Details

sample124.0ms

Algorithm

intervals

Results

59.0ms	54×	body	2560	valid
20.0ms	36×	body	1280	valid
17.0ms	46×	body	640	valid
9.0ms	30×	body	320	valid
7.0ms	77×	body	80	valid
3.0ms	13×	body	160	valid

simplify18.0ms

Counts

1 → 1

Iterations

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.0b

localize11.0ms

Local error

Found 2 expressions with local error:

2.4b	(- 1 (cos x))
16.0b	(/ (- 1 (cos x)) (* x x))

rewrite32.0ms

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:

14.0ms	(- 1 (cos x))
17.0ms	(/ (- 1 (cos x)) (* x x))

series102.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(- 1 (cos x))
69.0ms	(/ (- 1 (cos x)) (* x x))

simplify852.0ms

Counts

69 → 69

Iterations

Iter	Nodes
done	2048
3	2048
2	867
1	295
0	121

prune577.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

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))
16.3b	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

rewrite84.0ms

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:

36.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
21.0ms	(* (sin x) (sin x))
5.0ms	(+ 1 (cos x))
20.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

series167.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
36.0ms	(* (sin x) (sin x))
16.0ms	(+ 1 (cos x))
71.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

simplify1.3s

Counts

138 → 138

Iterations

Iter	Nodes
done	2000
3	2000
2	1777
1	525
0	190

prune1.2s

Pruning

6 alts after pruning (6 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))
0.2b	(/ (tan (/ x 2)) x)
0.2b	(/ (sin x) x)

rewrite49.0ms

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:

20.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
12.0ms	(/ (tan (/ x 2)) x)
15.0ms	(/ (sin x) x)

series223.0ms

Counts

3 → 9

Calls

3 calls:

97.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
88.0ms	(/ (tan (/ x 2)) x)
37.0ms	(/ (sin x) x)

simplify1.1s

Counts

123 → 123

Iterations

Iter	Nodes
done	2001
3	2001
2	1573
1	453
0	172

prune1.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 3 expressions with local error:

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

rewrite42.0ms

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:

17.0ms	(/ (* (/ (sin x) x) (tan (/ x 2))) x)
7.0ms	(/ (sin x) x)
17.0ms	(* (/ (sin x) x) (tan (/ x 2)))

series319.0ms

Counts

3 → 9

Calls

3 calls:

140.0ms	(/ (* (/ (sin x) x) (tan (/ x 2))) x)
57.0ms	(/ (sin x) x)
122.0ms	(* (/ (sin x) x) (tan (/ x 2)))

simplify939.0ms

Counts

105 → 105

Iterations

Iter	Nodes
done	2006
3	2006
2	1208
1	381
0	160

prune778.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes33.0ms

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
done	9
1	9
0	8

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.8s	1531×	body	2560	valid
853.0ms	1502×	body	640	valid
775.0ms	1265×	body	1280	valid
345.0ms	950×	body	320	valid
276.0ms	2299×	body	80	valid
89.0ms	453×	body	160	valid