Details

sample163.0ms

Algorithm

intervals

Results

67.0ms	55×	body	2560	valid
36.0ms	34×	body	1280	valid
25.0ms	45×	body	640	valid
15.0ms	42×	body	320	valid
8.0ms	73×	body	80	valid
2.0ms	7×	body	160	valid

simplify15.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	28
4	28
3	26
2	21
1	13
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.9b

localize11.0ms

Local error

Found 2 expressions with local error:

2.1b	(- 1 (cos x))
16.1b	(/ (- 1 (cos x)) (* x x))

rewrite38.0ms

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:

6.0ms	(- 1 (cos x))
31.0ms	(/ (- 1 (cos x)) (* x x))

series88.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(- 1 (cos x))
61.0ms	(/ (- 1 (cos x)) (* x x))

simplify1.7s

Counts

69 → 69

Iterations

Iter	Nodes
3	3060
2	858
1	288
0	121

prune492.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
0.3b	(* (sin x) (sin x))
0.3b	(+ 1 (cos x))
16.2b	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

rewrite73.0ms

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:

22.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
14.0ms	(* (sin x) (sin x))
5.0ms	(+ 1 (cos x))
30.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

series179.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
33.0ms	(* (sin x) (sin x))
12.0ms	(+ 1 (cos x))
78.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

simplify8.3s

Counts

138 → 138

Iterations

Iter	Nodes
3	9653
2	1861
1	512
0	190

prune1.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 3 expressions with local error:

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

rewrite31.0ms

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:

15.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
8.0ms	(/ (sin x) x)
7.0ms	(/ (tan (/ x 2)) x)

series237.0ms

Counts

3 → 9

Calls

3 calls:

104.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
52.0ms	(/ (sin x) x)
81.0ms	(/ (tan (/ x 2)) x)

simplify8.8s

Counts

123 → 123

Iterations

Iter	Nodes
3	6069
2	1656
1	449
0	172

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ (sin x) x) (* (tan (/ x 2)) (/ 1 x)))
0.1b	(/ (sin x) x)
0.2b	(* (tan (/ x 2)) (/ 1 x))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-exp-log`
33×	`add-sqr-sqrt`
31×	`add-cbrt-cube`
29×	`times-frac`
27×	`*-un-lft-identity`
26×	`add-cube-cbrt`
22×	`prod-exp`
16×	`associate-l`
14×	`associate-r`
12×	`div-exp` `cbrt-unprod`
10×	`pow1`
7×	`frac-times` `cbrt-undiv` `associate-*r/`
6×	`tan-quot`
4×	`pow-prod-down` `associate-*l/`
3×	`expm1-log1p-u` `rec-exp` `associate-/r` `1-exp` `un-div-inv` `insert-posit16` `log1p-expm1-u` `div-inv` `associate-/l` `add-log-exp` `unswap-sqr`
2×	`*-commutative`
1×	`clear-num` `frac-2neg`

Counts

3 → 123

Calls

3 calls:

67.0ms	(* (/ (sin x) x) (* (tan (/ x 2)) (/ 1 x)))
8.0ms	(/ (sin x) x)
15.0ms	(* (tan (/ x 2)) (/ 1 x))

series247.0ms

Counts

3 → 9

Calls

3 calls:

118.0ms	(* (/ (sin x) x) (* (tan (/ x 2)) (/ 1 x)))
57.0ms	(/ (sin x) x)
72.0ms	(* (tan (/ x 2)) (/ 1 x))

simplify22.2s

Counts

132 → 132

Iterations

Iter	Nodes
3	8868
2	1983
1	516
0	199

prune1.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes83.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
2	9
1	9
0	8

end0.0ms

sample4.7s

Algorithm

intervals

Results

2.1s	1598×	body	2560	valid
959.0ms	1273×	body	1280	valid
723.0ms	1492×	body	640	valid
340.0ms	920×	body	320	valid
323.0ms	2276×	body	80	valid
97.0ms	441×	body	160	valid