Details

sample34.0ms

Algorithm

intervals

Results

23.0ms

278×

body

valid

simplify17.0ms

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: 28.1b

localize40.0ms

Local error

Found 2 expressions with local error:

28.1b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
0.5b	(+ (* a c) (* b d))

rewrite34.0ms

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`

Calls

2 calls:

Slowest

27.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
7.0ms	(+ (* a c) (* b d))

series164.0ms

Calls

2 calls:

Slowest

105.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
59.0ms	(+ (* a c) (* b d))

simplify1.7s

Calls

36 calls:

Slowest

367.0ms	(- (* (* a c) (* a c)) (* (* b d) (* b d)))
299.0ms	(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))
259.0ms	(/ (* (* (+ (* a c) (* b d)) (+ (* a c) (* b d))) (+ (* a c) (* b d))) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))))
232.0ms	(+ (pow (* a c) 3) (pow (* b d) 3))
176.0ms	(* (exp (* a c)) (exp (* b d)))

prune619.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 27.6b

localize44.0ms

Local error

Found 4 expressions with local error:

32.0b	(sqrt (+ (* c c) (* d d)))
32.0b	(sqrt (+ (* c c) (* d d)))
15.0b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
0.5b	(+ (* a c) (* b 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`
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`

Calls

4 calls:

Slowest

31.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
7.0ms	(+ (* a c) (* b d))
6.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

series292.0ms

Calls

4 calls:

Slowest

128.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
64.0ms	(sqrt (+ (* c c) (* d d)))
58.0ms	(sqrt (+ (* c c) (* d d)))
42.0ms	(+ (* a c) (* b d))

simplify3.5s

Calls

77 calls:

Slowest

391.0ms	(- (* (* a c) (* a c)) (* (* b d) (* b d)))
309.0ms	(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
305.0ms	(sqrt (+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d)))))
291.0ms	(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))
272.0ms	(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))

prune1.4s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 26.2b

localize40.0ms

Local error

Found 3 expressions with local error:

28.3b	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))
0.5b	(+ (* a c) (* b d))
0.4b	(/ 1 (+ (* c c) (* d d)))

rewrite56.0ms

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`

Calls

3 calls:

Slowest

34.0ms	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))
12.0ms	(/ 1 (+ (* c c) (* d d)))
8.0ms	(+ (* a c) (* b d))

series238.0ms

Calls

3 calls:

Slowest

95.0ms	(/ 1 (+ (* c c) (* d d)))
84.0ms	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))
58.0ms	(+ (* a c) (* b d))

simplify5.2s

Calls

77 calls:

Slowest

555.0ms	(/ (* (* 1 1) 1) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))))
433.0ms	(* (+ (pow (* a c) 3) (pow (* b d) 3)) (/ 1 (+ (* c c) (* d d))))
349.0ms	(* (* (* (+ (* 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)))))
340.0ms	(* (- (* (* a c) (* a c)) (* (* b d) (* b d))) 1)
322.0ms	(* (+ (pow (* a c) 3) (pow (* b d) 3)) 1)

prune1.1s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 26.2b

localize56.0ms

Local error

Found 4 expressions with local error:

32.0b	(sqrt (+ (* c c) (* d d)))
32.0b	(sqrt (+ (* c c) (* d d)))
32.0b	(sqrt (+ (* c c) (* d d)))
32.0b	(sqrt (+ (* c c) (* d d)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `*-un-lft-identity` `sqrt-div` `add-cube-cbrt`
4×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `pow1/2` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`

Calls

4 calls:

Slowest

6.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

series208.0ms

Calls

4 calls:

Slowest

70.0ms	(sqrt (+ (* c c) (* d d)))
47.0ms	(sqrt (+ (* c c) (* d d)))
47.0ms	(sqrt (+ (* c c) (* d d)))
44.0ms	(sqrt (+ (* c c) (* d d)))

simplify2.8s

Calls

40 calls:

Slowest

692.0ms	(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
303.0ms	(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
288.0ms	(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
280.0ms	(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))
267.0ms	(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))

prune1.2s

Pruning

12 alts after pruning (8 fresh and 4 done)

Merged error: 26.2b

regimes568.0ms

Accuracy

0% (2.4b remaining)

Error of 25.5b against oracle of 23.1b and baseline of 25.5b

bsearch4.0ms

end0.0ms

sample1.3s

Algorithm

intervals

Results

1.1s

8476×

body

valid