Details

sample3.5s

Algorithm

intervals

Results

47.0ms	111×	body	1280	valid
18.0ms	74×	body	640	valid
18.0ms	256×	pre	80	true
3.0ms	19×	body	320	valid
2.0ms	17×	body	160	valid
2.0ms	35×	body	80	valid

simplify357.0ms

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: 12.6b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
3.7b	(tan (+ y z))

rewrite28.0ms

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:

14.0ms	(+ x (- (tan (+ y z)) (tan a)))
6.0ms	(- (tan (+ y z)) (tan a))
6.0ms	(tan (+ y z))

series103.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(+ x (- (tan (+ y z)) (tan a)))
33.0ms	(- (tan (+ y z)) (tan a))
26.0ms	(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

prune106.0ms

Filtered

39 candidates to 51 candidates (-30.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	41	10	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	42	10	52

Merged error: 0.1b

Counts

52 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

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)) (- 1 (* (tan y) (tan z)))) (tan a))
0.2b	(* (tan y) (tan z))

rewrite34.0ms

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:

4.0ms	(+ (tan y) (tan z))
12.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
11.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
5.0ms	(* (tan y) (tan z))

series284.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+ (tan y) (tan z))
124.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
118.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
21.0ms	(* (tan y) (tan z))

simplify73.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 2 (23.0ms)

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

prune137.0ms

Filtered

59 candidates to 79 candidates (-33.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	71	8	79
Fresh	7	2	9
Picked	1	0	1
Done	0	0	0
Total	79	10	89

Merged error: 0.0b

Counts

89 → 10

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos y) (sin z))
0.2b	(- (/ (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z))) (- 1 (* (tan y) (tan z)))) (tan a))
0.2b	(* (tan y) (tan z))
0.3b	(/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

4.0ms	(* (cos y) (sin z))
19.0ms	(- (/ (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z))) (- 1 (* (tan y) (tan z)))) (tan a))
5.0ms	(* (tan y) (tan z))
9.0ms	(/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z)))

series180.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (cos y) (sin z))
119.0ms	(- (/ (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z))) (- 1 (* (tan y) (tan z)))) (tan a))
21.0ms	(* (tan y) (tan z))
31.0ms	(/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z)))

simplify52.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	475	1176
1	1826	1041
2	5001	1026

prune130.0ms

Filtered

68 candidates to 91 candidates (-33.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	91	10	101

Merged error: 0.0b

Counts

101 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

7.0ms	(* (+ (tan y) (tan z)) (cos a))
5.0ms	(* (tan y) (tan z))
5.0ms	(* (tan y) (tan z))
16.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

series222.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (+ (tan y) (tan z)) (cos a))
22.0ms	(* (tan y) (tan z))
23.0ms	(* (tan y) (tan z))
143.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

simplify70.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	587	1304
1	2701	1144
2	5003	1128

prune118.0ms

Filtered

83 candidates to 108 candidates (-30.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	108	10	118

Merged error: 0.0b

Counts

118 → 10

regimes833.0ms

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	30	19
1	30	19

end0.0ms

sample6.5s

Algorithm

intervals

Results

1.7s	3987×	body	1280	valid
534.0ms	8000×	pre	80	true
489.0ms	1987×	body	640	valid
118.0ms	667×	body	320	valid
56.0ms	1073×	body	80	valid
38.0ms	286×	body	160	valid

Details

sample3.5s

simplify357.0ms

prune6.0ms

localize13.0ms

rewrite28.0ms

series103.0ms

simplify38.0ms

prune106.0ms

localize15.0ms

rewrite34.0ms

series284.0ms

simplify73.0ms

prune137.0ms

localize28.0ms

rewrite40.0ms

series180.0ms

simplify52.0ms

prune130.0ms

localize21.0ms

rewrite36.0ms

series222.0ms

simplify70.0ms

prune118.0ms

regimes833.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample6.5s

Profiling