Details

sample171.0ms

Algorithm

intervals

Results

98.0ms	121×	body	1280	valid
29.0ms	66×	body	640	valid
10.0ms	256×	pre	80	true
6.0ms	18×	body	320	valid
4.0ms	38×	body	80	valid
3.0ms	13×	body	160	valid

simplify20.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(- (tan (+ y z)) (tan a))
0.2b	(+ x (- (tan (+ y z)) (tan a)))
2.4b	(tan (+ y z))

rewrite18.0ms

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	(- (tan (+ y z)) (tan a))
6.0ms	(+ x (- (tan (+ y z)) (tan a)))
4.0ms	(tan (+ y z))

series297.0ms

Counts

3 → 9

Calls

3 calls:

116.0ms	(- (tan (+ y z)) (tan a))
122.0ms	(+ x (- (tan (+ y z)) (tan a)))
59.0ms	(tan (+ y z))

simplify41.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (13.0ms)

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

prune159.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

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:

13.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
5.0ms	(+ (tan y) (tan z))
17.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
5.0ms	(* (tan y) (tan z))

series925.0ms

Counts

4 → 12

Calls

4 calls:

387.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
95.0ms	(+ (tan y) (tan z))
345.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
97.0ms	(* (tan y) (tan z))

simplify78.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	367	860
1	1074	821
2	3057	814
3	5001	814

prune283.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan y) (tan z))
0.2b	(* (tan z) (tan z))
0.3b	(* (tan y) (tan y))
5.0b	(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (- (tan y) (tan z)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
38×	`tan-quot`
35×	`*-un-lft-identity`
25×	`add-cube-cbrt`
20×	`pow1` `times-frac`
12×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/l/` `difference-of-squares`
10×	`frac-sub`
9×	`frac-times` `associate-r/` `associate-r` `associate-l` `associate-l/`
6×	`swap-sqr`
5×	`associate-/r*` `distribute-lft-out--`
4×	`associate-/l*` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`pow2` `flip3--` `pow-plus` `pow-sqr` `pow-prod-up` `flip--`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 133

Calls

4 calls:

5.0ms	(* (tan y) (tan z))
5.0ms	(* (tan z) (tan z))
5.0ms	(* (tan y) (tan y))
15.0ms	(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (- (tan y) (tan z)))

series396.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (tan y) (tan z))
33.0ms	(* (tan z) (tan z))
38.0ms	(* (tan y) (tan y))
230.0ms	(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (- (tan y) (tan z)))

simplify74.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	521	1251
1	2392	1138
2	5001	1094

prune517.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan y) (tan y))
0.6b	(pow (tan z) 6)
5.0b	(/ (- (* (tan y) (tan y)) (cbrt (pow (tan z) 6))) (- (tan y) (tan z)))
11.8b	(cbrt (pow (tan z) 6))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
35×	`times-frac`
32×	`difference-of-squares`
26×	`add-cube-cbrt`
25×	`cbrt-prod`
12×	`pow1` `unpow-prod-down`
9×	`add-exp-log`
8×	`add-cbrt-cube` `distribute-lft-out--` `sqr-pow`
7×	`associate-/l*`
6×	`tan-quot`
5×	`associate-/r*`
4×	`add-log-exp`
3×	`pow-unpow` `swap-sqr` `associate-r` `associate-l` `associate-/r/`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-times` `pow-to-exp` `pow-pow` `frac-2neg` `pow-plus` `pow1/3` `div-sub` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `pow-exp` `prod-exp` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `frac-sub` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 125

Calls

4 calls:

5.0ms	(* (tan y) (tan y))
3.0ms	(pow (tan z) 6)
16.0ms	(/ (- (* (tan y) (tan y)) (cbrt (pow (tan z) 6))) (- (tan y) (tan z)))
3.0ms	(cbrt (pow (tan z) 6))

series369.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (tan y) (tan y))
60.0ms	(pow (tan z) 6)
236.0ms	(/ (- (* (tan y) (tan y)) (cbrt (pow (tan z) 6))) (- (tan y) (tan z)))
34.0ms	(cbrt (pow (tan z) 6))

simplify62.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	558	1534
1	1966	1377
2	5001	1364

prune526.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.1b

regimes254.0ms

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	19
1	24	19

end0.0ms

sample5.2s

Algorithm

intervals

Results

3.2s	3877×	body	1280	valid
929.0ms	1986×	body	640	valid
329.0ms	8000×	pre	80	true
213.0ms	711×	body	320	valid
111.0ms	1150×	body	80	valid
57.0ms	276×	body	160	valid