Details

sample161.0ms

Algorithm

intervals

Results

83.0ms	120×	body	1280	valid
31.0ms	65×	body	640	valid
10.0ms	256×	pre	80	true
6.0ms	23×	body	320	valid
4.0ms	42×	body	80	valid
1.0ms	6×	body	160	valid

simplify85.0ms

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: 15.7b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(- (tan (+ y z)) (tan a))
0.2b	(+ x (- (tan (+ y z)) (tan a)))
4.1b	(tan (+ y z))

rewrite46.0ms

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×	`pow1` `add-exp-log` `expm1-log1p-u` `fma-def` `fma-neg` `add-cbrt-cube` `log1p-expm1-u`
2×	`sub-neg` `tan-sum` `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 → 72

Calls

3 calls:

19.0ms	(- (tan (+ y z)) (tan a))
17.0ms	(+ x (- (tan (+ y z)) (tan a)))
7.0ms	(tan (+ y z))

series359.0ms

Counts

3 → 9

Calls

3 calls:

139.0ms	(- (tan (+ y z)) (tan a))
153.0ms	(+ x (- (tan (+ y z)) (tan a)))
66.0ms	(tan (+ y z))

simplify2.4s

Counts

81 → 81

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	128	1195
1	274	1008
2	641	882
3	2380	793
done	5001	773

prune251.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite318.0ms

Algorithm

rewrite-expression-head

Rules

165×	`*-un-lft-identity`
115×	`add-sqr-sqrt`
108×	`add-cube-cbrt` `prod-diff`
97×	`times-frac`
56×	`associate-+r+`
27×	`distribute-lft-out`
18×	`fma-neg`
16×	`associate-/r/`
11×	`add-log-exp`
9×	`flip3--` `flip--`
8×	`add-exp-log` `add-cbrt-cube` `div-inv`
7×	`tan-quot`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-def` `associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`sub-neg` `flip3-+` `diff-log` `sum-log` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `frac-times` `associate-+r-` `frac-2neg` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `clear-num` `*-commutative` `frac-sub` `cbrt-unprod` `unswap-sqr`

Counts

4 → 227

Calls

4 calls:

30.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
19.0ms	(* (tan y) (tan z))
151.0ms	(+ 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))

series1.2s

Counts

4 → 12

Calls

4 calls:

247.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
115.0ms	(* (tan y) (tan z))
423.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
454.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))

simplify1.0s

Counts

239 → 239

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	303	7323
1	688	6202
2	1780	5656
done	5001	5023

prune815.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin y) (sin z))
0.2b	(/ (sin z) (* (- 1 (/ (* (sin y) (sin z)) (* (cos z) (cos y)))) (cos z)))
0.3b	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))
0.3b	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `add-sqr-sqrt` `div-exp` `prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1`
5×	`times-frac` `associate-/l*`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `associate-r` `associate-l` `clear-num` `associate-/r*` `div-inv` `sin-mult`
2×	`associate-*l/` `cos-mult` `associate-/l/`
1×	`flip3--` `pow-prod-down` `*-commutative` `flip--` `unswap-sqr`

Counts

4 → 96

Calls

4 calls:

13.0ms	(* (sin y) (sin z))
35.0ms	(/ (sin z) (* (- 1 (/ (* (sin y) (sin z)) (* (cos z) (cos y)))) (cos z)))
18.0ms	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))
21.0ms	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))

series451.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (sin y) (sin z))
171.0ms	(/ (sin z) (* (- 1 (/ (* (sin y) (sin z)) (* (cos z) (cos y)))) (cos z)))
112.0ms	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))
114.0ms	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))

simplify733.0ms

Counts

108 → 108

Iterations

Useful iterations: done (729.0ms)

Iter	Nodes	Cost
0	150	1802
1	379	1727
2	1565	1414
done	5000	1412

prune553.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite387.0ms

Algorithm

rewrite-expression-head

Rules

61×	`*-un-lft-identity`
32×	`add-sqr-sqrt`
30×	`add-cube-cbrt`
24×	`times-frac`
19×	`fma-def`
14×	`distribute-lft-out`
13×	`add-log-exp`
12×	`prod-diff`
6×	`tan-quot` `add-exp-log` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `flip3-+` `fma-neg` `flip-+` `log1p-expm1-u` `associate-/l*`
3×	`associate-/r*` `sum-log` `associate-/l/`
2×	`+-commutative` `diff-log` `frac-add` `frac-sub` `div-inv` `distribute-lft-out--`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `div-exp` `associate--l+` `clear-num` `flip--` `difference-of-squares`

Counts

4 → 121

Calls

4 calls:

9.0ms	(+ (tan y) (tan z))
26.0ms	(/ (+ (tan y) (tan z)) (fma (tan y) (- (tan z)) 1))
46.0ms	(+ (/ (+ (tan y) (tan z)) (fma (tan y) (- (tan z)) 1)) x)
302.0ms	(- (+ (/ (+ (tan y) (tan z)) (fma (tan y) (- (tan z)) 1)) x) (tan a))

series1.5s

Counts

4 → 12

Calls

4 calls:

103.0ms	(+ (tan y) (tan z))
255.0ms	(/ (+ (tan y) (tan z)) (fma (tan y) (- (tan z)) 1))
535.0ms	(+ (/ (+ (tan y) (tan z)) (fma (tan y) (- (tan z)) 1)) x)
635.0ms	(- (+ (/ (+ (tan y) (tan z)) (fma (tan y) (- (tan z)) 1)) x) (tan a))

simplify1.9s

Counts

133 → 133

Iterations

Useful iterations: 3 (831.0ms)

Iter	Nodes	Cost
0	189	2845
1	433	2605
2	1190	2407
3	4228	2209
done	5000	2209

prune751.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes309.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	18
1	18	18
done	18	18

end0.0ms

sample4.9s

Algorithm

intervals

Results

2.9s	3856×	body	1280	valid
859.0ms	2018×	body	640	valid
309.0ms	8000×	pre	80	true
200.0ms	697×	body	320	valid
97.0ms	1145×	body	80	valid
55.0ms	284×	body	160	valid