Details

sample82.0ms

Algorithm

intervals

Results

36.0ms	63×	body	2560	valid
22.0ms	41×	body	1280	valid
10.0ms	46×	body	640	valid
3.0ms	74×	body	80	valid
3.0ms	17×	body	320	valid
2.0ms	15×	body	160	valid

simplify15.0ms

Counts

1 → 1

Iterations

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize21.0ms

Local error

Found 2 expressions with local error:

0.9b	(- 1 (cos x))
19.2b	(/ (- 1 (cos x)) (* x x))

rewrite69.0ms

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:

32.0ms	(- 1 (cos x))
34.0ms	(/ (- 1 (cos x)) (* x x))

series110.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(- 1 (cos x))
75.0ms	(/ (- 1 (cos x)) (* x x))

simplify2.6s

Counts

69 → 69

Iterations

Iter	Nodes
done	5001
3	4370
2	867
1	295
0	121

prune280.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
0.2b	(* (sin x) (sin x))
0.3b	(+ 1 (cos x))
18.9b	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

rewrite61.0ms

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:

17.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
11.0ms	(* (sin x) (sin x))
5.0ms	(+ 1 (cos x))
25.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

series155.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
20.0ms	(* (sin x) (sin x))
11.0ms	(+ 1 (cos x))
68.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

simplify1.4s

Counts

138 → 138

Iterations

Iter	Nodes
done	5001
2	1777
1	525
0	190

prune566.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) x)
0.1b	(/ (sin x) x)
0.2b	(* (/ (sin x) x) (/ (sin x) x))
0.3b	(+ (cos x) 1)

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
58×	`times-frac`
51×	`*-un-lft-identity`
49×	`add-cube-cbrt`
20×	`add-cbrt-cube` `add-exp-log`
13×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
6×	`cbrt-undiv` `associate-/r` `div-exp` `div-inv` `associate-/l` `add-log-exp`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`fma-def`
2×	`clear-num` `frac-2neg`
1×	`pow2` `frac-times` `+-commutative` `sum-log` `flip3-+` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip-+` `distribute-lft-out`

Counts

4 → 148

Calls

4 calls:

15.0ms	(/ (sin x) x)
14.0ms	(/ (sin x) x)
24.0ms	(* (/ (sin x) x) (/ (sin x) x))
9.0ms	(+ (cos x) 1)

series170.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (sin x) x)
41.0ms	(/ (sin x) x)
71.0ms	(* (/ (sin x) x) (/ (sin x) x))
18.0ms	(+ (cos x) 1)

simplify1.9s

Counts

160 → 160

Iterations

Iter	Nodes
done	5005
2	1827
1	520
0	168

prune669.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (sin x) x) (/ (sin x) x))
0.3b	(+ (cos x) 1)
0.3b	(+ (cos x) 1)
0.8b	(* (sqrt (+ (cos x) 1)) (sqrt (+ (cos x) 1)))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
60×	`*-un-lft-identity`
42×	`add-cube-cbrt`
40×	`times-frac`
26×	`pow1` `sqrt-prod`
24×	`swap-sqr`
20×	`associate-r` `associate-l`
18×	`add-cbrt-cube` `add-exp-log`
12×	`sqrt-div`
8×	`sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `distribute-lft-out` `add-log-exp` `unswap-sqr`
6×	`fma-def` `pow-prod-up`
5×	`frac-times` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `pow-prod-down` `pow-sqr` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`associate-l/` `associate-r/`
2×	`pow2` `+-commutative` `sum-log` `pow-plus` `*-commutative`
1×	`rem-square-sqrt` `sqrt-unprod`

Counts

4 → 171

Calls

4 calls:

30.0ms	(* (/ (sin x) x) (/ (sin x) x))
12.0ms	(+ (cos x) 1)
12.0ms	(+ (cos x) 1)
64.0ms	(* (sqrt (+ (cos x) 1)) (sqrt (+ (cos x) 1)))

series113.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (/ (sin x) x) (/ (sin x) x))
15.0ms	(+ (cos x) 1)
18.0ms	(+ (cos x) 1)
23.0ms	(* (sqrt (+ (cos x) 1)) (sqrt (+ (cos x) 1)))

simplify1.6s

Counts

183 → 183

Iterations

Iter	Nodes
done	5005
2	1852
1	597
0	208

prune731.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes57.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	11
1	11
0	8

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.2s	1584×	body	2560	valid
732.0ms	1487×	body	640	valid
579.0ms	1210×	body	1280	valid
213.0ms	2328×	body	80	valid
208.0ms	910×	body	320	valid
64.0ms	481×	body	160	valid