Details

sample115.0ms

Algorithm

intervals

Results

57.0ms	132×	body	1280	valid
17.0ms	256×	pre	80	true
14.0ms	58×	body	640	valid
4.0ms	25×	body	320	valid
2.0ms	32×	body	80	valid
1.0ms	9×	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

prune2.0ms

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: 14.3b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
4.8b	(tan (+ y z))

rewrite17.0ms

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))
4.0ms	(tan (+ y z))

series274.0ms

Counts

3 → 9

Calls

3 calls:

113.0ms	(+ x (- (tan (+ y z)) (tan a)))
109.0ms	(- (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

prune144.0ms

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

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan y) (tan z))
0.2b	(+ 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))

rewrite36.0ms

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))
13.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
12.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
5.0ms	(* (tan y) (tan z))

series892.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(+ (tan y) (tan z))
340.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
370.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
90.0ms	(* (tan y) (tan z))

simplify77.0ms

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

prune268.0ms

Filtered

79 candidates to 59 candidates (74.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	71	8	79
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	75	13	88

Merged error: 0.1b

Counts

88 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

8.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
5.0ms	(+ (tan y) (tan z))
14.0ms	(- (+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (tan a))
5.0ms	(* (tan y) (tan z))

series713.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
88.0ms	(+ (tan y) (tan z))
331.0ms	(- (+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (tan a))
90.0ms	(* (tan y) (tan z))

simplify47.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	456	1169
1	1596	1113
2	5001	1095

prune305.0ms

Filtered

101 candidates to 76 candidates (75.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	97	4	101
Fresh	5	7	12
Picked	0	1	1
Done	0	0	0
Total	102	12	114

Merged error: 0.1b

Counts

114 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (tan z)) (cbrt (tan z)))
0.6b	(cbrt (tan z))
0.6b	(cbrt (tan z))
0.6b	(cbrt (tan z))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
7×	`tan-quot` `cbrt-div`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 79

Calls

4 calls:

7.0ms	(* (cbrt (tan z)) (cbrt (tan z)))
2.0ms	(cbrt (tan z))
2.0ms	(cbrt (tan z))
2.0ms	(cbrt (tan z))

series478.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(* (cbrt (tan z)) (cbrt (tan z)))
111.0ms	(cbrt (tan z))
113.0ms	(cbrt (tan z))
116.0ms	(cbrt (tan z))

simplify81.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 3 (72.0ms)

Iter	Nodes	Cost
0	168	505
1	527	468
2	2101	436
3	5001	432

prune298.0ms

Filtered

91 candidates to 65 candidates (71.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	91	12	103

Merged error: 0.1b

Counts

103 → 12

regimes516.0ms

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	19	11
1	19	11

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.6s	3822×	body	1280	valid
517.0ms	8000×	pre	80	true
502.0ms	2067×	body	640	valid
116.0ms	697×	body	320	valid
56.0ms	1119×	body	80	valid
34.0ms	295×	body	160	valid