Details

sample161.0ms

Algorithm

intervals

Results

25.0ms	40×	body	1280	valid
19.0ms	46×	body	640	valid
11.0ms	30×	body	320	valid
10.0ms	127×	body	80	valid
3.0ms	13×	body	160	valid

simplify75.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	7	15
1	13	15
2	22	14
3	29	14
4	37	14
5	42	14
6	44	14
done	44	14

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (* (tan x) (tan x)))
0.2b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `*-un-lft-identity`
18×	`pow1`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-neg` `prod-diff` `associate-/r*`
2×	`pow2` `frac-times` `flip3--` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 119

Calls

4 calls:

11.0ms	(- 1.0 (* (tan x) (tan x)))
33.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
32.0ms	(* (tan x) (tan x))
47.0ms	(* (tan x) (tan x))

series301.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- 1.0 (* (tan x) (tan x)))
138.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
41.0ms	(* (tan x) (tan x))
80.0ms	(* (tan x) (tan x))

simplify3.1s

Counts

131 → 131

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	151	1789
1	338	1638
2	941	1453
3	2995	1419
done	5000	1411

prune439.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(fma (tan x) (tan x) 1.0)
0.2b	(/ (fma (tan x) (tan x) (- 1.0)) (- (fma (tan x) (tan x) 1.0)))
0.3b	(fma (tan x) (tan x) (- 1.0))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

30×	`times-frac`
26×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
10×	`associate-/r*`
5×	`add-exp-log` `add-cbrt-cube`
4×	`neg-mul-1`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`fma-udef`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 77

Calls

3 calls:

0.0ms	(fma (tan x) (tan x) 1.0)
7.0ms	(/ (fma (tan x) (tan x) (- 1.0)) (- (fma (tan x) (tan x) 1.0)))
0.0ms	(fma (tan x) (tan x) (- 1.0))

series303.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(fma (tan x) (tan x) 1.0)
170.0ms	(/ (fma (tan x) (tan x) (- 1.0)) (- (fma (tan x) (tan x) 1.0)))
71.0ms	(fma (tan x) (tan x) (- 1.0))

simplify3.7s

Counts

86 → 86

Iterations

Useful iterations: 4 (2.2s)

Iter	Nodes	Cost
0	134	1812
1	240	1779
2	581	1693
3	1593	1693
4	4766	1690
done	5000	1690

prune396.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sin x) (tan x)) (cos x))
0.2b	(* (sin x) (tan x))
0.2b	(/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
0.3b	(* (tan x) (tan x))

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`times-frac`
15×	`add-exp-log` `add-cbrt-cube`
13×	`pow1`
6×	`tan-quot` `associate-r` `associate-l` `associate-/r` `associate-/l`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`cbrt-undiv` `associate-*r/` `swap-sqr` `div-exp` `prod-exp` `cbrt-unprod` `associate-/l/`
2×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r/` `*-commutative` `div-inv` `unswap-sqr`
1×	`pow2` `frac-times` `flip3--` `flip3-+` `pow-plus` `div-sub` `associate-*l/` `pow-sqr` `pow-prod-up` `flip--` `flip-+`

Counts

4 → 117

Calls

4 calls:

17.0ms	(/ (* (sin x) (tan x)) (cos x))
13.0ms	(* (sin x) (tan x))
70.0ms	(/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
40.0ms	(* (tan x) (tan x))

series399.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (* (sin x) (tan x)) (cos x))
90.0ms	(* (sin x) (tan x))
150.0ms	(/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
51.0ms	(* (tan x) (tan x))

simplify1.4s

Counts

129 → 129

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	198	2029
1	454	1923
2	1473	1708
done	5001	1702

prune596.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sin x) (tan x)) (cos x))
0.2b	(* (sin x) (tan x))
0.2b	(* (sin x) (tan x))
0.2b	(/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (+ 1.0 (/ (* (sin x) (tan x)) (cos x))))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
35×	`add-sqr-sqrt`
23×	`times-frac`
21×	`add-cube-cbrt`
15×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
7×	`associate-/r*`
6×	`associate-r` `associate-l` `distribute-lft-out` `associate-/l*`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`tan-quot` `cbrt-undiv` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `associate-/l/`
2×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r/` `*-commutative` `div-inv` `unswap-sqr`
1×	`flip3--` `flip3-+` `div-sub` `flip--` `flip-+`

Counts

4 → 114

Calls

4 calls:

20.0ms	(/ (* (sin x) (tan x)) (cos x))
18.0ms	(* (sin x) (tan x))
18.0ms	(* (sin x) (tan x))
77.0ms	(/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (+ 1.0 (/ (* (sin x) (tan x)) (cos x))))

series447.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ (* (sin x) (tan x)) (cos x))
91.0ms	(* (sin x) (tan x))
55.0ms	(* (sin x) (tan x))
187.0ms	(/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (+ 1.0 (/ (* (sin x) (tan x)) (cos x))))

simplify1.7s

Counts

126 → 126

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	174	2328
1	403	2249
2	1259	2096
done	5000	2032

prune537.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes123.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	12	21
done	12	21

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.4s	1456×	body	1280	valid
1.2s	4341×	body	80	valid
1.0s	1307×	body	640	valid
305.0ms	621×	body	320	valid
81.0ms	275×	body	160	valid