Details

sample54.0ms

Algorithm

intervals

Results

37.0ms

268×

body

valid

simplify13.0ms

Counts: 1 → 1

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.5b

localize25.0ms

Local error

Found 3 expressions with local error:

27.5b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
1.0b	(+ (* a c) (* b d))
0.0b	(+ (* c c) (* d d))

rewrite46.0ms

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×	`expm1-log1p-u` `pow1` `associate-/r` `insert-posit16` `log1p-expm1-u` `associate-/l`
2×	`+-commutative` `sum-log` `fma-def` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 64

Calls

3 calls:

Slowest

31.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
7.0ms	(+ (* c c) (* d d))
7.0ms	(+ (* a c) (* b d))

series197.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

101.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
57.0ms	(+ (* a c) (* b d))
39.0ms	(+ (* c c) (* d d))

simplify332.0ms

Counts: 83 → 73

prune727.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 27.1b

localize39.0ms

Local error

Found 4 expressions with local error:

27.6b	(sqrt (+ (* c c) (* d d)))
27.6b	(sqrt (+ (* c c) (* d d)))
17.5b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
1.0b	(+ (* a c) (* b d))

rewrite73.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `hypot-def` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `fma-def` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 99

Calls

4 calls:

Slowest

43.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
10.0ms	(sqrt (+ (* c c) (* d d)))
10.0ms	(sqrt (+ (* c c) (* d d)))
9.0ms	(+ (* a c) (* b d))

series277.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

153.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
46.0ms	(sqrt (+ (* c c) (* d d)))
39.0ms	(sqrt (+ (* c c) (* d d)))
39.0ms	(+ (* a c) (* b d))

simplify324.0ms

Counts: 134 → 111

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 24.6b

localize29.0ms

Local error

Found 4 expressions with local error:

27.6b	(sqrt (+ (* c c) (* d d)))
17.5b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
1.0b	(+ (* a c) (* b d))
0.1b	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (hypot c d))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
98×	`add-sqr-sqrt`
97×	`*-un-lft-identity` `add-cube-cbrt`
51×	`sqrt-prod`
27×	`associate-/l*`
12×	`sqrt-div`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r/`
9×	`associate-/r*`
8×	`flip3-+` `flip-+`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `fma-def` `sqrt-pow1` `pow1/2` `hypot-def`

Counts

4 → 197

Calls

4 calls:

Slowest

39.0ms	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (hypot c d))
27.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
7.0ms	(sqrt (+ (* c c) (* d d)))
7.0ms	(+ (* a c) (* b d))

series385.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

178.0ms	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (hypot c d))
129.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
42.0ms	(+ (* a c) (* b d))
37.0ms	(sqrt (+ (* c c) (* d d)))

simplify381.0ms

Counts: 303 → 209

prune2.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.0b

localize44.0ms

Local error

Found 4 expressions with local error:

17.6b	(/ (hypot c d) (fma a c (* b d)))
0.3b	(fma a c (* b d))
0.2b	(/ 1 (/ (hypot c d) (fma a c (* b d))))
0.1b	(/ (/ 1 (/ (hypot c d) (fma a c (* b d)))) (hypot c d))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

480×	`times-frac`
239×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
50×	`associate-/l*`
36×	`add-exp-log`
23×	`div-inv`
22×	`div-exp`
20×	`add-cbrt-cube`
19×	`associate-/r*`
10×	`cbrt-undiv`
5×	`pow1` `associate-/r/`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
1×	`fma-udef` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 323

Calls

4 calls:

Slowest

10.0ms	(/ (/ 1 (/ (hypot c d) (fma a c (* b d)))) (hypot c d))
6.0ms	(/ 1 (/ (hypot c d) (fma a c (* b d))))
4.0ms	(/ (hypot c d) (fma a c (* b d)))
0.0ms	(fma a c (* b d))

series559.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

217.0ms	(/ (/ 1 (/ (hypot c d) (fma a c (* b d)))) (hypot c d))
170.0ms	(/ 1 (/ (hypot c d) (fma a c (* b d))))
121.0ms	(/ (hypot c d) (fma a c (* b d)))
51.0ms	(fma a c (* b d))

simplify717.0ms

Counts: 517 → 335

prune2.9s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.0b

regimes236.0ms

Accuracy

33.6% (7.2b remaining)

Error of 13.1b against oracle of 5.9b and baseline of 16.8b

bsearch74.0ms

end0.0ms

sample1.3s

Algorithm

intervals

Results

1.0s

8453×

body

valid