Details

sample28.0ms

Algorithm

intervals

Results

20.0ms

274×

body

valid

simplify8.0ms

Calls

1 calls:

Slowest

8.0ms

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.0b

localize37.0ms

Local error

Found 3 expressions with local error:

27.0b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
0.5b	(+ (* a c) (* b d))
0.0b	(+ (* c c) (* d d))

rewrite34.0ms

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`

Calls

3 calls:

Slowest

28.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
2.0ms	(+ (* a c) (* b d))
2.0ms	(+ (* c c) (* d d))

series122.0ms

Calls

3 calls:

Slowest

73.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
26.0ms	(+ (* a c) (* b d))
22.0ms	(+ (* c c) (* d d))

simplify1.6s

Calls

40 calls:

Slowest

366.0ms	(- (* (* a c) (* a c)) (* (* b d) (* b d)))
272.0ms	(/ (* (* (+ (* a c) (* b d)) (+ (* a c) (* b d))) (+ (* a c) (* b d))) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))))
258.0ms	(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))
111.0ms	(+ (pow (* a c) 3) (pow (* b d) 3))
65.0ms	(/ (* (cbrt (+ (* a c) (* b d))) (cbrt (+ (* a c) (* b d)))) (* (cbrt (+ (* c c) (* d d))) (cbrt (+ (* c c) (* d d)))))

prune724.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 26.5b

localize8.0ms

Local error

Found 4 expressions with local error:

28.3b	(sqrt (+ (* c c) (* d d)))
28.3b	(sqrt (+ (* c c) (* d d)))
18.5b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
0.5b	(+ (* a c) (* b d))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`associate-/r*` `add-cbrt-cube` `sqrt-div` `add-exp-log` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`pow1` `insert-posit16`
3×	`associate-/l*`
2×	`rem-sqrt-square` `pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `div-exp` `div-inv`

Calls

4 calls:

Slowest

11.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
2.0ms	(+ (* a c) (* b d))
2.0ms	(sqrt (+ (* c c) (* d d)))
2.0ms	(sqrt (+ (* c c) (* d d)))

series163.0ms

Calls

4 calls:

Slowest

85.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
33.0ms	(+ (* a c) (* b d))
23.0ms	(sqrt (+ (* c c) (* d d)))
22.0ms	(sqrt (+ (* c c) (* d d)))

simplify2.5s

Calls

75 calls:

Slowest

404.0ms	(- (* (* a c) (* a c)) (* (* b d) (* b d)))
210.0ms	(sqrt (+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d)))))
191.0ms	(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))
179.0ms	(+ (pow (* a c) 3) (pow (* b d) 3))
176.0ms	(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))

prune1.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 23.8b

localize12.0ms

Local error

Found 4 expressions with local error:

28.3b	(sqrt (+ (* c c) (* d d)))
28.3b	(sqrt (+ (* c c) (* d d)))
18.5b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
0.5b	(+ (* a c) (* b d))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`associate-/r*` `add-cbrt-cube` `sqrt-div` `add-exp-log` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`pow1` `insert-posit16`
3×	`associate-/l*`
2×	`rem-sqrt-square` `pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `div-exp` `div-inv`

Calls

4 calls:

Slowest

23.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
5.0ms	(+ (* a c) (* b d))
4.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series197.0ms

Calls

4 calls:

Slowest

104.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
40.0ms	(+ (* a c) (* b d))
31.0ms	(sqrt (+ (* c c) (* d d)))
22.0ms	(sqrt (+ (* c c) (* d d)))

simplify2.5s

Calls

75 calls:

Slowest

325.0ms	(- (* (* a c) (* a c)) (* (* b d) (* b d)))
227.0ms	(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))
211.0ms	(sqrt (+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d)))))
195.0ms	(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))
142.0ms	(/ (* (* (+ (* a c) (* b d)) (+ (* a c) (* b d))) (+ (* a c) (* b d))) (* (* (sqrt (+ (* c c) (* d d))) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d)))))

prune1.6s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 23.8b

localize7.0ms

Local error

Found 4 expressions with local error:

26.4b	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))
0.6b	(/ 1 (+ (* c c) (* d d)))
0.5b	(+ (* a c) (* b d))
0.0b	(+ (* c c) (* d d))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

7.0ms	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))
3.0ms	(+ (* c c) (* d d))
2.0ms	(+ (* a c) (* b d))
2.0ms	(/ 1 (+ (* c c) (* d d)))

series127.0ms

Calls

4 calls:

Slowest

67.0ms	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))
24.0ms	(+ (* a c) (* b d))
18.0ms	(/ 1 (+ (* c c) (* d d)))
17.0ms	(+ (* c c) (* d d))

simplify2.6s

Calls

40 calls:

Slowest

358.0ms	(* (+ (pow (* a c) 3) (pow (* b d) 3)) 1)
264.0ms	(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))
260.0ms	(* (- (* (* a c) (* a c)) (* (* b d) (* b d))) (/ 1 (+ (* c c) (* d d))))
244.0ms	(* (- (* (* a c) (* a c)) (* (* b d) (* b d))) 1)
234.0ms	(* (+ (pow (* a c) 3) (pow (* b d) 3)) (/ 1 (+ (* c c) (* d d))))

prune895.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 23.8b

regimes452.0ms

Accuracy

-5.5% (2.6b remaining)

Error of 26.0b against oracle of 23.4b and baseline of 25.8b

bsearch150.0ms

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.1s

8482×

body

valid