Details

sample59.0ms

Algorithm

intervals

Results

40.0ms

270×

body

valid

simplify18.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

18.0ms

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.8b

localize40.0ms

Local error

Found 2 expressions with local error:

22.8b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
0.9b	(+ (* a c) (* b 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` `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

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

series176.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

117.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
59.0ms	(+ (* a c) (* b d))

simplify4.1s

Counts

61 → 50

Calls

61 calls:

Slowest

713.0ms	(/ (+ (* a c) (* b d)) (+ (pow (* c c) 3) (pow (* d d) 3)))
373.0ms	(- (* (* a c) (* a c)) (* (* b d) (* b d)))
321.0ms	(/ (* (* (+ (* a c) (* b d)) (+ (* a c) (* b d))) (+ (* a c) (* b d))) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))))
285.0ms	(* (+ (* c c) (* d d)) (- (* a c) (* b d)))
255.0ms	(/ (+ (* a c) (* b d)) (- (* (* c c) (* c c)) (* (* d d) (* d d))))

prune599.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 22.4b

localize55.0ms

Local error

Found 4 expressions with local error:

24.7b	(sqrt (+ (* c c) (* d d)))
24.7b	(sqrt (+ (* c c) (* d d)))
16.0b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
0.9b	(+ (* 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

48.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
12.0ms	(sqrt (+ (* c c) (* d d)))
12.0ms	(sqrt (+ (* c c) (* d d)))
10.0ms	(+ (* a c) (* b d))

series332.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

163.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
63.0ms	(+ (* a c) (* b d))
55.0ms	(sqrt (+ (* c c) (* d d)))
51.0ms	(sqrt (+ (* c c) (* d d)))

simplify6.2s

Counts

126 → 100

Calls

126 calls:

Slowest

371.0ms	(- (* (* a c) (* a c)) (* (* b d) (* b d)))
353.0ms	(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
335.0ms	(sqrt (+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d)))))
310.0ms	(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
295.0ms	(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 18.7b

localize50.0ms

Local error

Found 3 expressions with local error:

22.5b	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))
0.9b	(+ (* a c) (* b d))
0.5b	(/ 1 (+ (* c c) (* d d)))

rewrite71.0ms

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×	`flip3-+` `flip-+` `add-log-exp`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`associate-/r` `associate-l` `insert-posit16` `associate-/l` `unswap-sqr`
2×	`frac-times` `cbrt-undiv` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Counts

3 → 89

Calls

3 calls:

Slowest

35.0ms	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))
25.0ms	(/ 1 (+ (* c c) (* d d)))
9.0ms	(+ (* a c) (* b d))

series214.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

117.0ms	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))
55.0ms	(/ 1 (+ (* c c) (* d d)))
42.0ms	(+ (* a c) (* b d))

simplify10.9s

Counts

111 → 98

Calls

111 calls:

Slowest

550.0ms	(/ (* (* 1 1) 1) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))))
435.0ms	(* (+ (pow (* a c) 3) (pow (* b d) 3)) (/ 1 (+ (* c c) (* d d))))
400.0ms	(* (+ (* a c) (* b d)) (/ 1 (* (cbrt (+ (* c c) (* d d))) (cbrt (+ (* c c) (* d d))))))
372.0ms	(* (* (* (+ (* a c) (* b d)) (+ (* a c) (* b d))) (+ (* a c) (* b d))) (/ (* (* 1 1) 1) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d)))))
371.0ms	(* (+ (pow (* a c) 3) (pow (* b d) 3)) 1)

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 18.7b

localize36.0ms

Local error

Found 4 expressions with local error:

24.7b	(sqrt (+ (* c c) (* d d)))
24.7b	(sqrt (+ (* c c) (* d d)))
16.1b	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
0.9b	(+ (* a c) (* b d))

rewrite67.0ms

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`
5×	`flip3-+` `flip-+`
4×	`insert-posit16`
3×	`associate-/r*`
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

34.0ms	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
14.0ms	(+ (* a c) (* b d))
12.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

series282.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

113.0ms	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
67.0ms	(sqrt (+ (* c c) (* d d)))
63.0ms	(sqrt (+ (* c c) (* d d)))
38.0ms	(+ (* a c) (* b d))

simplify6.4s

Counts

126 → 100

Calls

126 calls:

Slowest

482.0ms	(* (* (/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d))) (/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))) (/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d))))
445.0ms	(* (+ (* a c) (* b d)) (sqrt (+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))))
355.0ms	(/ (sqrt (+ (* c c) (* d d))) (- (* (* a c) (* a c)) (* (* b d) (* b d))))
337.0ms	(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
337.0ms	(- (* (* a c) (* a c)) (* (* b d) (* b d)))

prune1.2s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 18.7b

regimes485.0ms

Accuracy

0% (2.9b remaining)

Error of 25.5b against oracle of 22.6b and baseline of 25.5b

bsearch2.0ms

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.5s

8528×

body

valid