Details

sample98.0ms

Algorithm

intervals

Results

53.0ms	87×	body	1280	valid
18.0ms	51×	body	640	valid
7.0ms	16×	body	2560	valid
5.0ms	22×	body	320	valid
4.0ms	69×	body	80	valid
1.0ms	11×	body	160	valid

simplify11.0ms

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.2b

localize13.0ms

Local error

Found 3 expressions with local error:

11.9b	(sqrt (+ (* x x) 1))
2.6b	(log (+ x (sqrt (+ (* x x) 1))))
1.6b	(+ x (sqrt (+ (* x x) 1)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `add-log-exp`
4×	`log-prod` `add-exp-log`
3×	`flip3-+` `add-cbrt-cube` `sqrt-prod` `flip-+` `insert-posit16`
2×	`log-div` `sqrt-div` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `rem-log-exp` `log-pow`

Counts

3 → 45

Calls

3 calls:

Slowest

28.0ms	(log (+ x (sqrt (+ (* x x) 1))))
24.0ms	(+ x (sqrt (+ (* x x) 1)))
7.0ms	(sqrt (+ (* x x) 1))

series280.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

167.0ms	(log (+ x (sqrt (+ (* x x) 1))))
59.0ms	(+ x (sqrt (+ (* x x) 1)))
54.0ms	(sqrt (+ (* x x) 1))

simplify2.3s

Counts: 54 → 54

prune591.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

14.4b	(+ (* 3/40 (* (* x x) (* (* x x) x))) (- x (* (* (* x x) x) 1/6)))
0.1b	(* (* (* x x) x) 1/6)
0.1b	(* (* x x) x)
0.1b	(* (* x x) x)

rewrite291.0ms

Algorithm

rewrite-expression-head

Rules

51×	`pow1`
23×	`add-cbrt-cube` `add-exp-log`
12×	`pow-plus` `pow-prod-down` `prod-exp` `pow-prod-up` `cbrt-unprod`
9×	`add-sqr-sqrt` `associate-r` `add-log-exp`
7×	`*-un-lft-identity` `add-cube-cbrt`
4×	`pow2` `pow-sqr` `insert-posit16`
3×	`associate-l` `*-commutative`
2×	`associate-+r+` `sum-log` `pow3` `unswap-sqr`
1×	`+-commutative` `associate-+r-` `sub-neg` `flip3-+` `diff-log` `flip-+`

Counts

4 → 96

Calls

4 calls:

Slowest

177.0ms	(+ (* 3/40 (* (* x x) (* (* x x) x))) (- x (* (* (* x x) x) 1/6)))
54.0ms	(* (* (* x x) x) 1/6)
29.0ms	(* (* x x) x)
29.0ms	(* (* x x) x)

series250.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

103.0ms	(+ (* 3/40 (* (* x x) (* (* x x) x))) (- x (* (* (* x x) x) 1/6)))
54.0ms	(* (* (* x x) x) 1/6)
52.0ms	(* (* x x) x)
41.0ms	(* (* x x) x)

simplify1.7s

Counts: 108 → 108

prune782.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

12.4b	(log (+ x (+ x (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x)))))
0.2b	(/ -1/8 (* (* x x) x))
0.1b	(* (* x x) x)
0.0b	(+ (/ -1/8 (* (* x x) x)) (/ 1/2 x))

rewrite429.0ms

Algorithm

rewrite-expression-head

Rules

24×	`pow1`
19×	`*-un-lft-identity` `add-exp-log`
18×	`add-cbrt-cube`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt`
7×	`distribute-lft-out`
6×	`log-prod` `pow-plus` `prod-exp` `pow-prod-up` `cbrt-unprod` `add-log-exp`
4×	`insert-posit16`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-r` `pow-prod-down` `associate-/l*`
2×	`pow2` `log-div` `flip3-+` `pow-sqr` `flip-+`
1×	`+-commutative` `clear-num` `associate-/r` `sum-log` `frac-2neg` `rem-log-exp` `associate-l` `pow3` `frac-add` `log-pow` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

Slowest

329.0ms	(log (+ x (+ x (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x)))))
69.0ms	(+ (/ -1/8 (* (* x x) x)) (/ 1/2 x))
15.0ms	(* (* x x) x)
13.0ms	(/ -1/8 (* (* x x) x))

series338.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

122.0ms	(+ (/ -1/8 (* (* x x) x)) (/ 1/2 x))
115.0ms	(log (+ x (+ x (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x)))))
51.0ms	(* (* x x) x)
50.0ms	(/ -1/8 (* (* x x) x))

simplify2.2s

Counts: 97 → 97

prune793.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

21.5b	(- (/ -1/16 (* (* x x) (* (* x x) x))) (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x)))
14.8b	(log (- (/ -1/16 (* (* x x) (* (* x x) x))) (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x))))
0.2b	(/ -1/16 (* (* x x) (* (* x x) x)))
0.2b	(/ -1/8 (* (* x x) x))

rewrite564.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-exp-log`
42×	`add-cbrt-cube`
19×	`*-un-lft-identity`
18×	`prod-exp` `cbrt-unprod`
13×	`add-sqr-sqrt`
10×	`cbrt-undiv` `div-exp`
9×	`add-cube-cbrt` `add-log-exp`
6×	`log-prod` `times-frac` `frac-sub` `associate-/l*`
5×	`pow1` `log-div`
4×	`insert-posit16` `distribute-lft-out--`
2×	`clear-num` `associate-/r*` `frac-2neg` `flip3-+` `flip3--` `diff-log` `frac-add` `flip-+` `div-inv` `flip--` `distribute-lft-out` `difference-of-squares`
1×	`sum-log` `sub-neg` `rem-log-exp` `log-pow` `associate--r+`

Counts

4 → 98

Calls

4 calls:

Slowest

287.0ms	(- (/ -1/16 (* (* x x) (* (* x x) x))) (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x)))
200.0ms	(log (- (/ -1/16 (* (* x x) (* (* x x) x))) (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x))))
51.0ms	(/ -1/16 (* (* x x) (* (* x x) x)))
23.0ms	(/ -1/8 (* (* x x) x))

series316.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

137.0ms	(log (- (/ -1/16 (* (* x x) (* (* x x) x))) (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x))))
64.0ms	(- (/ -1/16 (* (* x x) (* (* x x) x))) (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x)))
60.0ms	(/ -1/16 (* (* x x) (* (* x x) x)))
54.0ms	(/ -1/8 (* (* x x) x))

simplify956.0ms

Counts: 110 → 110

prune849.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes85.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.6b

bsearch132.0ms

end0.0ms

sample4.5s

Algorithm

intervals

Results

2.0s	2326×	body	1280	valid
966.0ms	790×	body	2560	valid
904.0ms	1538×	body	640	valid
253.0ms	749×	body	320	valid
178.0ms	2201×	body	80	valid
111.0ms	396×	body	160	valid