c c) (* d d)))
16.4b	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
0.5b	(+ (* a c) (* b d))

rewrite71.0ms

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

43.0ms	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
14.0ms	(+ (* a c) (* b d))
6.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

series309.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

146.0ms	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
61.0ms	(sqrt (+ (* c c) (* d d)))
56.0ms	(sqrt (+ (* c c) (* d d)))
45.0ms	(+ (* a c) (* b d))

simplify5.7s

Counts

78 → 110

Calls

78 calls:

Slowest

494.0ms	(* (+ (pow (* a c) 3) (pow (* b d) 3)) (/ 1 (sqrt (+ (* c c) (* d d)))))
371.0ms	(* (- (* (* a c) (* a c)) (* (* b d) (* b d))) (/ 1 (sqrt (+ (* c c) (* d d)))))
327.0ms	(sqrt (+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d)))))
326.0ms	(* (- (* (* a c) (* a c)) (* (* b d) (* b d))) 1)
317.0ms	(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))

prune1.3s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 21.0b

localize33.0ms

Local error

Found 4 expressions with local error:

25.6b	(sqrt (+ (* c c) (* d d)))
25.6b	(sqrt (+ (* c c) (* d d)))
16.3b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
0.5b	(+ (* a c) (* b d))

rewrite75.0ms

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

40.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
14.0ms	(+ (* a c) (* b d))
13.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

series321.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

162.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
67.0ms	(sqrt (+ (* c c) (* d d)))
50.0ms	(sqrt (+ (* c c) (* d d)))
41.0ms	(+ (* a c) (* b d))

simplify3.5s

Counts

77 → 100

Calls

77 calls:

Slowest

418.0ms	(- (* (* a c) (* a c)) (* (* b d) (* b d)))
346.0ms	(sqrt (+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d)))))
301.0ms	(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
290.0ms	(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
228.0ms	(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))

prune1.3s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 21.0b

regimes597.0ms

Accuracy

4.5% (2.4b remaining)

Error of 25.6b against oracle of 23.2b and baseline of 25.7b

bsearch65.0ms

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.2s

8461×

body

valid