Details

sample27.0ms

Algorithm

intervals

Results

12.0ms

274×

body

valid

simplify62.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.7b	(- (* b c) (* a d))
26.4b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite93.0ms

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`
3×	`pow1` `associate-/r` `associate-/l`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 55

Calls

3 calls:

16.0ms	(+ (* c c) (* d d))
16.0ms	(- (* b c) (* a d))
58.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series207.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(+ (* c c) (* d d))
47.0ms	(- (* b c) (* a d))
124.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify718.0ms

Counts: 64 → 64

prune265.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 26.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* b c) (* a d))
16.0b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
29.2b	(sqrt (+ (* c c) (* d d)))
29.2b	(sqrt (+ (* c c) (* d d)))

rewrite108.0ms

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`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 86

Calls

4 calls:

14.0ms	(- (* b c) (* a d))
65.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
12.0ms	(sqrt (+ (* c c) (* d d)))
12.0ms	(sqrt (+ (* c c) (* d d)))

series596.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* b c) (* a d))
168.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
39.0ms	(sqrt (+ (* c c) (* d d)))
340.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.6s

Counts: 98 → 98

prune405.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 23.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.6b	(/ 1 (+ (* c c) (* d d)))
0.7b	(- (* b c) (* a d))
26.2b	(* (- (* b c) (* a d)) (/ 1 (+ (* c c) (* d d))))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

9.0ms	(+ (* c c) (* d d))
18.0ms	(/ 1 (+ (* c c) (* d d)))
9.0ms	(- (* b c) (* a d))
74.0ms	(* (- (* b c) (* a d)) (/ 1 (+ (* c c) (* d d))))

series268.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+ (* c c) (* d d))
58.0ms	(/ 1 (+ (* c c) (* d d)))
51.0ms	(- (* b c) (* a d))
119.0ms	(* (- (* b c) (* a d)) (/ 1 (+ (* c c) (* d d))))

simplify831.0ms

Counts: 110 → 110

prune369.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 23.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* b c) (* a d))
26.2b	(* (- (* b c) (* a d)) (/ (/ 1 (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d)))))
29.2b	(sqrt (+ (* c c) (* d d)))
29.2b	(sqrt (+ (* c c) (* d d)))

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

270×	`times-frac`
173×	`add-sqr-sqrt`
150×	`associate-r`
141×	`sqrt-prod`
138×	`*-un-lft-identity`
134×	`add-cube-cbrt`
19×	`add-exp-log`
18×	`sqrt-div`
14×	`associate-/r/`
13×	`add-cbrt-cube`
12×	`unswap-sqr`
9×	`flip3-+` `flip-+`
8×	`pow1` `div-inv`
6×	`div-exp` `add-log-exp`
5×	`prod-exp`
3×	`cbrt-undiv` `flip3--` `associate-l` `flip--` `cbrt-unprod`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*l/`
1×	`sub-neg` `rec-exp` `diff-log` `1-exp` `associate-r/` `pow-prod-down` `-commutative`

Counts

4 → 229

Calls

4 calls:

10.0ms	(- (* b c) (* a d))
137.0ms	(* (- (* b c) (* a d)) (/ (/ 1 (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d)))))
9.0ms	(sqrt (+ (* c c) (* d d)))
9.0ms	(sqrt (+ (* c c) (* d d)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* b c) (* a d))
104.0ms	(* (- (* b c) (* a d)) (/ (/ 1 (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d)))))
43.0ms	(sqrt (+ (* c c) (* d d)))
57.0ms	(sqrt (+ (* c c) (* d d)))

simplify489.0ms

Counts: 241 → 241

prune801.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 23.2b

regimes190.0ms

Accuracy

-2.5% (2.7b remaining)

Error of 26.5b against oracle of 23.8b and baseline of 26.4b

bsearch0.0ms

simplify106.0ms

end0.0ms

sample941.0ms

Algorithm

intervals

Results

554.0ms

8506×

body

valid