Details

sample108.0ms

Algorithm

intervals

Results

34.0ms	43×	body	2560	valid
21.0ms	39×	body	1280	valid
18.0ms	32×	body	320	valid
17.0ms	50×	body	640	valid
7.0ms	77×	body	80	valid
3.0ms	15×	body	160	valid

simplify20.0ms

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize16.0ms

Local error

Found 2 expressions with local error:

2.1b	(- 1 (cos x))
13.5b	(/ (- 1 (cos x)) (* x x))

rewrite45.0ms

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` `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 → 61

Calls

2 calls:

10.0ms	(- 1 (cos x))
32.0ms	(/ (- 1 (cos x)) (* x x))

series142.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(- 1 (cos x))
99.0ms	(/ (- 1 (cos x)) (* x x))

simplify1.5s

Counts

67 → 67

Iterations

Iter	Nodes
3	2884
2	855
1	286
0	119

prune488.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
0.3b	(* (sin x) (sin x))
0.4b	(+ 1 (cos x))
13.5b	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

rewrite55.0ms

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-+` `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 → 122

Calls

4 calls:

15.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
10.0ms	(* (sin x) (sin x))
5.0ms	(+ 1 (cos x))
23.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

series214.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
40.0ms	(* (sin x) (sin x))
20.0ms	(+ 1 (cos x))
90.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

simplify8.0s

Counts

134 → 134

Iterations

Iter	Nodes
3	9300
2	1849
1	508
0	186

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize31.0ms

Local error

Found 3 expressions with local error:

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

rewrite36.0ms

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` `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 → 111

Calls

3 calls:

21.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
7.0ms	(/ (sin x) x)
6.0ms	(/ (tan (/ x 2)) x)

series263.0ms

Counts

3 → 9

Calls

3 calls:

128.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
49.0ms	(/ (sin x) x)
86.0ms	(/ (tan (/ x 2)) x)

simplify10.1s

Counts

120 → 120

Iterations

Iter	Nodes
3	5890
2	1652
1	446
0	169

prune1.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (* (sin x) (/ (tan (/ x 2)) x)) x)
0.2b	(/ (tan (/ x 2)) x)
0.2b	(* (sin x) (/ (tan (/ x 2)) x))

rewrite59.0ms

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` `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 → 90

Calls

3 calls:

24.0ms	(/ (* (sin x) (/ (tan (/ x 2)) x)) x)
11.0ms	(/ (tan (/ x 2)) x)
21.0ms	(* (sin x) (/ (tan (/ x 2)) x))

series368.0ms

Counts

3 → 9

Calls

3 calls:

148.0ms	(/ (* (sin x) (/ (tan (/ x 2)) x)) x)
94.0ms	(/ (tan (/ x 2)) x)
126.0ms	(* (sin x) (/ (tan (/ x 2)) x))

simplify7.2s

Counts

99 → 99

Iterations

Iter	Nodes
3	7227
2	1358
1	365
0	151

prune819.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes42.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	9
1	9
0	8

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.2s	1540×	body	2560	valid
857.0ms	1498×	body	640	valid
847.0ms	1225×	body	1280	valid
335.0ms	926×	body	320	valid
268.0ms	2324×	body	80	valid
111.0ms	487×	body	160	valid