Details

sample321.0ms

Algorithm

intervals

Results

186.0ms	124×	body	1280	valid
47.0ms	62×	body	640	valid
18.0ms	256×	pre	80	true
12.0ms	25×	body	320	valid
7.0ms	34×	body	80	valid
4.0ms	11×	body	160	valid

simplify177.0ms

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: 15.6b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
4.4b	(tan (+ y z))

rewrite74.0ms

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:

27.0ms	(+ x (- (tan (+ y z)) (tan a)))
36.0ms	(- (tan (+ y z)) (tan a))
7.0ms	(tan (+ y z))

series558.0ms

Counts

3 → 9

Calls

3 calls:

244.0ms	(+ x (- (tan (+ y z)) (tan a)))
220.0ms	(- (tan (+ y z)) (tan a))
94.0ms	(tan (+ y z))

simplify3.7s

Counts

81 → 81

Iterations

Useful iterations: done (3.7s)

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

prune311.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize54.0ms

Local error

Found 4 expressions with local error:

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

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 95

Calls

4 calls:

73.0ms	(* (+ (tan y) (tan z)) (cos a))
14.0ms	(/ (fma (+ (* (tan z) (tan y)) -1) (sin a) (* (+ (tan y) (tan z)) (cos a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
22.0ms	(* (tan z) (tan y))
31.0ms	(* (tan y) (tan z))

series1.5s

Counts

4 → 12

Calls

4 calls:

300.0ms	(* (+ (tan y) (tan z)) (cos a))
854.0ms	(/ (fma (+ (* (tan z) (tan y)) -1) (sin a) (* (+ (tan y) (tan z)) (cos a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
158.0ms	(* (tan z) (tan y))
228.0ms	(* (tan y) (tan z))

simplify1.7s

Counts

107 → 107

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	196	1852
1	454	1756
2	1479	1548
done	5000	1536

prune955.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize85.0ms

Local error

Found 4 expressions with local error:

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

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

17.0ms	(/ (fma (+ (/ (* (sin y) (sin z)) (* (cos z) (cos y))) -1) (sin a) (* (+ (tan y) (tan z)) (cos a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
14.0ms	(* (sin y) (sin z))
17.0ms	(* (tan y) (tan z))
19.0ms	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))

series1.3s

Counts

4 → 12

Calls

4 calls:

898.0ms	(/ (fma (+ (/ (* (sin y) (sin z)) (* (cos z) (cos y))) -1) (sin a) (* (+ (tan y) (tan z)) (cos a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
103.0ms	(* (sin y) (sin z))
171.0ms	(* (tan y) (tan z))
162.0ms	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))

simplify1.7s

Counts

106 → 106

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	210	2164
1	502	2129
2	1947	1749
done	5002	1743

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

21.0ms	(/ (fma (+ (* (tan z) (tan y)) -1) (sin a) (* (cos a) (+ (/ (sin z) (cos z)) (/ (sin y) (cos y))))) (* (- 1 (* (tan y) (tan z))) (cos a)))
10.0ms	(/ (sin y) (cos y))
25.0ms	(* (tan y) (tan z))
17.0ms	(* (tan z) (tan y))

series1.3s

Counts

4 → 12

Calls

4 calls:

809.0ms	(/ (fma (+ (* (tan z) (tan y)) -1) (sin a) (* (cos a) (+ (/ (sin z) (cos z)) (/ (sin y) (cos y))))) (* (- 1 (* (tan y) (tan z))) (cos a)))
36.0ms	(/ (sin y) (cos y))
217.0ms	(* (tan y) (tan z))
194.0ms	(* (tan z) (tan y))

simplify3.2s

Counts

113 → 113

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	211	2047
1	453	1965
2	1306	1713
3	4418	1701
done	5000	1701

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes1.4s

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	36
1	31	36
done	31	36

end0.0ms

sample12.6s

Algorithm

intervals

Results

7.5s	3924×	body	1280	valid
1.8s	1956×	body	640	valid
1.2s	8000×	pre	80	true
850.0ms	693×	body	320	valid
225.0ms	298×	body	160	valid
193.0ms	1129×	body	80	valid