Details

sample316.0ms

Algorithm

intervals

Results

158.0ms	127×	body	1280	valid
53.0ms	256×	pre	80	true
52.0ms	68×	body	640	valid
13.0ms	25×	body	320	valid
5.0ms	26×	body	80	valid
4.0ms	10×	body	160	valid

simplify176.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	9
1	15	9
2	22	9
3	33	9
4	38	9
5	45	9
6	51	9
7	61	9
8	74	9
9	86	9
10	95	9
done	95	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.5b

localize25.0ms

Local error

Found 3 expressions with local error:

0.2b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
3.2b	(tan (+ y z))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 42

Calls

3 calls:

21.0ms	(+ x (- (tan (+ y z)) (tan a)))
20.0ms	(- (tan (+ y z)) (tan a))
13.0ms	(tan (+ y z))

series430.0ms

Counts

3 → 9

Calls

3 calls:

200.0ms	(+ x (- (tan (+ y z)) (tan a)))
155.0ms	(- (tan (+ y z)) (tan a))
75.0ms	(tan (+ y z))

simplify2.9s

Counts

51 → 51

Iterations

Useful iterations: 3 (297.0ms)

Iter	Nodes	Cost
0	91	627
1	196	590
2	453	572
3	1243	570
4	4659	570
done	5000	570

prune209.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite231.0ms

Algorithm

rewrite-expression-head

Rules

16×	`associate-*l/`
14×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
12×	`tan-quot` `*-un-lft-identity`
10×	`add-cube-cbrt`
8×	`pow1` `associate-/l/`
6×	`associate-r` `associate-l` `frac-sub` `add-log-exp`
5×	`flip3--` `flip--`
3×	`flip3-+` `times-frac` `prod-exp` `cbrt-unprod` `flip-+` `associate-/l*`
2×	`cbrt-undiv` `frac-times` `div-sub` `associate-r/` `div-exp` `pow-prod-down` `frac-add` `associate-/r/` `-commutative` `unswap-sqr`
1×	`+-commutative` `associate-+r-` `frac-2neg` `clear-num` `associate-/r*` `sum-log` `div-inv` `distribute-lft-out`

Counts

4 → 87

Calls

4 calls:

55.0ms	(+ x (/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a))))
29.0ms	(* (tan y) (tan z))
23.0ms	(* (tan y) (tan z))
118.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

series2.5s

Counts

4 → 12

Calls

4 calls:

1.2s	(+ x (/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a))))
141.0ms	(* (tan y) (tan z))
134.0ms	(* (tan y) (tan z))
1.1s	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

simplify1.7s

Counts

99 → 99

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	194	2683
1	600	2517
2	2376	2064
done	5000	1933

prune792.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize55.0ms

Local error

Found 4 expressions with local error:

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

rewrite245.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log` `add-cbrt-cube`
16×	`add-sqr-sqrt`
15×	`associate-*l/`
12×	`add-cube-cbrt` `*-un-lft-identity`
10×	`tan-quot`
9×	`associate-/l/`
8×	`pow1`
6×	`times-frac` `associate-r` `associate-l` `frac-sub`
5×	`flip3--` `flip--`
4×	`cbrt-undiv` `div-exp` `prod-exp` `associate-/r` `cbrt-unprod` `associate-/l` `add-log-exp`
3×	`associate-*r/`
2×	`frac-2neg` `flip3-+` `pow-prod-down` `frac-add` `clear-num` `associate-/r/` `*-commutative` `flip-+` `div-inv` `unswap-sqr`
1×	`frac-times` `div-sub`

Counts

4 → 94

Calls

4 calls:

30.0ms	(/ (* (sin y) (tan z)) (cos y))
34.0ms	(* (tan y) (tan z))
28.0ms	(* (sin y) (tan z))
146.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (/ (* (sin y) (tan z)) (cos y))) (cos a)))

series1.4s

Counts

4 → 12

Calls

4 calls:

226.0ms	(/ (* (sin y) (tan z)) (cos y))
158.0ms	(* (tan y) (tan z))
161.0ms	(* (sin y) (tan z))
904.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (/ (* (sin y) (tan z)) (cos y))) (cos a)))

simplify1.8s

Counts

106 → 106

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	215	2247
1	624	2170
2	2546	1873
done	5000	1836

prune988.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize73.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin y) (tan z))
0.2b	(* (sin y) (tan z))
0.2b	(* (sin y) (tan z))
0.2b	(* (/ (* (sin y) (tan z)) (cos y)) (/ (* (sin y) (tan z)) (cos y)))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-exp-log` `add-cbrt-cube`
26×	`add-sqr-sqrt`
18×	`add-cube-cbrt` `*-un-lft-identity` `prod-exp` `cbrt-unprod`
17×	`pow1`
16×	`associate-r` `associate-l`
12×	`cbrt-undiv` `times-frac` `div-exp`
7×	`swap-sqr`
4×	`associate-r/` `pow-prod-down` `-commutative` `div-inv` `add-log-exp` `unswap-sqr`
3×	`tan-quot`
1×	`pow2` `frac-times` `pow-plus` `associate-*l/` `pow-sqr` `pow-prod-up`

Counts

4 → 113

Calls

4 calls:

15.0ms	(* (sin y) (tan z))
18.0ms	(* (sin y) (tan z))
15.0ms	(* (sin y) (tan z))
64.0ms	(* (/ (* (sin y) (tan z)) (cos y)) (/ (* (sin y) (tan z)) (cos y)))

series595.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(* (sin y) (tan z))
90.0ms	(* (sin y) (tan z))
129.0ms	(* (sin y) (tan z))
253.0ms	(* (/ (* (sin y) (tan z)) (cos y)) (/ (* (sin y) (tan z)) (cos y)))

simplify1.2s

Counts

125 → 125

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	145	2002
1	395	1762
2	1510	1325
done	5000	1232

prune725.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.1b

regimes644.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	52
1	34	52
done	34	52

end0.0ms

sample9.0s

Algorithm

intervals

Results

4.8s	3849×	body	1280	valid
2.4s	2029×	body	640	valid
606.0ms	8000×	pre	80	true
412.0ms	722×	body	320	valid
185.0ms	1135×	body	80	valid
74.0ms	265×	body	160	valid