Details

sample116.0ms

Algorithm

intervals

Results

46.0ms	51×	body	2560	valid
22.0ms	38×	body	1280	valid
18.0ms	42×	body	640	valid
10.0ms	34×	body	320	valid
8.0ms	78×	body	80	valid
3.0ms	13×	body	160	valid

simplify61.0ms

Counts: 1 → 1

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.0b

localize24.0ms

Local error

Found 2 expressions with local error:

14.0b	(/ (- 1 (cos x)) (* x x))
1.5b	(- 1 (cos x))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`prod-diff`
7×	`add-cbrt-cube` `add-exp-log`
6×	`times-frac` `associate-/l*` `difference-of-squares`
4×	`add-log-exp`
3×	`fma-neg` `distribute-lft-out--`
2×	`expm1-log1p-u` `pow1` `cbrt-undiv` `flip3--` `div-exp` `insert-posit16` `log1p-expm1-u` `flip--` `associate-/l/`
1×	`clear-num` `associate-/r*` `sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

2 → 63

Calls

2 calls:

Slowest

35.0ms	(/ (- 1 (cos x)) (* x x))
7.0ms	(- 1 (cos x))

series86.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

66.0ms	(/ (- 1 (cos x)) (* x x))
20.0ms	(- 1 (cos x))

simplify960.0ms

Counts: 69 → 69

prune455.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

14.2b	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
0.4b	(+ 1 (cos x))
0.3b	(* (sin x) (sin x))
0.2b	(/ (* (sin x) (sin x)) (+ 1 (cos x)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-cbrt-cube` `add-exp-log`
25×	`*-un-lft-identity`
22×	`times-frac`
17×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
12×	`cbrt-undiv` `div-exp`
11×	`pow1` `associate-/l*`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-/r/` `add-log-exp`
5×	`associate-/r*` `distribute-lft-out`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`fma-def` `div-sub` `swap-sqr` `associate-r` `associate-l` `sqr-sin`
2×	`clear-num` `frac-2neg` `sin-mult` `associate-/l/`
1×	`pow2` `+-commutative` `sum-log` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `unswap-sqr`

Counts

4 → 126

Calls

4 calls:

Slowest

20.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
18.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
15.0ms	(* (sin x) (sin x))
8.0ms	(+ 1 (cos x))

series163.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

82.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
48.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
19.0ms	(* (sin x) (sin x))
14.0ms	(+ 1 (cos x))

simplify632.0ms

Counts: 138 → 138

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize37.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (tan (/ x 2)) x)
0.1b	(/ (sin x) x)
0.1b	(* (/ (sin x) x) (/ (tan (/ x 2)) x))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
40×	`times-frac`
33×	`*-un-lft-identity` `add-cube-cbrt`
19×	`add-cbrt-cube` `add-exp-log`
13×	`associate-r` `associate-l`
6×	`cbrt-undiv` `associate-/r` `div-exp` `associate-/l`
5×	`pow1`
4×	`prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`frac-times` `pow-prod-down` `associate-l/` `tan-quot` `associate-r/` `*-commutative` `associate-/l/`

Counts

3 → 114

Calls

3 calls:

Slowest

15.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
13.0ms	(/ (tan (/ x 2)) x)
9.0ms	(/ (sin x) x)

series219.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

127.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
56.0ms	(/ (tan (/ x 2)) x)
36.0ms	(/ (sin x) x)

simplify1.9s

Counts: 123 → 123

prune1.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (tan (/ x 2)) x)
0.2b	(* (sin x) (/ (tan (/ x 2)) x))
0.1b	(/ (* (sin x) (/ (tan (/ x 2)) x)) x)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
22×	`times-frac`
21×	`*-un-lft-identity` `add-cube-cbrt`
19×	`add-cbrt-cube` `add-exp-log`
13×	`associate-r`
6×	`cbrt-undiv` `associate-/r*` `div-exp`
5×	`pow1`
4×	`prod-exp` `cbrt-unprod` `associate-/l*`
3×	`expm1-log1p-u` `associate-l` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-*r/` `unswap-sqr` `associate-/l/`
1×	`pow-prod-down` `tan-quot` `*-commutative`

Counts

3 → 93

Calls

3 calls:

Slowest

25.0ms	(/ (* (sin x) (/ (tan (/ x 2)) x)) x)
16.0ms	(* (sin x) (/ (tan (/ x 2)) x))
6.0ms	(/ (tan (/ x 2)) x)

series265.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

101.0ms	(/ (* (sin x) (/ (tan (/ x 2)) x)) x)
91.0ms	(* (sin x) (/ (tan (/ x 2)) x))
74.0ms	(/ (tan (/ x 2)) x)

simplify1.9s

Counts: 102 → 102

prune819.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes62.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch2.0ms

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.2s	1533×	body	2560	valid
868.0ms	1245×	body	1280	valid
761.0ms	1503×	body	640	valid
355.0ms	2320×	body	80	valid
332.0ms	898×	body	320	valid
106.0ms	501×	body	160	valid