Details

sample327.0ms

Algorithm

intervals

Results

148.0ms	118×	body	1280	valid
65.0ms	256×	pre	80	true
54.0ms	66×	body	640	valid
13.0ms	24×	body	320	valid
7.0ms	43×	body	80	valid
2.0ms	5×	body	160	valid

simplify7.1s

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	39	9
5	89	9
6	193	9
7	451	9
8	1380	9
9	4837	9
done	5001	9

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

localize21.0ms

Local error

Found 3 expressions with local error:

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

rewrite77.0ms

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:

32.0ms	(+ x (- (tan (+ y z)) (tan a)))
27.0ms	(- (tan (+ y z)) (tan a))
15.0ms	(tan (+ y z))

series448.0ms

Counts

3 → 9

Calls

3 calls:

167.0ms	(+ x (- (tan (+ y z)) (tan a)))
177.0ms	(- (tan (+ y z)) (tan a))
103.0ms	(tan (+ y z))

simplify932.0ms

Counts

51 → 51

Iterations

Useful iterations: 3 (294.0ms)

Iter	Nodes	Cost
0	91	627
1	197	590
2	475	572
3	1729	570
done	5000	570

prune219.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite388.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

111.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
231.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
13.0ms	(+ (tan y) (tan z))
30.0ms	(* (tan y) (tan z))

series1.4s

Counts

4 → 12

Calls

4 calls:

645.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
531.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
125.0ms	(+ (tan y) (tan z))
131.0ms	(* (tan y) (tan z))

simplify730.0ms

Counts

79 → 79

Iterations

Useful iterations: done (728.0ms)

Iter	Nodes	Cost
0	154	1433
1	375	1362
2	1173	1304
done	5001	1291

prune324.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin y) (sin z))
0.2b	(* (sin y) (sin z))
0.3b	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))
0.3b	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`pow1` `cbrt-undiv` `add-cube-cbrt` `*-un-lft-identity` `div-exp`
6×	`associate-r` `associate-l`
4×	`sin-mult` `add-log-exp`
2×	`frac-2neg` `times-frac` `pow-prod-down` `clear-num` `associate-/r` `associate-/r/` `cos-mult` `-commutative` `div-inv` `associate-/l/` `associate-/l*` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

25.0ms	(* (sin y) (sin z))
23.0ms	(* (sin y) (sin z))
19.0ms	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))
33.0ms	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))

series391.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (sin y) (sin z))
67.0ms	(* (sin y) (sin z))
140.0ms	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))
134.0ms	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))

simplify1.0s

Counts

96 → 96

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	95	1194
1	249	1172
2	1344	928
done	5000	908

prune576.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan y) (tan z))
0.2b	(* (tan y) (tan z))
0.4b	(- (* x x) (* (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))
0.4b	(* (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))

rewrite571.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
16×	`tan-quot`
15×	`pow1`
12×	`add-cube-cbrt` `associate-r` `associate-l`
11×	`frac-times`
10×	`add-exp-log` `add-cbrt-cube`
9×	`flip3--` `flip--` `difference-of-squares`
8×	`swap-sqr` `frac-sub`
6×	`distribute-lft-out--` `add-log-exp`
5×	`sub-neg` `associate-r/` `associate-l/`
4×	`distribute-rgt-in` `distribute-lft-in` `times-frac` `associate--r+`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`pow2` `pow-plus` `diff-log` `pow-sqr` `pow-prod-up`

Counts

4 → 114

Calls

4 calls:

17.0ms	(* (tan y) (tan z))
17.0ms	(* (tan y) (tan z))
42.0ms	(- (* x x) (* (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))
489.0ms	(* (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))

series2.3s

Counts

4 → 12

Calls

4 calls:

123.0ms	(* (tan y) (tan z))
125.0ms	(* (tan y) (tan z))
1.4s	(- (* x x) (* (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))
665.0ms	(* (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))

simplify1.5s

Counts

126 → 126

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	222	4559
1	686	4270
2	3595	3848
done	5000	3489

prune597.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes310.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	56
1	23	56
done	23	56

end0.0ms

sample9.0s

Algorithm

intervals

Results

5.1s	3828×	body	1280	valid
1.8s	2000×	body	640	valid
535.0ms	8000×	pre	80	true
523.0ms	1173×	body	80	valid
370.0ms	697×	body	320	valid
120.0ms	302×	body	160	valid