Details

sample114.0ms

Algorithm

intervals

Results

57.0ms	137×	body	1280	valid
17.0ms	256×	pre	80	true
14.0ms	62×	body	640	valid
3.0ms	16×	body	320	valid
2.0ms	38×	body	80	valid
0.0ms	3×	body	160	valid

simplify18.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 14.5b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(- (tan (+ y z)) (tan a))
0.2b	(+ x (- (tan (+ y z)) (tan a)))
4.3b	(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))
5.0ms	(+ x (- (tan (+ y z)) (tan a)))
4.0ms	(tan (+ y z))

series274.0ms

Counts

3 → 9

Calls

3 calls:

108.0ms	(- (tan (+ y z)) (tan a))
114.0ms	(+ x (- (tan (+ y z)) (tan a)))
52.0ms	(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

prune138.0ms

Filtered

51 candidates to 39 candidates (76.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	42	9	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	9	52

Merged error: 0.1b

Counts

52 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

9.0ms	(+ x (/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a))))
15.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
5.0ms	(* (tan y) (tan z))
5.0ms	(* (tan y) (tan z))

series1.3s

Counts

4 → 12

Calls

4 calls:

670.0ms	(+ x (/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a))))
440.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
86.0ms	(* (tan y) (tan z))
87.0ms	(* (tan y) (tan z))

simplify72.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	607	1601
1	2692	1448
2	5002	1435

prune411.0ms

Filtered

99 candidates to 78 candidates (78.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	92	7	99
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	97	11	108

Merged error: 0.1b

Counts

108 → 11

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan y) (tan z))
0.2b	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (pow (* (tan y) (tan z)) 3)) (cos a)))
0.2b	(* (* (tan y) (tan z)) (* (tan y) (tan z)))
0.3b	(pow (* (tan y) (tan z)) 3)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

48×	`pow1`
44×	`tan-quot`
27×	`associate-*l/`
26×	`add-exp-log` `add-cbrt-cube`
19×	`frac-times` `pow-prod-down`
13×	`associate-*r/`
11×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`associate-/l/`
6×	`frac-sub`
5×	`flip3--` `flip--`
4×	`associate-r` `associate-l` `pow-sqr` `pow-prod-up` `add-log-exp`
3×	`cube-div` `pow-unpow` `times-frac` `associate-/l*`
2×	`cbrt-undiv` `pow-pow` `flip3-+` `pow-plus` `div-exp` `frac-add` `pow-exp` `associate-/r/` `*-commutative` `flip-+` `rem-cube-cbrt`
1×	`pow2` `cube-mult` `pow-to-exp` `unpow-prod-down` `frac-2neg` `unpow3` `div-sub` `cube-prod` `swap-sqr` `clear-num` `associate-/r*` `div-inv` `unswap-sqr` `sqr-pow`

Counts

4 → 127

Calls

4 calls:

5.0ms	(* (tan y) (tan z))
17.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (pow (* (tan y) (tan z)) 3)) (cos a)))
11.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))
6.0ms	(pow (* (tan y) (tan z)) 3)

series844.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (tan y) (tan z))
517.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (pow (* (tan y) (tan z)) 3)) (cos a)))
112.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))
122.0ms	(pow (* (tan y) (tan z)) 3)

simplify123.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (109.0ms)

Iter	Nodes	Cost
0	812	1495
1	4453	1335
2	5001	1331

prune569.0ms

Filtered

139 candidates to 88 candidates (63.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	138	1	139
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	139	11	150

Merged error: 0.1b

Counts

150 → 11

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan y) (tan z))
0.2b	(* (tan y) (tan z))
0.3b	(pow (* (tan y) (tan z)) 3)
25.6b	(cbrt (pow (* (tan y) (tan z)) 3))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

16×	`tan-quot`
14×	`add-sqr-sqrt`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`cbrt-prod`
6×	`cube-div` `associate-r` `associate-l`
4×	`frac-times` `associate-r/` `associate-l/` `add-log-exp`
3×	`pow-unpow` `cbrt-div` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-exp` `*-commutative` `rem-cube-cbrt` `unswap-sqr` `sqr-pow`
1×	`pow-to-exp` `pow1/3` `rem-cbrt-cube`

Counts

4 → 87

Calls

4 calls:

5.0ms	(* (tan y) (tan z))
5.0ms	(* (tan y) (tan z))
5.0ms	(pow (* (tan y) (tan z)) 3)
4.0ms	(cbrt (pow (* (tan y) (tan z)) 3))

series399.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (tan y) (tan z))
92.0ms	(* (tan y) (tan z))
127.0ms	(pow (* (tan y) (tan z)) 3)
88.0ms	(cbrt (pow (* (tan y) (tan z)) 3))

simplify45.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	263	510
1	1337	490
2	5002	489

prune356.0ms

Filtered

99 candidates to 72 candidates (72.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	99	11	110

Merged error: 0.1b

Counts

110 → 11

regimes582.0ms

Accuracy

0% (0.2b 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	30	22
1	30	22

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.7s	3896×	body	1280	valid
522.0ms	8000×	pre	80	true
501.0ms	2062×	body	640	valid
119.0ms	714×	body	320	valid
54.0ms	1072×	body	80	valid
29.0ms	256×	body	160	valid

Details

sample114.0ms

simplify18.0ms

prune3.0ms

localize11.0ms

rewrite18.0ms

series274.0ms

simplify38.0ms

prune138.0ms

localize21.0ms

rewrite36.0ms

series1.3s

simplify72.0ms

prune411.0ms

localize34.0ms

rewrite44.0ms

series844.0ms

simplify123.0ms

prune569.0ms

localize25.0ms

rewrite22.0ms

series399.0ms

simplify45.0ms

prune356.0ms

regimes582.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.2s

Profiling