Details

sample39.0ms

Algorithm

intervals

Results

27.0ms

265×

body

valid

simplify88.0ms

Counts: 1 → 1

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.4b

localize19.0ms

Local error

Found 3 expressions with local error:

25.4b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
0.5b	(- (* b c) (* a d))
0.0b	(+ (* c c) (* d d))

rewrite40.0ms

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`
3×	`expm1-log1p-u` `pow1` `associate-/r` `insert-posit16` `log1p-expm1-u` `associate-/l`
2×	`flip3-+` `flip3--` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `fma-def` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `div-inv`

Counts

3 → 67

Calls

3 calls:

Slowest

25.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
8.0ms	(- (* b c) (* a d))
7.0ms	(+ (* c c) (* d d))

series166.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

88.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
48.0ms	(- (* b c) (* a d))
30.0ms	(+ (* c c) (* d d))

simplify343.0ms

Counts: 90 → 76

prune718.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 25.0b

localize23.0ms

Local error

Found 4 expressions with local error:

27.5b	(sqrt (+ (* c c) (* d d)))
27.5b	(sqrt (+ (* c c) (* d d)))
17.1b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
0.5b	(- (* b c) (* a d))

rewrite46.0ms

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`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-/r/` `hypot-def` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `div-inv`

Counts

4 → 102

Calls

4 calls:

Slowest

21.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
10.0ms	(sqrt (+ (* c c) (* d d)))
7.0ms	(- (* b c) (* a d))
6.0ms	(sqrt (+ (* c c) (* d d)))

series237.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

114.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
45.0ms	(- (* b c) (* a d))
40.0ms	(sqrt (+ (* c c) (* d d)))
37.0ms	(sqrt (+ (* c c) (* d d)))

simplify332.0ms

Counts: 141 → 114

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 23.8b

localize24.0ms

Local error

Found 4 expressions with local error:

27.5b	(sqrt (+ (* c c) (* d d)))
27.5b	(sqrt (+ (* c c) (* d d)))
17.1b	(/ (fma b c (- (* a d))) (sqrt (+ (* c c) (* d d))))
0.5b	(fma b c (- (* a d)))

rewrite36.0ms

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`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `hypot-def`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `fma-udef` `div-inv`

Counts

4 → 93

Calls

4 calls:

Slowest

15.0ms	(sqrt (+ (* c c) (* d d)))
10.0ms	(/ (fma b c (- (* a d))) (sqrt (+ (* c c) (* d d))))
9.0ms	(sqrt (+ (* c c) (* d d)))
0.0ms	(fma b c (- (* a d)))

series309.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

147.0ms	(/ (fma b c (- (* a d))) (sqrt (+ (* c c) (* d d))))
59.0ms	(fma b c (- (* a d)))
57.0ms	(sqrt (+ (* c c) (* d d)))
46.0ms	(sqrt (+ (* c c) (* d d)))

simplify561.0ms

Counts: 128 → 105

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 23.8b

localize38.0ms

Local error

Found 4 expressions with local error:

27.5b	(sqrt (+ (* c c) (* d d)))
17.1b	(/ (fma b c (- (* a d))) (sqrt (+ (* c c) (* d d))))
0.5b	(fma b c (- (* a d)))
0.1b	(/ (/ (fma b c (- (* a d))) (sqrt (+ (* c c) (* d d)))) (hypot c d))

rewrite51.0ms

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*`
6×	`flip3-+` `flip-+` `div-inv`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef` `hypot-def` `associate-/l/`

Counts

4 → 191

Calls

4 calls:

Slowest

30.0ms	(/ (/ (fma b c (- (* a d))) (sqrt (+ (* c c) (* d d)))) (hypot c d))
10.0ms	(/ (fma b c (- (* a d))) (sqrt (+ (* c c) (* d d))))
6.0ms	(sqrt (+ (* c c) (* d d)))
0.0ms	(fma b c (- (* a d)))

series462.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

209.0ms	(/ (/ (fma b c (- (* a d))) (sqrt (+ (* c c) (* d d)))) (hypot c d))
147.0ms	(/ (fma b c (- (* a d))) (sqrt (+ (* c c) (* d d))))
57.0ms	(fma b c (- (* a d)))
50.0ms	(sqrt (+ (* c c) (* d d)))

simplify322.0ms

Counts: 297 → 203

prune1.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.3b

regimes572.0ms

Accuracy

37.6% (6.8b remaining)

Error of 12.8b against oracle of 6.0b and baseline of 16.9b

bsearch79.0ms

end0.0ms

sample1.0s

Algorithm

intervals

Results

821.0ms

8453×

body

valid