Details

sample396.0ms

Algorithm

intervals

Results

246.0ms	123×	body	1280	valid
63.0ms	59×	body	640	valid
18.0ms	256×	pre	80	true
13.0ms	21×	body	320	valid
8.0ms	39×	body	80	valid
6.0ms	14×	body	160	valid

simplify6.2s

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.1b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b	(- x (- (tan a) (tan (+ y z))))
0.2b	(- (tan a) (tan (+ y z)))
4.2b	(tan (+ y z))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity` `add-log-exp`
7×	`add-sqr-sqrt`
4×	`diff-log` `tan-quot` `distribute-lft-out--`
3×	`pow1` `sub-neg` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
2×	`tan-sum` `flip3--` `frac-sub` `flip--` `associate--r+` `difference-of-squares`
1×	`associate--r-`

Counts

3 → 44

Calls

3 calls:

24.0ms	(- x (- (tan a) (tan (+ y z))))
27.0ms	(- (tan a) (tan (+ y z)))
7.0ms	(tan (+ y z))

series481.0ms

Counts

3 → 9

Calls

3 calls:

231.0ms	(- x (- (tan a) (tan (+ y z))))
159.0ms	(- (tan a) (tan (+ y z)))
91.0ms	(tan (+ y z))

simplify657.0ms

Counts

53 → 53

Iterations

Iter	Nodes
done	5000
3	1680
2	461
1	200
0	96

prune361.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

24.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y))))
93.0ms	(- x (- (tan a) (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y))))))
21.0ms	(* (tan z) (tan y))
27.0ms	(- (tan a) (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))))

series1.7s

Counts

4 → 12

Calls

4 calls:

346.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y))))
562.0ms	(- x (- (tan a) (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y))))))
133.0ms	(* (tan z) (tan y))
705.0ms	(- (tan a) (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))))

simplify890.0ms

Counts

104 → 104

Iterations

Iter	Nodes
done	5000
2	1665
1	473
0	195

prune819.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `pow1`
17×	`tan-quot`
14×	`*-un-lft-identity` `add-cube-cbrt`
10×	`add-cbrt-cube` `add-exp-log`
9×	`associate-r` `associate-l`
6×	`swap-sqr` `add-log-exp`
5×	`frac-times` `associate-*r/` `frac-sub`
4×	`associate-*l/`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`pow2` `flip3-+` `pow-plus` `pow-sqr` `pow-prod-up` `flip-+` `associate--r+`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3--` `diff-log` `flip--`

Counts

4 → 96

Calls

4 calls:

26.0ms	(* (tan z) (tan y))
12.0ms	(- (tan a) (* (/ (+ (tan y) (tan z)) (- 1 (* (* (tan y) (tan y)) (* (tan z) (tan z))))) (+ 1 (* (tan z) (tan y)))))
13.0ms	(* (tan z) (tan z))
23.0ms	(* (tan y) (tan y))

series2.5s

Counts

4 → 12

Calls

4 calls:

126.0ms	(* (tan z) (tan y))
1.9s	(- (tan a) (* (/ (+ (tan y) (tan z)) (- 1 (* (* (tan y) (tan y)) (* (tan z) (tan z))))) (+ 1 (* (tan z) (tan y)))))
39.0ms	(* (tan z) (tan z))
449.0ms	(* (tan y) (tan y))

simplify2.5s

Counts

108 → 108

Iterations

Iter	Nodes
done	5001
2	4552
1	667
0	219

prune812.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (tan a) (/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (* (- (tan y) (tan z)) (- 1 (* (tan y) (tan z))))))
0.2b	(* (tan z) (tan z))
0.2b	(* (tan y) (tan y))
3.4b	(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (* (- (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))

rewrite200.0ms

Algorithm

rewrite-expression-head

Rules

39×	`tan-quot`
20×	`add-sqr-sqrt`
18×	`pow1`
16×	`*-un-lft-identity`
14×	`frac-times` `add-cube-cbrt`
13×	`add-cbrt-cube` `add-exp-log` `frac-sub`
11×	`associate-*l/` `associate-/r/` `associate-/l/`
10×	`associate-*r/`
9×	`flip3--` `flip--`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
4×	`times-frac` `associate-/l*`
3×	`prod-exp` `cbrt-unprod` `difference-of-squares`
2×	`pow2` `cbrt-undiv` `pow-plus` `div-sub` `div-exp` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `unswap-sqr`
1×	`clear-num` `associate-/r*` `sub-neg` `frac-2neg` `diff-log` `div-inv` `distribute-lft-out--` `associate--r-`

Counts

4 → 118

Calls

4 calls:

83.0ms	(- (tan a) (/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (* (- (tan y) (tan z)) (- 1 (* (tan y) (tan z))))))
24.0ms	(* (tan z) (tan z))
24.0ms	(* (tan y) (tan y))
62.0ms	(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (* (- (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))

series1.5s

Counts

4 → 12

Calls

4 calls:

965.0ms	(- (tan a) (/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (* (- (tan y) (tan z)) (- 1 (* (tan y) (tan z))))))
40.0ms	(* (tan z) (tan z))
35.0ms	(* (tan y) (tan y))
476.0ms	(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (* (- (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))

simplify1.8s

Counts

130 → 130

Iterations

Iter	Nodes
done	5000
2	4484
1	725
0	244

prune891.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes708.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	22
1	22
0	18

end0.0ms

sample10.1s

Algorithm

intervals

Results

6.0s	3893×	body	1280	valid
1.9s	1992×	body	640	valid
697.0ms	695×	body	320	valid
605.0ms	8000×	pre	80	true
230.0ms	1131×	body	80	valid
140.0ms	289×	body	160	valid