Details

sample311.0ms

Algorithm

intervals

Results

177.0ms	127×	body	1280	valid
54.0ms	68×	body	640	valid
16.0ms	256×	pre	80	true
12.0ms	25×	body	320	valid
4.0ms	26×	body	80	valid
4.0ms	10×	body	160	valid

simplify8.0ms

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.5b

localize72.0ms

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))

rewrite77.0ms

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:

28.0ms	(+ x (- (tan (+ y z)) (tan a)))
35.0ms	(- (tan (+ y z)) (tan a))
13.0ms	(tan (+ y z))

series442.0ms

Counts

3 → 9

Calls

3 calls:

183.0ms	(+ x (- (tan (+ y z)) (tan a)))
172.0ms	(- (tan (+ y z)) (tan a))
87.0ms	(tan (+ y z))

simplify32.0ms

Counts: 51 → 51

prune281.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

40.0ms	(+ x (/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a))))
15.0ms	(* (tan y) (tan z))
25.0ms	(* (tan y) (tan z))
71.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

series2.1s

Counts

4 → 12

Calls

4 calls:

1.1s	(+ x (/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a))))
131.0ms	(* (tan y) (tan z))
139.0ms	(* (tan y) (tan z))
739.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

simplify84.0ms

Counts: 99 → 99

prune744.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize68.0ms

Local error

Found 4 expressions with local error:

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

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

32.0ms	(/ (* (sin y) (tan z)) (cos y))
30.0ms	(* (tan y) (tan z))
18.0ms	(* (sin y) (tan z))
70.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (/ (* (sin y) (tan z)) (cos y))) (cos a)))

series1.2s

Counts

4 → 12

Calls

4 calls:

172.0ms	(/ (* (sin y) (tan z)) (cos y))
162.0ms	(* (tan y) (tan z))
92.0ms	(* (sin y) (tan z))
761.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (/ (* (sin y) (tan z)) (cos y))) (cos a)))

simplify91.0ms

Counts: 106 → 106

prune810.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize86.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin y) (tan z))
0.2b	(* (sin y) (tan z))
0.2b	(* (/ (* (sin y) (tan z)) (cos y)) (/ (* (sin y) (tan z)) (cos y)))
0.3b	(pow (/ (* (sin y) (tan z)) (cos y)) 3)

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-exp-log` `add-cbrt-cube`
27×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `prod-exp` `cbrt-unprod`
16×	`pow1`
14×	`cbrt-undiv` `div-exp`
13×	`associate-r` `associate-l`
7×	`unpow-prod-down` `cube-prod` `swap-sqr`
6×	`div-inv`
4×	`add-log-exp`
3×	`pow-unpow` `associate-r/` `pow-prod-down` `pow-exp` `-commutative` `rem-cube-cbrt` `unswap-sqr`
2×	`tan-quot`
1×	`cube-div` `pow2` `cube-mult` `frac-times` `pow-to-exp` `pow-pow` `pow-plus` `unpow3` `associate-*l/` `pow-sqr` `pow-prod-up` `sqr-pow`

Counts

4 → 130

Calls

4 calls:

26.0ms	(* (sin y) (tan z))
18.0ms	(* (sin y) (tan z))
54.0ms	(* (/ (* (sin y) (tan z)) (cos y)) (/ (* (sin y) (tan z)) (cos y)))
17.0ms	(pow (/ (* (sin y) (tan z)) (cos y)) 3)

series620.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(* (sin y) (tan z))
128.0ms	(* (sin y) (tan z))
189.0ms	(* (/ (* (sin y) (tan z)) (cos y)) (/ (* (sin y) (tan z)) (cos y)))
181.0ms	(pow (/ (* (sin y) (tan z)) (cos y)) 3)

simplify102.0ms

Counts: 142 → 142

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

regimes786.0ms

Accuracy

-4.7% (0.2b remaining)

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

bsearch0.0ms

simplify68.0ms

end0.0ms

sample10.9s

Algorithm

intervals

Results

5.7s	3849×	body	1280	valid
2.3s	2029×	body	640	valid
1.1s	8000×	pre	80	true
947.0ms	722×	body	320	valid
184.0ms	1135×	body	80	valid
89.0ms	265×	body	160	valid