Details

sample57.0ms

Algorithm

intervals

Results

41.0ms

274×

body

valid

simplify18.0ms

Calls

1 calls:

Slowest

18.0ms

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.7b

localize53.0ms

Local error

Found 3 expressions with local error:

25.7b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
0.4b	(+ (* a c) (* b d))
0.0b	(+ (* c c) (* d d))

rewrite60.0ms

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

35.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
14.0ms	(+ (* c c) (* d d))
10.0ms	(+ (* a c) (* b d))

series238.0ms

Calls

3 calls:

Slowest

141.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
49.0ms	(+ (* a c) (* b d))
48.0ms	(+ (* c c) (* d d))

simplify2.2s

Calls

40 calls:

Slowest

353.0ms	(- (* (* a c) (* a c)) (* (* b d) (* b d)))
327.0ms	(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))
311.0ms	(/ (* (* (+ (* a c) (* b d)) (+ (* a c) (* b d))) (+ (* a c) (* b d))) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))))
221.0ms	(+ (pow (* a c) 3) (pow (* b d) 3))
196.0ms	(* (exp (* a c)) (exp (* b d)))

prune737.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 25.3b

localize49.0ms

Local error

Found 4 expressions with local error:

27.5b	(sqrt (+ (* c c) (* d d)))
27.5b	(sqrt (+ (* c c) (* d d)))
16.1b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
0.4b	(+ (* a c) (* b d))

rewrite78.0ms

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

38.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
19.0ms	(sqrt (+ (* c c) (* d d)))
12.0ms	(sqrt (+ (* c c) (* d d)))
7.0ms	(+ (* a c) (* b d))

series312.0ms

Calls

4 calls:

Slowest

141.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
63.0ms	(sqrt (+ (* c c) (* d d)))
62.0ms	(sqrt (+ (* c c) (* d d)))
47.0ms	(+ (* a c) (* b d))

simplify4.0s

Calls

77 calls:

Slowest

590.0ms	(/ (* (* (+ (* 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)))))
409.0ms	(- (* (* a c) (* a c)) (* (* b d) (* b d)))
366.0ms	(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
363.0ms	(sqrt (+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d)))))
280.0ms	(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 23.7b

localize22.0ms

Local error

Found 4 expressions with local error:

25.5b	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))
0.5b	(/ 1 (+ (* c c) (* d d)))
0.4b	(+ (* a c) (* b d))
0.0b	(+ (* c c) (* d d))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

42.0ms	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))
15.0ms	(/ 1 (+ (* c c) (* d d)))
14.0ms	(+ (* a c) (* b d))
14.0ms	(+ (* c c) (* d d))

series251.0ms

Calls

4 calls:

Slowest

104.0ms	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))
65.0ms	(/ 1 (+ (* c c) (* d d)))
43.0ms	(+ (* a c) (* b d))
39.0ms	(+ (* c c) (* d d))

simplify5.9s

Calls

81 calls:

Slowest

600.0ms	(/ (* (* 1 1) 1) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))))
479.0ms	(* (+ (pow (* a c) 3) (pow (* b d) 3)) (/ 1 (+ (* c c) (* d d))))
413.0ms	(* (- (* (* a c) (* a c)) (* (* b d) (* b d))) (/ 1 (+ (* c c) (* d d))))
380.0ms	(* (* (* (+ (* 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)))))
329.0ms	(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))

prune1.2s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 23.7b

localize33.0ms

Local error

Found 4 expressions with local error:

27.5b	(sqrt (+ (* c c) (* d d)))
27.5b	(sqrt (+ (* c c) (* d d)))
16.2b	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
0.4b	(+ (* a c) (* b d))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
24×	`associate-r`
22×	`*-un-lft-identity` `times-frac`
20×	`add-cube-cbrt`
17×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
6×	`flip3-+` `sqrt-div` `flip-+` `add-log-exp`
5×	`unswap-sqr`
4×	`prod-exp` `insert-posit16`
3×	`associate-l`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `sum-log` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Calls

4 calls:

Slowest

47.0ms	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
14.0ms	(+ (* a c) (* b d))
12.0ms	(sqrt (+ (* c c) (* d d)))
11.0ms	(sqrt (+ (* c c) (* d d)))

series314.0ms

Calls

4 calls:

Slowest

157.0ms	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
62.0ms	(+ (* a c) (* b d))
49.0ms	(sqrt (+ (* c c) (* d d)))
46.0ms	(sqrt (+ (* c c) (* d d)))

simplify5.7s

Calls

78 calls:

Slowest

400.0ms	(* (+ (pow (* a c) 3) (pow (* b d) 3)) (/ 1 (sqrt (+ (* c c) (* d d)))))
357.0ms	(* (+ (* (* a c) (* a c)) (- (* (* b d) (* b d)) (* (* a c) (* b d)))) (sqrt (+ (* c c) (* d d))))
353.0ms	(sqrt (+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d)))))
342.0ms	(* (+ (pow (* a c) 3) (pow (* b d) 3)) 1)
320.0ms	(* (* (* (+ (* a c) (* b d)) (+ (* a c) (* b d))) (+ (* a c) (* b d))) (/ (* (* 1 1) 1) (* (* (sqrt (+ (* c c) (* d d))) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))))

prune1.3s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 23.7b

regimes522.0ms

Accuracy

22.6% (2.0b remaining)

Error of 25.1b against oracle of 23.1b and baseline of 25.6b

bsearch5.0ms

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.1s

8446×

body

valid