Details

sample163.0ms

Algorithm

intervals

Results

86.0ms	118×	body	1280	valid
25.0ms	61×	body	640	valid
10.0ms	256×	pre	80	true
9.0ms	37×	body	80	valid
8.0ms	30×	body	320	valid
2.0ms	10×	body	160	valid

simplify19.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	5
1	22	5
2	33	5
3	39	5
4	50	5
5	70	5
6	99	5
7	124	5
8	166	5
9	259	5
10	260	5
11	260	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.8b

localize11.0ms

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))

rewrite43.0ms

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:

15.0ms	(+ x (- (tan (+ y z)) (tan a)))
21.0ms	(- (tan (+ y z)) (tan a))
6.0ms	(tan (+ y z))

series305.0ms

Counts

3 → 9

Calls

3 calls:

129.0ms	(+ x (- (tan (+ y z)) (tan a)))
123.0ms	(- (tan (+ y z)) (tan a))
53.0ms	(tan (+ y z))

simplify38.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	196	346
1	467	335
2	1316	334
3	5002	334

prune130.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite249.0ms

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

Counts

4 → 90

Calls

4 calls:

29.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
127.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
75.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
15.0ms	(* (tan y) (tan z))

series1.1s

Counts

4 → 12

Calls

4 calls:

221.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
371.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
401.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
95.0ms	(* (tan y) (tan z))

simplify48.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	449	1259
1	1503	1211
2	5001	1204

prune322.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.2b	(* (tan y) (tan z))
0.4b	(exp (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
2.8b	(log (exp (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))

rewrite396.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

74.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
14.0ms	(* (tan y) (tan z))
146.0ms	(exp (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
159.0ms	(log (exp (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))

series1.3s

Counts

4 → 12

Calls

4 calls:

402.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
94.0ms	(* (tan y) (tan z))
440.0ms	(exp (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
405.0ms	(log (exp (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))

simplify54.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	286	1083
1	807	991
2	1997	984
3	5002	984

prune309.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan y) (tan z))
0.2b	(* (tan y) (tan z))
0.2b	(* (tan y) (tan z))
0.3b	(* (* (tan y) (tan z)) (* (tan y) (tan z)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

49×	`pow1`
44×	`tan-quot`
22×	`add-exp-log` `add-cbrt-cube`
20×	`frac-times` `pow-prod-down`
16×	`add-sqr-sqrt`
14×	`associate-r/` `associate-l/`
11×	`prod-exp` `cbrt-unprod`
10×	`add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*`
4×	`pow-sqr` `*-commutative` `pow-prod-up` `add-log-exp`
3×	`unswap-sqr`
2×	`pow-plus`
1×	`pow2` `swap-sqr`

Counts

4 → 112

Calls

4 calls:

14.0ms	(* (tan y) (tan z))
15.0ms	(* (tan y) (tan z))
15.0ms	(* (tan y) (tan z))
66.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))

series397.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (tan y) (tan z))
94.0ms	(* (tan y) (tan z))
93.0ms	(* (tan y) (tan z))
116.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))

simplify42.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	311	770
1	1417	646
2	5001	625

prune349.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes201.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	20
1	24	20

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.9s	3864×	body	1280	valid
888.0ms	2022×	body	640	valid
335.0ms	8000×	pre	80	true
183.0ms	639×	body	320	valid
101.0ms	1175×	body	80	valid
59.0ms	300×	body	160	valid