Details

sample314.0ms

Algorithm

intervals

Results

148.0ms	127×	body	1280	valid
91.0ms	68×	body	640	valid
14.0ms	256×	pre	80	true
12.0ms	25×	body	320	valid
5.0ms	26×	body	80	valid
3.0ms	10×	body	160	valid

simplify157.0ms

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

localize13.0ms

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))

rewrite402.0ms

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:

37.0ms	(+ x (- (tan (+ y z)) (tan a)))
32.0ms	(- (tan (+ y z)) (tan a))
330.0ms	(tan (+ y z))

series495.0ms

Counts

3 → 9

Calls

3 calls:

250.0ms	(+ x (- (tan (+ y z)) (tan a)))
157.0ms	(- (tan (+ y z)) (tan a))
87.0ms	(tan (+ y z))

simplify3.5s

Counts

81 → 81

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	128	1195
1	274	1008
2	644	882
3	2382	793
done	5000	773

prune365.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

1.0ms	(fma (+ (* (tan z) (tan y)) -1) (sin a) (* (+ (tan y) (tan z)) (cos a)))
20.0ms	(* (tan z) (tan y))
16.0ms	(* (tan y) (tan z))
36.0ms	(/ (fma (+ (* (tan z) (tan y)) -1) (sin a) (* (+ (tan y) (tan z)) (cos a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

series1.5s

Counts

4 → 12

Calls

4 calls:

419.0ms	(fma (+ (* (tan z) (tan y)) -1) (sin a) (* (+ (tan y) (tan z)) (cos a)))
143.0ms	(* (tan z) (tan y))
178.0ms	(* (tan y) (tan z))
740.0ms	(/ (fma (+ (* (tan z) (tan y)) -1) (sin a) (* (+ (tan y) (tan z)) (cos a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

simplify3.1s

Counts

93 → 93

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	159	1853
1	353	1769
2	1098	1543
3	4043	1513
done	5000	1513

prune776.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

19.0ms	(/ (* (sin z) (tan y)) (cos z))
16.0ms	(* (tan z) (tan y))
17.0ms	(* (sin z) (tan y))
24.0ms	(/ (fma (+ (* (tan z) (tan y)) -1) (sin a) (* (+ (tan y) (tan z)) (cos a))) (* (- 1 (/ (* (sin z) (tan y)) (cos z))) (cos a)))

series1.0s

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ (* (sin z) (tan y)) (cos z))
121.0ms	(* (tan z) (tan y))
111.0ms	(* (sin z) (tan y))
664.0ms	(/ (fma (+ (* (tan z) (tan y)) -1) (sin a) (* (+ (tan y) (tan z)) (cos a))) (* (- 1 (/ (* (sin z) (tan y)) (cos z))) (cos a)))

simplify1.3s

Counts

105 → 105

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	193	1937
1	456	1862
2	1562	1601
done	5001	1583

prune765.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan z) (tan y))
0.2b	(* (sin z) (tan y))
0.2b	(/ (fma (+ (* (tan z) (tan y)) -1) (sin a) (* (+ (tan y) (tan z)) (cos a))) (* (- 1 (/ 1 (/ (cos z) (* (sin z) (tan y))))) (cos a)))
0.3b	(/ (cos z) (* (sin z) (tan y)))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

17.0ms	(* (tan z) (tan y))
15.0ms	(* (sin z) (tan y))
61.0ms	(/ (fma (+ (* (tan z) (tan y)) -1) (sin a) (* (+ (tan y) (tan z)) (cos a))) (* (- 1 (/ 1 (/ (cos z) (* (sin z) (tan y))))) (cos a)))
20.0ms	(/ (cos z) (* (sin z) (tan y)))

series1.0s

Counts

4 → 12

Calls

4 calls:

145.0ms	(* (tan z) (tan y))
113.0ms	(* (sin z) (tan y))
637.0ms	(/ (fma (+ (* (tan z) (tan y)) -1) (sin a) (* (+ (tan y) (tan z)) (cos a))) (* (- 1 (/ 1 (/ (cos z) (* (sin z) (tan y))))) (cos a)))
151.0ms	(/ (cos z) (* (sin z) (tan y)))

simplify1.3s

Counts

105 → 105

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	203	2004
1	487	1949
2	1579	1606
done	5000	1589

prune693.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes1.0s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	30	68
1	41	64
done	41	64

end0.0ms

sample10.3s

Algorithm

intervals

Results

5.0s	3849×	body	1280	valid
2.3s	2029×	body	640	valid
1.1s	722×	body	320	valid
582.0ms	8000×	pre	80	true
582.0ms	1135×	body	80	valid
160.0ms	265×	body	160	valid