Details

sample182.0ms

Algorithm

intervals

Results

73.0ms	71×	body	1280	valid
56.0ms	59×	body	640	valid
23.0ms	28×	body	2560	valid
7.0ms	68×	body	80	valid
6.0ms	15×	body	320	valid
4.0ms	15×	body	160	valid

simplify21.0ms

Counts: 1 → 1

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.9b

localize18.0ms

Local error

Found 3 expressions with local error:

15.7b	(sqrt (+ (* x x) 1))
2.4b	(log (+ x (sqrt (+ (* x x) 1))))
1.1b	(+ x (sqrt (+ (* x x) 1)))

rewrite40.0ms

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

21.0ms	(+ x (sqrt (+ (* x x) 1)))
11.0ms	(log (+ x (sqrt (+ (* x x) 1))))
7.0ms	(sqrt (+ (* x x) 1))

series256.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

125.0ms	(log (+ x (sqrt (+ (* x x) 1))))
86.0ms	(+ x (sqrt (+ (* x x) 1)))
44.0ms	(sqrt (+ (* x x) 1))

simplify755.0ms

Counts: 54 → 54

prune433.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

20.7b	(- (* 3/40 (pow x 5)) (* (* 1/6 (* x x)) x))
0.2b	(* 1/6 (* x x))
0.1b	(* (* 1/6 (* x x)) x)
0.0b	(* 3/40 (pow x 5))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
20×	`add-cbrt-cube`
18×	`pow1`
15×	`add-sqr-sqrt`
12×	`prod-exp`
11×	`associate-r`
10×	`cbrt-unprod`
9×	`*-un-lft-identity` `pow-prod-down` `add-cube-cbrt`
7×	`associate-l`
6×	`add-log-exp`
4×	`unpow-prod-down` `insert-posit16` `unswap-sqr`
3×	`*-commutative`
2×	`sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `pow-exp` `flip--`

Counts

4 → 81

Calls

4 calls:

Slowest

72.0ms	(* (* 1/6 (* x x)) x)
16.0ms	(* 3/40 (pow x 5))
14.0ms	(* 1/6 (* x x))
9.0ms	(- (* 3/40 (pow x 5)) (* (* 1/6 (* x x)) x))

series435.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

229.0ms	(- (* 3/40 (pow x 5)) (* (* 1/6 (* x x)) x))
91.0ms	(* 3/40 (pow x 5))
62.0ms	(* (* 1/6 (* x x)) x)
52.0ms	(* 1/6 (* x x))

simplify1.6s

Counts: 93 → 93

prune959.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

22.4b	(- (* 3/40 (pow x 5)) (* (log (exp (* 1/6 (* x x)))) x))
1.7b	(log (exp (* 1/6 (* x x))))
0.2b	(* 1/6 (* x x))
0.0b	(* 3/40 (pow x 5))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
14×	`add-exp-log`
11×	`add-cbrt-cube`
10×	`pow1`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`associate-r`
7×	`add-log-exp`
6×	`associate-l` `prod-exp`
4×	`unpow-prod-down` `cbrt-unprod` `insert-posit16` `unswap-sqr`
3×	`log-prod` `pow-prod-down` `log-pow`
2×	`*-commutative` `sqr-pow`
1×	`pow-to-exp` `exp-prod` `sub-neg` `flip3--` `exp-to-pow` `diff-log` `rem-log-exp` `pow-exp` `flip--`

Counts

4 → 74

Calls

4 calls:

Slowest

26.0ms	(* 1/6 (* x x))
16.0ms	(* 3/40 (pow x 5))
14.0ms	(log (exp (* 1/6 (* x x))))
13.0ms	(- (* 3/40 (pow x 5)) (* (log (exp (* 1/6 (* x x)))) x))

series366.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

196.0ms	(- (* 3/40 (pow x 5)) (* (log (exp (* 1/6 (* x x)))) x))
75.0ms	(* 3/40 (pow x 5))
47.0ms	(* 1/6 (* x x))
47.0ms	(log (exp (* 1/6 (* x x))))

simplify1.2s

Counts: 86 → 86

prune1.0s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

17.9b	(- (- (/ 1/8 (* (* x x) x)) (/ 1/2 x)) (/ 1/16 (pow x 5)))
12.6b	(log (- (- (/ 1/8 (* (* x x) x)) (/ 1/2 x)) (/ 1/16 (pow x 5))))
0.4b	(/ 1/8 (* (* x x) x))
0.1b	(* (* x x) x)

rewrite499.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

Slowest

335.0ms	(- (- (/ 1/8 (* (* x x) x)) (/ 1/2 x)) (/ 1/16 (pow x 5)))
126.0ms	(log (- (- (/ 1/8 (* (* x x) x)) (/ 1/2 x)) (/ 1/16 (pow x 5))))
22.0ms	(* (* x x) x)
13.0ms	(/ 1/8 (* (* x x) x))

series322.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

150.0ms	(log (- (- (/ 1/8 (* (* x x) x)) (/ 1/2 x)) (/ 1/16 (pow x 5))))
75.0ms	(- (- (/ 1/8 (* (* x x) x)) (/ 1/2 x)) (/ 1/16 (pow x 5)))
59.0ms	(/ 1/8 (* (* x x) x))
37.0ms	(* (* x x) x)

simplify2.7s

Counts: 115 → 115

prune1.2s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes59.0ms

Accuracy

100% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 30.8b

bsearch164.0ms

end0.0ms

sample4.5s

Algorithm

intervals

Results

2.2s	2376×	body	1280	valid
988.0ms	1536×	body	640	valid
567.0ms	771×	body	2560	valid
266.0ms	781×	body	320	valid
238.0ms	2102×	body	80	valid
112.0ms	434×	body	160	valid