Details

sample358.0ms

Algorithm

intervals

Results

167.0ms	126×	body	1280	valid
73.0ms	26×	body	320	valid
47.0ms	57×	body	640	valid
17.0ms	256×	pre	80	true
6.0ms	39×	body	80	valid
3.0ms	8×	body	160	valid

simplify130.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.2b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
4.0b	(tan (+ y z))

rewrite90.0ms

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:

38.0ms	(+ x (- (tan (+ y z)) (tan a)))
35.0ms	(- (tan (+ y z)) (tan a))
14.0ms	(tan (+ y z))

series448.0ms

Counts

3 → 9

Calls

3 calls:

202.0ms	(+ x (- (tan (+ y z)) (tan a)))
169.0ms	(- (tan (+ y z)) (tan a))
77.0ms	(tan (+ y z))

simplify675.0ms

Counts: 51 → 51

prune609.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite347.0ms

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:

10.0ms	(+ (tan y) (tan z))
205.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
114.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
16.0ms	(* (tan y) (tan z))

series1.6s

Counts

4 → 12

Calls

4 calls:

147.0ms	(+ (tan y) (tan z))
624.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
722.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
139.0ms	(* (tan y) (tan z))

simplify1.4s

Counts: 79 → 79

prune490.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

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

rewrite553.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

19.0ms	(/ (sin y) (cos y))
19.0ms	(/ (sin z) (cos z))
479.0ms	(- (/ (+ (/ (sin z) (cos z)) (/ (sin y) (cos y))) (- 1 (* (tan y) (tan z)))) (tan a))
31.0ms	(* (tan y) (tan z))

series1.0s

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (sin y) (cos y))
32.0ms	(/ (sin z) (cos z))
781.0ms	(- (/ (+ (/ (sin z) (cos z)) (/ (sin y) (cos y))) (- 1 (* (tan y) (tan z)))) (tan a))
191.0ms	(* (tan y) (tan z))

simplify1.3s

Counts: 105 → 105

prune740.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize71.0ms

Local error

Found 4 expressions with local error:

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

rewrite269.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

13.0ms	(* (sin y) (cos z))
166.0ms	(- (/ (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z))) (- 1 (* (tan y) (tan z)))) (tan a))
21.0ms	(* (tan y) (tan z))
66.0ms	(/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z)))

series1.1s

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (sin y) (cos z))
635.0ms	(- (/ (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z))) (- 1 (* (tan y) (tan z)))) (tan a))
152.0ms	(* (tan y) (tan z))
255.0ms	(/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z)))

simplify781.0ms

Counts: 92 → 92

prune613.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes503.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify5.2s

end0.0ms

sample11.3s

Algorithm

intervals

Results

6.3s	3959×	body	1280	valid
1.9s	1969×	body	640	valid
782.0ms	648×	body	320	valid
693.0ms	1129×	body	80	valid
641.0ms	8000×	pre	80	true
234.0ms	295×	body	160	valid