Details

sample46.0ms

Algorithm

intervals

Results

34.0ms

274×

body

valid

simplify8.0ms

Calls

1 calls:

Slowest

8.0ms

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.3b

localize18.0ms

Local error

Found 2 expressions with local error:

23.3b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
0.9b	(+ (* a c) (* b d))

rewrite14.0ms

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

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

series150.0ms

Calls

2 calls:

Slowest

99.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
51.0ms	(+ (* a c) (* b d))

simplify1.5s

Calls

36 calls:

Slowest

323.0ms	(/ (* (cbrt (+ (* a c) (* b d))) (cbrt (+ (* a c) (* b d)))) (* (cbrt (+ (* c c) (* d d))) (cbrt (+ (* c c) (* d d)))))
247.0ms	(- (* (* a c) (* a c)) (* (* b d) (* b d)))
208.0ms	(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))
196.0ms	(/ (* (* (+ (* a c) (* b d)) (+ (* a c) (* b d))) (+ (* a c) (* b d))) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))))
106.0ms	(+ (pow (* a c) 3) (pow (* b d) 3))

prune541.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 22.9b

localize17.0ms

Local error

Found 4 expressions with local error:

27.8b	(sqrt (+ (* c c) (* d d)))
27.8b	(sqrt (+ (* c c) (* d d)))
14.5b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
0.9b	(+ (* a c) (* b d))

rewrite31.0ms

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

19.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
4.0ms	(+ (* a c) (* b d))
4.0ms	(sqrt (+ (* c c) (* d d)))
3.0ms	(sqrt (+ (* c c) (* d d)))

series284.0ms

Calls

4 calls:

Slowest

146.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
53.0ms	(sqrt (+ (* c c) (* d d)))
45.0ms	(sqrt (+ (* c c) (* d d)))
40.0ms	(+ (* a c) (* b d))

simplify2.3s

Calls

75 calls:

Slowest

289.0ms	(- (* (* a c) (* a c)) (* (* b d) (* b d)))
239.0ms	(sqrt (+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d)))))
186.0ms	(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))
158.0ms	(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)))))

prune1.1s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 20.2b

localize1.0ms

Local error

Found 4 expressions with local error:

27.8b	(sqrt (+ (* c c) (* d d)))
27.8b	(sqrt (+ (* c c) (* d d)))
14.5b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
0.9b	(+ (* 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

12.0ms	(/ (+ (* 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)))

series249.0ms

Calls

4 calls:

Slowest

114.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
53.0ms	(+ (* a c) (* b d))
41.0ms	(sqrt (+ (* c c) (* d d)))
40.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.7s

Calls

75 calls:

Slowest

219.0ms	(- (* (* a c) (* a c)) (* (* b d) (* b d)))
153.0ms	(sqrt (+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d)))))
139.0ms	(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))
135.0ms	(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))
107.0ms	(+ (pow (* a c) 3) (pow (* b d) 3))

prune820.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 20.2b

localize8.0ms

Local error

Found 4 expressions with local error:

27.8b	(sqrt (+ (* c c) (* d d)))
27.8b	(sqrt (+ (* c c) (* d d)))
14.6b	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
0.9b	(+ (* a c) (* b d))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

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

series218.0ms

Calls

4 calls:

Slowest

104.0ms	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
40.0ms	(sqrt (+ (* c c) (* d d)))
36.0ms	(+ (* a c) (* b d))
36.0ms	(sqrt (+ (* c c) (* d d)))

simplify2.0s

Calls

45 calls:

Slowest

230.0ms	(* (+ (pow (* a c) 3) (pow (* b d) 3)) 1)
189.0ms	(* (+ (pow (* a c) 3) (pow (* b d) 3)) (/ 1 (sqrt (+ (* c c) (* d d)))))
180.0ms	(* (- (* (* a c) (* a c)) (* (* b d) (* b d))) 1)
171.0ms	(* (- (* (* a c) (* a c)) (* (* b d) (* b d))) (/ 1 (sqrt (+ (* c c) (* d d)))))
166.0ms	(* (+ (* (* a c) (* a c)) (- (* (* b d) (* b d)) (* (* a c) (* b d)))) (sqrt (+ (* c c) (* d d))))

prune674.0ms

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 20.2b

regimes406.0ms

Accuracy

0% (2.5b remaining)

Error of 25.6b against oracle of 23.0b and baseline of 25.6b

bsearch2.0ms

end0.0ms

sample959.0ms

Algorithm

intervals

Results

743.0ms

8451×

body

valid