Details

sample31.0ms

Algorithm

intervals

Results

20.0ms

260×

body

valid

simplify15.0ms

Calls

1 calls:

Slowest

15.0ms

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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.8b

localize35.0ms

Local error

Found 3 expressions with local error:

27.8b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
0.5b	(+ (* a c) (* b d))
0.0b	(+ (* c c) (* d d))

rewrite17.0ms

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

12.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
2.0ms	(+ (* a c) (* b d))
2.0ms	(+ (* c c) (* d d))

series125.0ms

Calls

3 calls:

Slowest

79.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
29.0ms	(+ (* a c) (* b d))
16.0ms	(+ (* c c) (* d d))

simplify1.3s

Calls

40 calls:

Slowest

299.0ms	(- (* (* a c) (* a c)) (* (* b d) (* b d)))
206.0ms	(/ (* (* (+ (* a c) (* b d)) (+ (* a c) (* b d))) (+ (* a c) (* b d))) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))))
186.0ms	(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))
139.0ms	(+ (pow (* a c) 3) (pow (* b d) 3))
48.0ms	(/ (* (cbrt (+ (* a c) (* b d))) (cbrt (+ (* a c) (* b d)))) (* (cbrt (+ (* c c) (* d d))) (cbrt (+ (* c c) (* d d)))))

prune660.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 27.4b

localize15.0ms

Local error

Found 4 expressions with local error:

33.3b	(sqrt (+ (* c c) (* d d)))
33.3b	(sqrt (+ (* c c) (* d d)))
16.2b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
0.5b	(+ (* a c) (* b d))

rewrite23.0ms

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))))
5.0ms	(sqrt (+ (* c c) (* d d)))
2.0ms	(+ (* a c) (* b d))
2.0ms	(sqrt (+ (* c c) (* d d)))

series169.0ms

Calls

4 calls:

Slowest

96.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
29.0ms	(+ (* a c) (* b d))
25.0ms	(sqrt (+ (* c c) (* d d)))
18.0ms	(sqrt (+ (* c c) (* d d)))

simplify2.2s

Calls

75 calls:

Slowest

290.0ms	(- (* (* a c) (* a c)) (* (* b d) (* b d)))
231.0ms	(sqrt (+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d)))))
189.0ms	(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))
164.0ms	(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))
139.0ms	(/ (* (* (+ (* 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)))))

prune842.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 25.7b

localize8.0ms

Local error

Found 4 expressions with local error:

33.3b	(sqrt (+ (* c c) (* d d)))
33.3b	(sqrt (+ (* c c) (* d d)))
16.3b	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
0.5b	(+ (* a c) (* b d))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`add-cbrt-cube` `sqrt-div` `add-exp-log` `associate-/l*` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`pow1` `insert-posit16`
3×	`associate-/r*`
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	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
3.0ms	(+ (* a c) (* b d))
2.0ms	(sqrt (+ (* c c) (* d d)))
2.0ms	(sqrt (+ (* c c) (* d d)))

series109.0ms

Calls

4 calls:

Slowest

47.0ms	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
25.0ms	(+ (* a c) (* b d))
19.0ms	(sqrt (+ (* c c) (* d d)))
18.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.6s

Calls

75 calls:

Slowest

220.0ms	(+ (* (* a c) (* a c)) (- (* (* b d) (* b d)) (* (* a c) (* b d))))
141.0ms	(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))
141.0ms	(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))
139.0ms	(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))
109.0ms	(/ (* (* (sqrt (+ (* c c) (* d d))) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d)))) (* (* (+ (* a c) (* b d)) (+ (* a c) (* b d))) (+ (* a c) (* b d))))

prune883.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 25.7b

localize8.0ms

Local error

Found 4 expressions with local error:

33.3b	(sqrt (+ (* c c) (* d d)))
33.3b	(sqrt (+ (* c c) (* d d)))
16.3b	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
0.5b	(+ (* a c) (* b d))

rewrite16.0ms

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

8.0ms	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
3.0ms	(+ (* a c) (* b d))
2.0ms	(sqrt (+ (* c c) (* d d)))
2.0ms	(sqrt (+ (* c c) (* d d)))

series128.0ms

Calls

4 calls:

Slowest

65.0ms	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
23.0ms	(+ (* a c) (* b d))
21.0ms	(sqrt (+ (* c c) (* d d)))
18.0ms	(sqrt (+ (* c c) (* d d)))

simplify2.2s

Calls

45 calls:

Slowest

248.0ms	(* (+ (pow (* a c) 3) (pow (* b d) 3)) 1)
196.0ms	(* (+ (pow (* a c) 3) (pow (* b d) 3)) (/ 1 (sqrt (+ (* c c) (* d d)))))
192.0ms	(* (- (* (* a c) (* a c)) (* (* b d) (* b d))) 1)
189.0ms	(* (- (* (* a c) (* a c)) (* (* b d) (* b d))) (/ 1 (sqrt (+ (* c c) (* d d)))))
175.0ms	(* (+ (* (* a c) (* a c)) (- (* (* b d) (* b d)) (* (* a c) (* b d)))) (sqrt (+ (* c c) (* d d))))

prune718.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 25.7b

regimes317.0ms

Accuracy

21.7% (2.0b remaining)

Error of 25.1b against oracle of 23.1b and baseline of 25.7b

bsearch6.0ms

end0.0ms

sample1.3s

Algorithm

intervals

Results

807.0ms

8465×

body

valid