Details

sample210.0ms

Algorithm

intervals

Results

105.0ms	124×	body	1280	valid
50.0ms	62×	body	640	valid
11.0ms	256×	pre	80	true
9.0ms	25×	body	320	valid
5.0ms	11×	body	160	valid
4.0ms	34×	body	80	valid

simplify6.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize43.0ms

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))

rewrite45.0ms

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:

16.0ms	(+ x (- (tan (+ y z)) (tan a)))
18.0ms	(- (tan (+ y z)) (tan a))
10.0ms	(tan (+ y z))

series326.0ms

Counts

3 → 9

Calls

3 calls:

137.0ms	(+ x (- (tan (+ y z)) (tan a)))
127.0ms	(- (tan (+ y z)) (tan a))
61.0ms	(tan (+ y z))

simplify34.0ms

Counts: 51 → 51

prune155.0ms

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

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

31.0ms	(* (+ (tan y) (tan z)) (cos a))
65.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
16.0ms	(* (tan y) (tan z))
23.0ms	(* (tan y) (tan z))

series909.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(* (+ (tan y) (tan z)) (cos a))
540.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
101.0ms	(* (tan y) (tan z))
103.0ms	(* (tan y) (tan z))

simplify72.0ms

Counts: 108 → 108

prune536.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite131.0ms

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:

72.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (/ (* (sin y) (tan z)) (cos y))) (cos a)))
16.0ms	(/ (* (sin y) (tan z)) (cos y))
23.0ms	(* (sin y) (tan z))
16.0ms	(* (tan y) (tan z))

series1.2s

Counts

4 → 12

Calls

4 calls:

562.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (/ (* (sin y) (tan z)) (cos y))) (cos a)))
114.0ms	(/ (* (sin y) (tan z)) (cos y))
90.0ms	(* (sin y) (tan z))
405.0ms	(* (tan y) (tan z))

simplify78.0ms

Counts: 106 → 106

prune609.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 107

Calls

4 calls:

31.0ms	(* (+ (tan y) (tan z)) (cos a))
65.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (sin y) (/ (tan z) (cos y)))) (cos a)))
24.0ms	(* (tan y) (tan z))
19.0ms	(* (sin y) (/ (tan z) (cos y)))

series947.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(* (+ (tan y) (tan z)) (cos a))
563.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (sin y) (/ (tan z) (cos y)))) (cos a)))
104.0ms	(* (tan y) (tan z))
116.0ms	(* (sin y) (/ (tan z) (cos y)))

simplify84.0ms

Counts: 119 → 119

prune636.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

regimes744.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

end0.0ms

sample8.2s

Algorithm

intervals

Results

5.1s	3924×	body	1280	valid
1.6s	1956×	body	640	valid
408.0ms	8000×	pre	80	true
290.0ms	693×	body	320	valid
240.0ms	1129×	body	80	valid
74.0ms	298×	body	160	valid