Details

sample287.0ms

Algorithm

intervals

Results

167.0ms	116×	body	1280	valid
49.0ms	74×	body	640	valid
15.0ms	256×	pre	80	true
11.0ms	22×	body	320	valid
5.0ms	36×	body	80	valid
2.0ms	8×	body	160	valid

simplify6.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
9	4724
8	1354
7	446
6	193
5	89
4	39
3	33
2	22
1	15
0	9

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.8b

localize42.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
2.5b	(tan (+ y z))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
18×	`prod-diff`
17×	`add-cube-cbrt`
11×	`associate-+r+`
10×	`add-log-exp`
4×	`tan-quot`
3×	`expm1-log1p-u` `pow1` `fma-def` `add-cbrt-cube` `fma-neg` `add-exp-log` `log1p-expm1-u`
2×	`tan-sum` `sum-log` `sub-neg` `diff-log` `frac-sub` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+r-` `flip3-+` `flip3--` `flip-+` `flip--` `difference-of-squares`

Counts

3 → 72

Calls

3 calls:

19.0ms	(+ x (- (tan (+ y z)) (tan a)))
29.0ms	(- (tan (+ y z)) (tan a))
12.0ms	(tan (+ y z))

series908.0ms

Counts

3 → 9

Calls

3 calls:

237.0ms	(+ x (- (tan (+ y z)) (tan a)))
158.0ms	(- (tan (+ y z)) (tan a))
513.0ms	(tan (+ y z))

simplify1.3s

Counts

81 → 81

Iterations

Iter	Nodes
done	5000
2	1003
1	284
0	128

prune576.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan y) (tan z))
0.1b	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
0.1b	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.2b	(* (tan y) (tan z))

rewrite350.0ms

Algorithm

rewrite-expression-head

Rules

151×	`*-un-lft-identity`
108×	`prod-diff`
107×	`add-sqr-sqrt`
100×	`add-cube-cbrt`
85×	`times-frac`
56×	`associate-+r+`
24×	`distribute-lft-out`
18×	`fma-neg`
14×	`associate-/r/`
13×	`add-log-exp`
8×	`flip3--` `flip--`
7×	`tan-quot` `div-inv`
6×	`pow1` `fma-def` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sum-log` `associate-r` `associate-l`
2×	`+-commutative` `sub-neg` `flip3-+` `diff-log` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`frac-times` `associate-+r-` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `associate-r/` `*-commutative` `frac-sub` `cbrt-unprod` `unswap-sqr`

Counts

4 → 207

Calls

4 calls:

14.0ms	(+ (tan y) (tan z))
185.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
105.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
25.0ms	(* (tan y) (tan z))

series1.6s

Counts

4 → 12

Calls

4 calls:

162.0ms	(+ (tan y) (tan z))
573.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
698.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
136.0ms	(* (tan y) (tan z))

simplify1.7s

Counts

219 → 219

Iterations

Iter	Nodes
done	5001
2	2697
1	700
0	297

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
0.1b	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.2b	(* (tan y) (tan z))
2.5b	(exp (+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))

rewrite686.0ms

Algorithm

rewrite-expression-head

Rules

154×	`*-un-lft-identity`
108×	`prod-diff`
107×	`add-sqr-sqrt`
100×	`add-cube-cbrt`
85×	`times-frac`
56×	`associate-+r+`
25×	`distribute-lft-out`
18×	`fma-neg`
17×	`add-log-exp`
14×	`associate-/r/`
8×	`flip3--` `flip--`
7×	`div-inv`
6×	`pow1` `add-cbrt-cube` `add-exp-log`
5×	`exp-prod` `tan-quot`
4×	`expm1-log1p-u` `sum-log` `log1p-expm1-u`
3×	`fma-def` `diff-log` `associate-r` `associate-l` `distribute-lft-out--` `rem-exp-log`
2×	`associate-+r-` `sub-neg` `difference-of-squares`
1×	`frac-times` `+-commutative` `flip3-+` `exp-diff` `exp-sum` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 208

Calls

4 calls:

147.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
81.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
16.0ms	(* (tan y) (tan z))
430.0ms	(exp (+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))

series1.8s

Counts

4 → 12

Calls

4 calls:

521.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
554.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
118.0ms	(* (tan y) (tan z))
635.0ms	(exp (+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))

simplify2.8s

Counts

220 → 220

Iterations

Iter	Nodes
done	5001
2	2595
1	673
0	292

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize85.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan a) (tan a))
0.4b	(* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))
1.1b	(/ (- (* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (* (tan a) (tan a))) (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
2.5b	(exp (+ x (/ (- (* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (* (tan a) (tan a))) (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

109×	`*-un-lft-identity`
80×	`times-frac`
69×	`add-sqr-sqrt`
55×	`add-cube-cbrt`
27×	`swap-sqr`
24×	`distribute-lft-out`
21×	`associate-r` `associate-l`
20×	`add-cbrt-cube` `add-exp-log`
18×	`pow1`
17×	`tan-quot`
11×	`associate-/r/` `associate-/l/`
9×	`frac-sub`
8×	`frac-times` `associate-l/` `associate-r/`
7×	`add-log-exp`
5×	`cbrt-undiv` `flip3--` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `flip--` `difference-of-squares` `unswap-sqr`
4×	`expm1-log1p-u` `exp-prod` `associate-/r` `log1p-expm1-u` `associate-/l`
2×	`pow2` `pow-plus` `div-sub` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `rem-exp-log`
1×	`clear-num` `associate-+r-` `sum-log` `frac-2neg` `flip3-+` `exp-diff` `exp-sum` `frac-add` `flip-+`

Counts

4 → 190

Calls

4 calls:

12.0ms	(* (tan a) (tan a))
92.0ms	(* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))
183.0ms	(/ (- (* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (* (tan a) (tan a))) (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
709.0ms	(exp (+ x (/ (- (* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (* (tan a) (tan a))) (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))))

series6.6s

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (tan a) (tan a))
335.0ms	(* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))
1.9s	(/ (- (* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (* (tan a) (tan a))) (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
4.4s	(exp (+ x (/ (- (* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (* (tan a) (tan a))) (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))))

simplify2.0s

Counts

202 → 202

Iterations

Iter	Nodes
done	5001
1	1145
0	351

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

regimes550.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	22
1	22
0	17

end0.0ms

sample9.3s

Algorithm

intervals

Results

5.4s	3836×	body	1280	valid
2.2s	2060×	body	640	valid
604.0ms	8000×	pre	80	true
325.0ms	720×	body	320	valid
186.0ms	1113×	body	80	valid
79.0ms	271×	body	160	valid