Details

sample283.0ms

Algorithm

intervals

Results

115.0ms	112×	body	1280	valid
65.0ms	256×	pre	80	true
47.0ms	77×	body	640	valid
7.0ms	13×	body	320	valid
6.0ms	43×	body	80	valid
4.0ms	11×	body	160	valid

simplify6.9s

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.1b	(- (tan (+ y z)) (tan a))
3.9b	(tan (+ y z))

rewrite76.0ms

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:

33.0ms	(+ x (- (tan (+ y z)) (tan a)))
33.0ms	(- (tan (+ y z)) (tan a))
7.0ms	(tan (+ y z))

series462.0ms

Counts

3 → 9

Calls

3 calls:

205.0ms	(+ x (- (tan (+ y z)) (tan a)))
184.0ms	(- (tan (+ y z)) (tan a))
73.0ms	(tan (+ y z))

simplify918.0ms

Counts

51 → 51

Iterations

Useful iterations: 3 (229.0ms)

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

prune207.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite320.0ms

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:

14.0ms	(+ (tan y) (tan z))
105.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
178.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
20.0ms	(* (tan y) (tan z))

series1.6s

Counts

4 → 12

Calls

4 calls:

185.0ms	(+ (tan y) (tan z))
644.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
592.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
147.0ms	(* (tan y) (tan z))

simplify796.0ms

Counts

79 → 79

Iterations

Useful iterations: done (791.0ms)

Iter	Nodes	Cost
0	154	1433
1	376	1362
2	1174	1304
done	5000	1291

prune583.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.2b	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
0.2b	(* (tan y) (tan z))
2.5b	(exp (+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

108.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
155.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
30.0ms	(* (tan y) (tan z))
714.0ms	(exp (+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))

series1.7s

Counts

4 → 12

Calls

4 calls:

507.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
493.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
108.0ms	(* (tan y) (tan z))
601.0ms	(exp (+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))

simplify637.0ms

Counts

83 → 83

Iterations

Useful iterations: done (634.0ms)

Iter	Nodes	Cost
0	144	1677
1	344	1612
2	1109	1517
done	5001	1506

prune422.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

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

rewrite532.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
8×	`add-cube-cbrt`
6×	`pow1`
5×	`tan-quot`
4×	`times-frac`
3×	`associate-r` `associate-l` `associate-/l*`
2×	`cbrt-undiv` `sub-neg` `associate-+r+` `flip3-+` `diff-log` `div-exp` `prod-exp` `sum-log` `cbrt-unprod` `flip-+` `associate-/l/` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `frac-times` `associate-+r-` `flip3--` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `associate-/r` `associate-/r/` `cos-mult` `-commutative` `frac-sub` `flip--` `div-inv` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

166.0ms	(- (/ (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z))) (- 1 (* (tan y) (tan z)))) (tan a))
282.0ms	(+ x (- (/ (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z))) (- 1 (* (tan y) (tan z)))) (tan a)))
29.0ms	(* (tan y) (tan z))
52.0ms	(/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z)))

series1.4s

Counts

4 → 12

Calls

4 calls:

561.0ms	(- (/ (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z))) (- 1 (* (tan y) (tan z)))) (tan a))
506.0ms	(+ x (- (/ (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z))) (- 1 (* (tan y) (tan z)))) (tan a)))
130.0ms	(* (tan y) (tan z))
211.0ms	(/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z)))

simplify830.0ms

Counts

90 → 90

Iterations

Useful iterations: done (827.0ms)

Iter	Nodes	Cost
0	193	2495
1	491	2391
2	1715	2209
done	5001	2184

prune568.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes374.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	32
1	31	32
done	31	32

end0.0ms

sample9.4s

Algorithm

intervals

Results

5.1s	3829×	body	1280	valid
1.7s	2050×	body	640	valid
1.1s	8000×	pre	80	true
547.0ms	691×	body	320	valid
249.0ms	1130×	body	80	valid
128.0ms	300×	body	160	valid