Details

sample235.0ms

Algorithm

intervals

Results

133.0ms	100×	body	1280	valid
37.0ms	62×	body	640	valid
31.0ms	14×	body	2560	valid
9.0ms	42×	body	80	valid
8.0ms	22×	body	320	valid
4.0ms	16×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize13.0ms

Local error

Found 2 expressions with local error:

1.8b	(- (tan (+ x eps)) (tan x))
3.0b	(tan (+ x eps))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`tan-quot` `add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `tan-sum` `frac-sub` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 41

Calls

2 calls:

38.0ms	(- (tan (+ x eps)) (tan x))
14.0ms	(tan (+ x eps))

series285.0ms

Counts

2 → 6

Calls

2 calls:

160.0ms	(- (tan (+ x eps)) (tan x))
125.0ms	(tan (+ x eps))

simplify2.5s

Counts

47 → 47

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	94	720
1	194	597
2	457	510
3	1461	450
done	5000	438

prune145.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
2.7b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

102×	`*-un-lft-identity`
73×	`add-sqr-sqrt`
66×	`add-cube-cbrt`
61×	`times-frac`
54×	`prod-diff`
18×	`fma-neg`
17×	`distribute-lft-out`
10×	`associate-/r/`
9×	`tan-quot`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1` `flip3--` `flip--`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-def` `associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`flip3-+` `frac-add` `flip-+` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `frac-times` `sub-neg` `frac-2neg` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 169

Calls

4 calls:

32.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
9.0ms	(+ (tan x) (tan eps))
16.0ms	(* (tan x) (tan eps))
127.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.2s

Counts

4 → 12

Calls

4 calls:

324.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
139.0ms	(+ (tan x) (tan eps))
170.0ms	(* (tan x) (tan eps))
562.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.7s

Counts

181 → 181

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	240	4762
1	560	3970
2	1558	3555
done	5000	3149

prune693.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (sin eps))
0.2b	(/ (* (tan x) (sin eps)) (cos eps))
2.7b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

rewrite339.0ms

Algorithm

rewrite-expression-head

Rules

183×	`*-un-lft-identity`
138×	`add-sqr-sqrt`
100×	`times-frac`
90×	`prod-diff`
83×	`add-cube-cbrt`
34×	`difference-of-squares`
30×	`fma-neg`
25×	`distribute-lft-out`
17×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r/` `add-log-exp`
6×	`pow1`
5×	`tan-quot` `flip3--` `flip--` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `associate-r` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod`
1×	`+-commutative` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `pow-prod-down` `frac-add` `clear-num` `sum-log` `-commutative` `frac-sub` `flip-+` `associate-/l/` `associate-/l` `unswap-sqr`

Counts

4 → 201

Calls

4 calls:

18.0ms	(+ (tan x) (tan eps))
15.0ms	(* (tan x) (sin eps))
18.0ms	(/ (* (tan x) (sin eps)) (cos eps))
269.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

series890.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(+ (tan x) (tan eps))
94.0ms	(* (tan x) (sin eps))
131.0ms	(/ (* (tan x) (sin eps)) (cos eps))
517.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

simplify1.6s

Counts

213 → 213

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	292	6707
1	671	5460
2	1873	4825
done	5000	4218

prune567.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 9.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (tan x) (sin eps)) (cos eps))
0.2b	(/ (tan x) (cos eps))
0.3b	(pow (/ (* (tan x) (sin eps)) (cos eps)) 3)
2.7b	(fma (/ (+ (tan x) (tan eps)) (- 1 (pow (/ (* (tan x) (sin eps)) (cos eps)) 3))) (fma (fma (/ (tan x) (cos eps)) (sin eps) 1) (/ (* (tan x) (sin eps)) (cos eps)) 1) (- (tan x)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
17×	`add-exp-log` `add-cbrt-cube`
7×	`unpow-prod-down` `cube-prod`
6×	`associate-/r*`
5×	`pow1` `cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
3×	`pow-unpow` `pow-exp` `rem-cube-cbrt`
2×	`tan-quot` `frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `associate-/l/`
1×	`cube-div` `cube-mult` `pow-to-exp` `pow-pow` `unpow3` `associate-*l/` `fma-udef` `sqr-pow`

Counts

4 → 102

Calls

4 calls:

16.0ms	(/ (* (tan x) (sin eps)) (cos eps))
7.0ms	(/ (tan x) (cos eps))
10.0ms	(pow (/ (* (tan x) (sin eps)) (cos eps)) 3)
0.0ms	(fma (/ (+ (tan x) (tan eps)) (- 1 (pow (/ (* (tan x) (sin eps)) (cos eps)) 3))) (fma (fma (/ (tan x) (cos eps)) (sin eps) 1) (/ (* (tan x) (sin eps)) (cos eps)) 1) (- (tan x)))

series1.7s

Counts

4 → 12

Calls

4 calls:

154.0ms	(/ (* (tan x) (sin eps)) (cos eps))
97.0ms	(/ (tan x) (cos eps))
169.0ms	(pow (/ (* (tan x) (sin eps)) (cos eps)) 3)
1.2s	(fma (/ (+ (tan x) (tan eps)) (- 1 (pow (/ (* (tan x) (sin eps)) (cos eps)) 3))) (fma (fma (/ (tan x) (cos eps)) (sin eps) 1) (/ (* (tan x) (sin eps)) (cos eps)) 1) (- (tan x)))

simplify1.5s

Counts

114 → 114

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	234	2237
1	641	2077
2	2699	1858
done	5000	1828

prune775.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

regimes204.0ms

Accuracy

0% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 0.6b

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	37	164
1	42	162
done	42	162

end0.0ms

sample9.9s

Algorithm

intervals

Results

5.0s	3324×	body	1280	valid
1.8s	1842×	body	640	valid
1.6s	603×	body	2560	valid
467.0ms	796×	body	320	valid
423.0ms	355×	body	160	valid
231.0ms	1080×	body	80	valid