Details

sample178.0ms

Algorithm

intervals

Results

51.0ms	39×	body	2560	valid
37.0ms	87×	body	80	valid
32.0ms	40×	body	1280	valid
28.0ms	48×	body	640	valid
11.0ms	24×	body	320	valid
7.0ms	18×	body	160	valid

simplify30.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	30
4	30
3	28
2	23
1	15
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.2b

localize24.0ms

Local error

Found 2 expressions with local error:

2.3b	(- 1 (cos x))
12.5b	(/ (- 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))

series84.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(- 1 (cos x))
63.0ms	(/ (- 1 (cos x)) (* x x))

simplify1.9s

Counts

69 → 69

Iterations

Iter	Nodes
3	2853
2	856
1	289
0	121

prune539.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
0.3b	(* (sin x) (sin x))
0.4b	(+ 1 (cos x))
12.3b	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

rewrite77.0ms

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:

16.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
11.0ms	(* (sin x) (sin x))
5.0ms	(+ 1 (cos x))
43.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

series191.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
27.0ms	(* (sin x) (sin x))
18.0ms	(+ 1 (cos x))
102.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

simplify7.8s

Counts

138 → 138

Iterations

Iter	Nodes
3	9178
2	1856
1	511
0	190

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize34.0ms

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)

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` `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:

19.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
8.0ms	(/ (sin x) x)
7.0ms	(/ (tan (/ x 2)) x)

series274.0ms

Counts

3 → 9

Calls

3 calls:

121.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
55.0ms	(/ (sin x) x)
98.0ms	(/ (tan (/ x 2)) x)

simplify2.9s

Counts

123 → 123

Iterations

Iter	Nodes
3	5682
2	1662
1	451
0	172

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 3 expressions with local error:

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

rewrite55.0ms

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

Counts

3 → 96

Calls

3 calls:

26.0ms	(/ (* (/ (sin x) x) (tan (/ x 2))) x)
8.0ms	(/ (sin x) x)
19.0ms	(* (/ (sin x) x) (tan (/ x 2)))

series289.0ms

Counts

3 → 9

Calls

3 calls:

119.0ms	(/ (* (/ (sin x) x) (tan (/ x 2))) x)
44.0ms	(/ (sin x) x)
125.0ms	(* (/ (sin x) x) (tan (/ x 2)))

simplify3.2s

Counts

105 → 105

Iterations

Iter	Nodes
3	6724
2	1334
1	381
0	160

prune801.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes57.0ms

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

sample5.0s

Algorithm

intervals

Results

2.0s	1621×	body	2560	valid
1.2s	1501×	body	640	valid
850.0ms	1235×	body	1280	valid
361.0ms	928×	body	320	valid
314.0ms	2287×	body	80	valid
99.0ms	428×	body	160	valid