Details

sample346.0ms

Algorithm

intervals

Results

148.0ms	123×	body	1280	valid
118.0ms	59×	body	640	valid
15.0ms	256×	pre	80	true
11.0ms	21×	body	320	valid
7.0ms	39×	body	80	valid
5.0ms	14×	body	160	valid

simplify5.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
9	4724
8	1354
7	446
6	193
5	89
4	39
3	33
2	22
1	15
0	9

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.1b

localize24.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
4.2b	(tan (+ y z))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity` `add-log-exp`
5×	`add-sqr-sqrt`
4×	`tan-quot`
3×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
2×	`tan-sum` `associate-+r+` `sum-log` `sub-neg` `diff-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:

12.0ms	(+ x (- (tan (+ y z)) (tan a)))
23.0ms	(- (tan (+ y z)) (tan a))
10.0ms	(tan (+ y z))

series443.0ms

Counts

3 → 9

Calls

3 calls:

168.0ms	(+ x (- (tan (+ y z)) (tan a)))
193.0ms	(- (tan (+ y z)) (tan a))
81.0ms	(tan (+ y z))

simplify668.0ms

Counts

51 → 51

Iterations

Iter	Nodes
done	5001
3	1734
2	475
1	198
0	91

prune321.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite291.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

27.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y))))
184.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a)))
13.0ms	(* (tan z) (tan y))
66.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a))

series1.7s

Counts

4 → 12

Calls

4 calls:

307.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y))))
605.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a)))
143.0ms	(* (tan z) (tan y))
606.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a))

simplify731.0ms

Counts

102 → 102

Iterations

Iter	Nodes
done	5001
2	1634
1	468
0	190

prune849.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

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

rewrite263.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

13.0ms	(* (cos y) (sin z))
12.0ms	(* (tan y) (tan z))
166.0ms	(- (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (* (cos y) (cos z)) (- 1 (* (tan y) (tan z))))) (tan a))
68.0ms	(/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (* (cos y) (cos z)) (- 1 (* (tan y) (tan z)))))

series1.3s

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (cos y) (sin z))
147.0ms	(* (tan y) (tan z))
660.0ms	(- (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (* (cos y) (cos z)) (- 1 (* (tan y) (tan z))))) (tan a))
429.0ms	(/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (* (cos y) (cos z)) (- 1 (* (tan y) (tan z)))))

simplify1.2s

Counts

96 → 96

Iterations

Iter	Nodes
done	5002
2	2656
1	582
0	220

prune993.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) x)
0.2b	(* (tan y) (tan z))
0.2b	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
2.4b	(exp (+ (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) x))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

313.0ms	(+ (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) x)
13.0ms	(* (tan y) (tan z))
88.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
889.0ms	(exp (+ (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) x))

series3.0s

Counts

4 → 12

Calls

4 calls:

1.6s	(+ (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) x)
152.0ms	(* (tan y) (tan z))
591.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
648.0ms	(exp (+ (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) x))

simplify630.0ms

Counts

83 → 83

Iterations

Iter	Nodes
done	5000
2	1125
1	353
0	148

prune599.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes710.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	33
1	33
0	24

end0.0ms

sample9.5s

Algorithm

intervals

Results

5.6s	3893×	body	1280	valid
2.1s	1992×	body	640	valid
507.0ms	8000×	pre	80	true
339.0ms	695×	body	320	valid
283.0ms	1131×	body	80	valid
120.0ms	289×	body	160	valid