Details

sample53.0ms

Algorithm

intervals

Results

29.0ms	256×	body	80	valid
10.0ms	256×	pre	80	true

simplify2.8s

Counts: 1 → 1

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.3b

localize26.0ms

Local error

Found 2 expressions with local error:

6.4b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.4b	(* (/ b a) (/ b a))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
40×	`times-frac`
31×	`*-un-lft-identity` `add-cube-cbrt`
14×	`add-cbrt-cube` `add-exp-log`
13×	`swap-sqr` `associate-r` `associate-l`
10×	`pow1`
4×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
3×	`sqrt-prod`
2×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow2` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

2 → 86

Calls

2 calls:

Slowest

25.0ms	(* (/ b a) (/ b a))
2.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series55.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

33.0ms	(* (/ b a) (/ b a))
22.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify1.2s

Counts: 92 → 92

prune971.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 6.3b

localize37.0ms

Local error

Found 4 expressions with local error:

6.4b	(sqrt (fabs (- 1 (* (/ (/ b (sqrt a)) a) (/ b (sqrt a))))))
0.3b	(/ (/ b (sqrt a)) a)
0.3b	(* (/ (/ b (sqrt a)) a) (/ b (sqrt a)))
0.2b	(/ b (sqrt a))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

317×	`times-frac`
218×	`add-sqr-sqrt`
170×	`*-un-lft-identity` `add-cube-cbrt`
94×	`sqrt-prod`
70×	`associate-l`
32×	`add-cbrt-cube` `add-exp-log`
25×	`associate-/l*`
22×	`associate-r`
13×	`cbrt-undiv` `div-exp`
12×	`unswap-sqr`
11×	`div-inv`
9×	`associate-/r*`
7×	`pow1`
6×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `associate-/l/`

Counts

4 → 298

Calls

4 calls:

Slowest

24.0ms	(* (/ (/ b (sqrt a)) a) (/ b (sqrt a)))
11.0ms	(/ (/ b (sqrt a)) a)
9.0ms	(/ b (sqrt a))
3.0ms	(sqrt (fabs (- 1 (* (/ (/ b (sqrt a)) a) (/ b (sqrt a))))))

series230.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

87.0ms	(/ (/ b (sqrt a)) a)
68.0ms	(/ b (sqrt a))
59.0ms	(* (/ (/ b (sqrt a)) a) (/ b (sqrt a)))
17.0ms	(sqrt (fabs (- 1 (* (/ (/ b (sqrt a)) a) (/ b (sqrt a))))))

simplify1.6s

Counts: 310 → 310

prune3.6s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 6.3b

localize38.0ms

Local error

Found 4 expressions with local error:

6.4b	(sqrt (fabs (- 1 (* (/ (sqrt b) 1) (* (/ (sqrt b) a) (/ b a))))))
1.4b	(* (/ (sqrt b) 1) (* (/ (sqrt b) a) (/ b a)))
0.3b	(* (/ (sqrt b) a) (/ b a))
0.3b	(/ (sqrt b) a)

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-exp-log`
73×	`add-sqr-sqrt`
70×	`times-frac`
59×	`add-cbrt-cube`
53×	`*-un-lft-identity` `add-cube-cbrt`
44×	`associate-l`
35×	`sqrt-prod`
31×	`prod-exp`
27×	`div-exp`
22×	`cbrt-unprod`
18×	`cbrt-undiv`
14×	`associate-r`
12×	`pow1`
6×	`frac-times` `associate-r/` `associate-/l` `unswap-sqr`
5×	`1-exp`
4×	`expm1-log1p-u` `pow-prod-down` `associate-*l/` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`associate-/r*`
2×	`*-commutative`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`

Counts

4 → 190

Calls

4 calls:

Slowest

61.0ms	(* (/ (sqrt b) 1) (* (/ (sqrt b) a) (/ b a)))
15.0ms	(* (/ (sqrt b) a) (/ b a))
5.0ms	(/ (sqrt b) a)
3.0ms	(sqrt (fabs (- 1 (* (/ (sqrt b) 1) (* (/ (sqrt b) a) (/ b a))))))

series235.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

86.0ms	(/ (sqrt b) a)
80.0ms	(* (/ (sqrt b) a) (/ b a))
47.0ms	(* (/ (sqrt b) 1) (* (/ (sqrt b) a) (/ b a)))
21.0ms	(sqrt (fabs (- 1 (* (/ (sqrt b) 1) (* (/ (sqrt b) a) (/ b a))))))

simplify891.0ms

Counts: 202 → 202

prune2.2s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 6.3b

localize34.0ms

Local error

Found 4 expressions with local error:

3.8b	(log (exp (* (/ b a) (/ b a))))
0.4b	(* (/ b a) (/ b a))
0.0b	(exp (* (/ b a) (/ b a)))
0.0b	(sqrt (fabs (- 1 (log (exp (* (/ b a) (/ b a)))))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
40×	`times-frac`
34×	`*-un-lft-identity` `add-cube-cbrt`
16×	`add-cbrt-cube` `add-exp-log`
13×	`pow1` `swap-sqr` `associate-r` `associate-l`
7×	`add-log-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `div-inv` `unswap-sqr`
3×	`log-prod` `log-pow` `sqrt-prod`
2×	`exp-prod` `exp-to-pow`
1×	`pow2` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `rem-log-exp` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `rem-exp-log`

Counts

4 → 116

Calls

4 calls:

Slowest

32.0ms	(* (/ b a) (/ b a))
8.0ms	(log (exp (* (/ b a) (/ b a))))
7.0ms	(exp (* (/ b a) (/ b a)))
2.0ms	(sqrt (fabs (- 1 (log (exp (* (/ b a) (/ b a)))))))

series130.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

45.0ms	(log (exp (* (/ b a) (/ b a))))
45.0ms	(* (/ b a) (/ b a))
27.0ms	(exp (* (/ b a) (/ b a)))
12.0ms	(sqrt (fabs (- 1 (log (exp (* (/ b a) (/ b a)))))))

simplify1.3s

Counts: 128 → 128

prune1.4s

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 6.3b

regimes113.0ms

Accuracy

0% (0.1b remaining)

Error of 7.8b against oracle of 7.7b and baseline of 7.8b

bsearch2.0ms

end0.0ms

sample1.4s

Algorithm

intervals

Results

831.0ms	8000×	body	80	valid
362.0ms	8000×	pre	80	true