Details

sample171.0ms

Algorithm

intervals

Results

94.0ms	126×	body	1280	valid
23.0ms	53×	body	640	valid
17.0ms	256×	pre	80	true
7.0ms	25×	body	320	valid
4.0ms	47×	body	80	valid
1.0ms	5×	body	160	valid

simplify65.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	9
1	15	9
2	22	9
3	31	9
4	37	9
5	47	9
6	54	9
7	64	9
8	82	9
9	99	9
10	107	9
done	107	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.1b	(- (tan (+ y z)) (tan a))
2.8b	(tan (+ y z))

rewrite19.0ms

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:

7.0ms	(+ x (- (tan (+ y z)) (tan a)))
7.0ms	(- (tan (+ y z)) (tan a))
3.0ms	(tan (+ y z))

series317.0ms

Counts

3 → 9

Calls

3 calls:

131.0ms	(+ x (- (tan (+ y z)) (tan a)))
126.0ms	(- (tan (+ y z)) (tan a))
59.0ms	(tan (+ y z))

simplify1.4s

Counts

51 → 51

Iterations

Useful iterations: 3 (135.0ms)

Iter	Nodes	Cost
0	91	627
1	197	590
2	430	572
3	1029	570
4	3628	570
done	5000	570

prune174.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

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))
0.1b	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
0.3b	(* (tan y) (tan z))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

3.0ms	(+ (tan y) (tan z))
41.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
12.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
5.0ms	(* (tan y) (tan z))

series885.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(+ (tan y) (tan z))
439.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
239.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
102.0ms	(* (tan y) (tan z))

simplify1.6s

Counts

98 → 98

Iterations

Useful iterations: 3 (737.0ms)

Iter	Nodes	Cost
0	174	1716
1	392	1641
2	1035	1571
3	2852	1559
done	5000	1559

prune406.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

84.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
18.0ms	(/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z))))
5.0ms	(/ (* (tan y) (sin z)) (cos z))
5.0ms	(* (tan y) (sin z))

series864.0ms

Counts

4 → 12

Calls

4 calls:

437.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
248.0ms	(/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z))))
107.0ms	(/ (* (tan y) (sin z)) (cos z))
72.0ms	(* (tan y) (sin z))

simplify709.0ms

Counts

120 → 120

Iterations

Useful iterations: done (700.0ms)

Iter	Nodes	Cost
0	217	2495
1	488	2396
2	1418	2272
done	5000	2256

prune509.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

4.0ms	(* (sin y) (cos z))
4.0ms	(* (cos y) (sin z))
4.0ms	(* (tan y) (sin z))
22.0ms	(/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (* (cos y) (cos z))))

series504.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (sin y) (cos z))
51.0ms	(* (cos y) (sin z))
79.0ms	(* (tan y) (sin z))
314.0ms	(/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (* (cos y) (cos z))))

simplify731.0ms

Counts

98 → 98

Iterations

Useful iterations: 2 (194.0ms)

Iter	Nodes	Cost
0	206	1800
1	549	1771
2	2009	1487
done	5000	1487

prune474.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes772.0ms

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	24	35
1	33	35
done	33	35

end0.0ms

sample5.6s

Algorithm

intervals

Results

3.1s	3982×	body	1280	valid
932.0ms	1980×	body	640	valid
663.0ms	8000×	pre	80	true
216.0ms	693×	body	320	valid
108.0ms	1076×	body	80	valid
56.0ms	269×	body	160	valid