Details

sample42.0ms

Algorithm

intervals

Results

29.0ms

267×

body

valid

simplify17.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

17.0ms

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.6b

localize31.0ms

Local error

Found 3 expressions with local error:

23.6b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
0.5b	(+ (* a c) (* b d))
0.0b	(+ (* c c) (* d d))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 56

Calls

3 calls:

Slowest

50.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
15.0ms	(+ (* c c) (* d d))
15.0ms	(+ (* a c) (* b d))

series202.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

105.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
60.0ms	(+ (* a c) (* b d))
37.0ms	(+ (* c c) (* d d))

simplify2.1s

Counts

40 → 65

Calls

40 calls:

Slowest

335.0ms	(- (* (* a c) (* a c)) (* (* b d) (* b d)))
292.0ms	(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))
251.0ms	(/ (* (* (+ (* a c) (* b d)) (+ (* a c) (* b d))) (+ (* a c) (* b d))) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))))
212.0ms	(+ (pow (* a c) 3) (pow (* b d) 3))
181.0ms	(* (exp (* c c)) (exp (* d d)))

prune823.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 23.2b

localize48.0ms

Local error

Found 4 expressions with local error:

27.9b	(sqrt (+ (* c c) (* d d)))
27.9b	(sqrt (+ (* c c) (* d d)))
13.0b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
0.5b	(+ (* a c) (* b d))

rewrite79.0ms

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

46.0ms	(/ (+ (* 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))

series268.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

140.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
49.0ms	(+ (* a c) (* b d))
40.0ms	(sqrt (+ (* c c) (* d d)))
39.0ms	(sqrt (+ (* c c) (* d d)))

simplify3.5s

Counts

77 → 100

Calls

77 calls:

Slowest

404.0ms	(- (* (* a c) (* a c)) (* (* b d) (* b d)))
339.0ms	(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
277.0ms	(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
262.0ms	(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))
250.0ms	(sqrt (+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d)))))

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 21.6b

localize31.0ms

Local error

Found 4 expressions with local error:

27.9b	(sqrt (+ (* c c) (* d d)))
27.9b	(sqrt (+ (* c c) (* d d)))
13.2b	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
0.5b	(+ (* a c) (* b d))

rewrite75.0ms

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

45.0ms	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
15.0ms	(+ (* a c) (* b d))
6.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

series343.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

166.0ms	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
64.0ms	(sqrt (+ (* c c) (* d d)))
56.0ms	(+ (* a c) (* b d))
56.0ms	(sqrt (+ (* c c) (* d d)))

simplify5.5s

Counts

78 → 110

Calls

78 calls:

Slowest

502.0ms	(* (+ (pow (* a c) 3) (pow (* b d) 3)) (/ 1 (sqrt (+ (* c c) (* d d)))))
334.0ms	(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
323.0ms	(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
314.0ms	(* (- (* (* a c) (* a c)) (* (* b d) (* b d))) (/ 1 (sqrt (+ (* c c) (* d d)))))
305.0ms	(* (+ (pow (* a c) 3) (pow (* b d) 3)) 1)

prune1.6s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 21.6b

localize21.0ms

Local error

Found 4 expressions with local error:

23.3b	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))
0.5b	(/ 1 (+ (* c c) (* d d)))
0.5b	(+ (* a c) (* b d))
0.0b	(+ (* c c) (* d d))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`times-frac` `add-cube-cbrt`
17×	`add-exp-log`
15×	`associate-r`
11×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`flip3-+` `flip-+`
4×	`div-exp` `prod-exp` `associate-/r/` `insert-posit16`
3×	`associate-/r` `associate-l` `associate-/l` `unswap-sqr`
2×	`frac-times` `cbrt-undiv` `+-commutative` `rec-exp` `sum-log` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 101

Calls

4 calls:

Slowest

53.0ms	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))
15.0ms	(/ 1 (+ (* c c) (* d d)))
8.0ms	(+ (* c c) (* d d))
7.0ms	(+ (* a c) (* b d))

series293.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

116.0ms	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))
69.0ms	(/ 1 (+ (* c c) (* d d)))
64.0ms	(+ (* a c) (* b d))
43.0ms	(+ (* c c) (* d d))

simplify5.5s

Counts

81 → 113

Calls

81 calls:

Slowest

556.0ms	(/ (* (* 1 1) 1) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))))
437.0ms	(* (+ (pow (* a c) 3) (pow (* b d) 3)) (/ 1 (+ (* c c) (* d d))))
359.0ms	(* (- (* (* a c) (* a c)) (* (* b d) (* b d))) 1)
339.0ms	(* (+ (pow (* a c) 3) (pow (* b d) 3)) 1)
326.0ms	(* (- (* (* a c) (* a c)) (* (* b d) (* b d))) (/ 1 (+ (* c c) (* d d))))

prune1.4s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 21.6b

regimes407.0ms

Accuracy

0% (2.6b remaining)

Error of 26.1b against oracle of 23.5b and baseline of 26.1b

bsearch2.0ms

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.6s

8449×

body

valid