Details

sample151.0ms

Algorithm

intervals

Results

73.0ms	54×	body	2560	valid
25.0ms	38×	body	1280	valid
22.0ms	47×	body	640	valid
10.0ms	32×	body	320	valid
8.0ms	70×	body	80	valid
3.0ms	15×	body	160	valid

simplify20.0ms

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: 31.8b

localize19.0ms

Local error

Found 2 expressions with local error:

1.5b	(- 1 (cos x))
15.6b	(/ (- 1 (cos x)) (* x x))

rewrite50.0ms

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:

20.0ms	(- 1 (cos x))
29.0ms	(/ (- 1 (cos x)) (* x x))

series96.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(- 1 (cos x))
66.0ms	(/ (- 1 (cos x)) (* x x))

simplify968.0ms

Counts

69 → 69

Iterations

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

prune269.0ms

Pruning

9 alts after pruning (9 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))
0.3b	(+ 1 (cos x))
15.4b	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

rewrite92.0ms

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:

18.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
21.0ms	(* (sin x) (sin x))
10.0ms	(+ 1 (cos x))
42.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

series190.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
29.0ms	(* (sin x) (sin x))
16.0ms	(+ 1 (cos x))
86.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

simplify1.4s

Counts

138 → 138

Iterations

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

prune472.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (sin x) (tan (/ x 2)))
15.4b	(/ (* (sin x) (tan (/ x 2))) (* x x))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 47

Calls

2 calls:

18.0ms	(* (sin x) (tan (/ x 2)))
22.0ms	(/ (* (sin x) (tan (/ x 2))) (* x x))

series182.0ms

Counts

2 → 6

Calls

2 calls:

72.0ms	(* (sin x) (tan (/ x 2)))
110.0ms	(/ (* (sin x) (tan (/ x 2))) (* x x))

simplify867.0ms

Counts

53 → 53

Iterations

Iter	Nodes
done	2033
3	2033
2	999
1	247
0	99

prune204.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

localize18.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (sin x) (/ (* x x) (tan (/ x 2))))
14.7b	(/ (* x x) (tan (/ x 2)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

39×	`times-frac`
21×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
16×	`add-cbrt-cube` `add-exp-log`
11×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `div-inv`
5×	`tan-quot`
4×	`associate-/l*`
2×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

2 → 80

Calls

2 calls:

14.0ms	(/ (sin x) (/ (* x x) (tan (/ x 2))))
10.0ms	(/ (* x x) (tan (/ x 2)))

series163.0ms

Counts

2 → 6

Calls

2 calls:

98.0ms	(/ (sin x) (/ (* x x) (tan (/ x 2))))
66.0ms	(/ (* x x) (tan (/ x 2)))

simplify1.2s

Counts

86 → 86

Iterations

Iter	Nodes
done	2045
3	2045
2	1640
1	421
0	159

prune356.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes31.0ms

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	8
0	8

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.5s	1616×	body	2560	valid
762.0ms	1163×	body	1280	valid
699.0ms	1476×	body	640	valid
584.0ms	2308×	body	80	valid
277.0ms	987×	body	320	valid
145.0ms	450×	body	160	valid