Details

sample36.0ms

Algorithm

intervals

Results

19.0ms

271×

body

valid

simplify16.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.7b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
1.2b	(+ (* a c) (* b d))
24.2b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
4×	`flip3-+` `flip-+`
3×	`pow1` `associate-/r` `associate-/l`
2×	`+-commutative` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 53

Calls

3 calls:

18.0ms	(+ (* c c) (* d d))
27.0ms	(+ (* a c) (* b d))
34.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series214.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(+ (* c c) (* d d))
48.0ms	(+ (* a c) (* b d))
116.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify1.8s

Counts: 62 → 62

prune283.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 24.0b

localize28.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ (* a c) (* b d))
15.7b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
26.0b	(sqrt (+ (* c c) (* d d)))
26.0b	(sqrt (+ (* c c) (* d d)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

8.0ms	(+ (* a c) (* b d))
57.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
8.0ms	(sqrt (+ (* c c) (* d d)))
11.0ms	(sqrt (+ (* c c) (* d d)))

series290.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(+ (* a c) (* b d))
143.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
55.0ms	(sqrt (+ (* c c) (* d d)))
45.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.3s

Counts: 96 → 96

prune383.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 21.8b

localize31.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ (* a c) (* b d))
15.8b	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
26.0b	(sqrt (+ (* c c) (* d d)))
26.0b	(sqrt (+ (* c c) (* d d)))

rewrite140.0ms

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`
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` `1-exp` `associate-r/` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 94

Calls

4 calls:

14.0ms	(+ (* a c) (* b d))
100.0ms	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
8.0ms	(sqrt (+ (* c c) (* d d)))
12.0ms	(sqrt (+ (* c c) (* d d)))

series322.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+ (* a c) (* b d))
167.0ms	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
52.0ms	(sqrt (+ (* c c) (* d d)))
62.0ms	(sqrt (+ (* c c) (* d d)))

simplify878.0ms

Counts: 106 → 106

prune370.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 21.8b

localize22.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ (* a c) (* b d))
15.7b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
26.0b	(sqrt (+ (* c c) (* d d)))
26.0b	(sqrt (+ (* c c) (* d d)))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

18.0ms	(+ (* a c) (* b d))
56.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
12.0ms	(sqrt (+ (* c c) (* d d)))
8.0ms	(sqrt (+ (* c c) (* d d)))

series266.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ (* a c) (* b d))
136.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
39.0ms	(sqrt (+ (* c c) (* d d)))
54.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.2s

Counts: 96 → 96

prune398.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 21.8b

regimes680.0ms

Accuracy

25% (2.2b remaining)

Error of 25.2b against oracle of 23.1b and baseline of 26.0b

bsearch2.0ms

simplify4.1s

end0.0ms

sample994.0ms

Algorithm

intervals

Results

614.0ms

8494×

body

valid