Details

sample58.0ms

Algorithm

intervals

Results

39.0ms

273×

body

valid

simplify17.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

17.0ms

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.7b

localize38.0ms

Local error

Found 2 expressions with local error:

24.7b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
0.2b	(+ (* a c) (* b d))

rewrite65.0ms

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`

Counts

2 → 44

Calls

2 calls:

Slowest

54.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
10.0ms	(+ (* a c) (* b d))

series161.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

117.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
44.0ms	(+ (* a c) (* b d))

simplify1.9s

Counts

36 → 50

Calls

36 calls:

Slowest

391.0ms	(- (* (* a c) (* a c)) (* (* b d) (* b d)))
326.0ms	(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))
234.0ms	(/ (* (* (+ (* a c) (* b d)) (+ (* a c) (* b d))) (+ (* a c) (* b d))) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))))
214.0ms	(* (exp (* a c)) (exp (* b d)))
200.0ms	(+ (pow (* a c) 3) (pow (* b d) 3))

prune568.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 24.3b

localize48.0ms

Local error

Found 4 expressions with local error:

29.2b	(sqrt (+ (* c c) (* d d)))
29.2b	(sqrt (+ (* c c) (* d d)))
15.2b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
0.3b	(* (/ 1 (sqrt (+ (* c c) (* d d)))) (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))))

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
76×	`times-frac`
53×	`*-un-lft-identity`
47×	`add-cube-cbrt` `sqrt-prod`
28×	`add-exp-log`
24×	`associate-r` `associate-l`
18×	`add-cbrt-cube`
15×	`unswap-sqr`
10×	`sqrt-div`
9×	`div-exp`
8×	`pow1` `prod-exp`
6×	`associate-/r*` `flip3-+` `associate-/r/` `flip-+`
5×	`cbrt-undiv`
4×	`cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-/l/`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 164

Calls

4 calls:

Slowest

90.0ms	(* (/ 1 (sqrt (+ (* c c) (* d d)))) (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))))
48.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
6.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

series439.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

173.0ms	(* (/ 1 (sqrt (+ (* c c) (* d d)))) (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))))
146.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
67.0ms	(sqrt (+ (* c c) (* d d)))
53.0ms	(sqrt (+ (* c c) (* d d)))

simplify11.5s

Counts

169 → 176

Calls

169 calls:

Slowest

602.0ms	(/ 1 (sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d)))))
496.0ms	(* (/ (* (* 1 1) 1) (* (* (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))) (* (* (sqrt (+ (* c c) (* d d))) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))))
408.0ms	(* (* (* (/ 1 (sqrt (+ (* c c) (* d d)))) (/ 1 (sqrt (+ (* c c) (* d d))))) (/ 1 (sqrt (+ (* c c) (* d d))))) (/ (* (* (+ (* 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))))))
384.0ms	(- (* (* a c) (* a c)) (* (* b d) (* b d)))
338.0ms	(sqrt (+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d)))))

prune2.2s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 22.1b

localize24.0ms

Local error

Found 3 expressions with local error:

24.2b	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))
0.9b	(/ 1 (+ (* c c) (* d d)))
0.2b	(+ (* a c) (* b d))

rewrite70.0ms

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`

Counts

3 → 89

Calls

3 calls:

Slowest

41.0ms	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))
14.0ms	(/ 1 (+ (* c c) (* d d)))
13.0ms	(+ (* a c) (* b d))

series207.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

97.0ms	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))
63.0ms	(/ 1 (+ (* c c) (* d d)))
46.0ms	(+ (* a c) (* b d))

simplify5.5s

Counts

77 → 98

Calls

77 calls:

Slowest

599.0ms	(/ (* (* 1 1) 1) (* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d))))
475.0ms	(* (+ (pow (* a c) 3) (pow (* b d) 3)) (/ 1 (+ (* c c) (* d d))))
408.0ms	(* (- (* (* a c) (* a c)) (* (* b d) (* b d))) (/ 1 (+ (* c c) (* d d))))
378.0ms	(* (* (* (+ (* 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)))))
368.0ms	(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))

prune1.1s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 22.1b

localize23.0ms

Local error

Found 3 expressions with local error:

24.3b	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))
0.7b	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
0.2b	(+ (* a c) (* b d))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
55×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`associate-/r*`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp`
7×	`flip3-+` `flip-+`
6×	`div-inv` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
3×	`insert-posit16`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `associate-/l/`
1×	`+-commutative` `sum-log` `pow-flip` `inv-pow`

Counts

3 → 129

Calls

3 calls:

Slowest

45.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))
33.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
7.0ms	(+ (* a c) (* b d))

series275.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

159.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
69.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))
47.0ms	(+ (* a c) (* b d))

simplify11.3s

Counts

154 → 138

Calls

154 calls:

Slowest

476.0ms	(/ (sqrt 1) (/ (+ (* c c) (* d d)) (+ (pow (* a c) 3) (pow (* b d) 3))))
379.0ms	(/ (* (cbrt 1) (cbrt 1)) (/ (+ (* c c) (* d d)) (+ (pow (* a c) 3) (pow (* b d) 3))))
365.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (pow (* a c) 3) (pow (* b d) 3))))
348.0ms	(/ (* (* 1 1) 1) (* (* (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))) (/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))) (/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))))
323.0ms	(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (+ (* c c) (* d d))) (cbrt (+ (* c c) (* d d)))) (* (cbrt (+ (* a c) (* b d))) (cbrt (+ (* a c) (* b d))))))

prune1.5s

Pruning

11 alts after pruning (7 fresh and 4 done)

Merged error: 22.1b

regimes481.0ms

Accuracy

20.4% (2.0b remaining)

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

bsearch10.0ms

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.3s

8472×

body

valid