Details

sample112.0ms

Algorithm

intervals

Results

45.0ms	55×	body	2560	valid
23.0ms	46×	body	1280	valid
20.0ms	48×	body	640	valid
6.0ms	23×	body	320	valid
6.0ms	69×	body	80	valid
3.0ms	15×	body	160	valid

simplify90.0ms

Counts: 1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize22.0ms

Local error

Found 2 expressions with local error:

16.2b	(/ (- 1 (cos x)) (* x x))
1.7b	(- 1 (cos x))

rewrite53.0ms

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

34.0ms	(/ (- 1 (cos x)) (* x x))
17.0ms	(- 1 (cos x))

series102.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

76.0ms	(/ (- 1 (cos x)) (* x x))
26.0ms	(- 1 (cos x))

simplify286.0ms

Counts: 90 → 69

prune460.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

16.1b	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
0.4b	(+ 1 (cos x))
0.2b	(* (sin x) (sin x))
0.2b	(/ (* (sin x) (sin x)) (+ 1 (cos x)))

rewrite67.0ms

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

21.0ms	(* (sin x) (sin x))
20.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
19.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
5.0ms	(+ 1 (cos x))

series158.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

72.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
51.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
23.0ms	(* (sin x) (sin x))
12.0ms	(+ 1 (cos x))

simplify568.0ms

Counts: 156 → 138

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize37.0ms

Local error

Found 3 expressions with local error:

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

rewrite66.0ms

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

35.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
15.0ms	(/ (sin x) x)
13.0ms	(/ (tan (/ x 2)) x)

series262.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

117.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
101.0ms	(/ (tan (/ x 2)) x)
43.0ms	(/ (sin x) x)

simplify517.0ms

Counts: 147 → 123

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize41.0ms

Local error

Found 3 expressions with local error:

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

rewrite39.0ms

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

18.0ms	(/ (* (sin x) (/ (tan (/ x 2)) x)) x)
14.0ms	(* (sin x) (/ (tan (/ x 2)) x))
6.0ms	(/ (tan (/ x 2)) x)

series317.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

139.0ms	(* (sin x) (/ (tan (/ x 2)) x))
103.0ms	(/ (* (sin x) (/ (tan (/ x 2)) x)) x)
74.0ms	(/ (tan (/ x 2)) x)

simplify459.0ms

Counts: 117 → 102

prune916.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

regimes48.0ms

Accuracy

0% (0.1b remaining)

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

bsearch1.0ms

end0.0ms

sample5.1s

Algorithm

intervals

Results

2.2s	1615×	body	2560	valid
1.2s	1314×	body	1280	valid
775.0ms	1460×	body	640	valid
340.0ms	907×	body	320	valid
260.0ms	2202×	body	80	valid
142.0ms	502×	body	160	valid