Details

sample316.0ms

Algorithm

intervals

Results

61.0ms	131×	body	1280	valid
18.0ms	256×	pre	80	true
14.0ms	59×	body	640	valid
4.0ms	24×	body	320	valid
2.0ms	33×	body	80	valid
1.0ms	9×	body	160	valid

simplify389.0ms

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

prune6.0ms

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: 14.3b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.1b	(- (tan (+ y z)) (tan a))
4.1b	(tan (+ y z))

rewrite20.0ms

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:

5.0ms	(+ x (- (tan (+ y z)) (tan a)))
6.0ms	(- (tan (+ y z)) (tan a))
6.0ms	(tan (+ y z))

series115.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(+ x (- (tan (+ y z)) (tan a)))
33.0ms	(- (tan (+ y z)) (tan a))
42.0ms	(tan (+ y z))

simplify37.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (11.0ms)

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

prune101.0ms

Filtered

39 candidates to 51 candidates (-30.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	43	8	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	8	52

Merged error: 0.1b

Counts

52 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite41.0ms

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:

12.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
8.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
11.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
7.0ms	(* (tan y) (tan z))

series321.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
57.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
118.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
22.0ms	(* (tan y) (tan z))

simplify119.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	449	1259
1	1503	1211
2	4992	1203
3	5001	1203

prune174.0ms

Filtered

75 candidates to 102 candidates (-36.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	94	8	102
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	98	12	110

Merged error: 0.0b

Counts

110 → 12

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

4.0ms	(* (sin y) (cos z))
16.0ms	(- (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (- 1 (* (tan y) (tan z))) (* (cos y) (cos z)))) (tan a))
5.0ms	(* (tan y) (tan z))
13.0ms	(/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (- 1 (* (tan y) (tan z))) (* (cos y) (cos z))))

series217.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin y) (cos z))
117.0ms	(- (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (- 1 (* (tan y) (tan z))) (* (cos y) (cos z)))) (tan a))
21.0ms	(* (tan y) (tan z))
70.0ms	(/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (- 1 (* (tan y) (tan z))) (* (cos y) (cos z))))

simplify63.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	582	1423
1	2392	1265
2	5001	1265

prune143.0ms

Filtered

72 candidates to 97 candidates (-34.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	97	12	109

Merged error: 0.0b

Counts

109 → 12

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

11.0ms	(/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (sin z)) (* (cos y) (cos z)))))
19.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (sin z)) (* (cos y) (cos z))))) (tan a))
7.0ms	(/ (* (sin y) (sin z)) (* (cos y) (cos z)))
5.0ms	(* (sin y) (sin z))

series205.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (sin z)) (* (cos y) (cos z)))))
117.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (sin z)) (* (cos y) (cos z))))) (tan a))
22.0ms	(/ (* (sin y) (sin z)) (* (cos y) (cos z)))
9.0ms	(* (sin y) (sin z))

simplify63.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	537	1821
1	2350	1683
2	5001	1683

prune109.0ms

Filtered

81 candidates to 121 candidates (-49.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	1	9	10
Picked	1	0	1
Done	0	1	1
Total	122	11	133

Merged error: 0.0b

Counts

133 → 11

regimes1.1s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	19
1	31	19

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.7s	3940×	body	1280	valid
527.0ms	8000×	pre	80	true
485.0ms	1989×	body	640	valid
110.0ms	657×	body	320	valid
57.0ms	1120×	body	80	valid
38.0ms	294×	body	160	valid

Details

sample316.0ms

simplify389.0ms

prune6.0ms

localize13.0ms

rewrite20.0ms

series115.0ms

simplify37.0ms

prune101.0ms

localize16.0ms

rewrite41.0ms

series321.0ms

simplify119.0ms

prune174.0ms

localize29.0ms

rewrite41.0ms

series217.0ms

simplify63.0ms

prune143.0ms

localize27.0ms

rewrite46.0ms

series205.0ms

simplify63.0ms

prune109.0ms

regimes1.1s

bsearch0.0ms

simplify2.0ms

end0.0ms

sample3.5s

Profiling