Details

sample310.0ms

Algorithm

intervals

Results

246.0ms	111×	body	2560	valid
36.0ms	74×	body	1280	valid
8.0ms	42×	body	640	valid
4.0ms	256×	pre	80	true
2.0ms	18×	body	320	valid
1.0ms	11×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	4
1	11	4
2	11	4

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: 59.9b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
3.1b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
19×	`times-frac`
12×	`add-cube-cbrt`
5×	`distribute-lft-out--`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
3×	`associate-/r` `div-inv` `associate-/l`
2×	`pow1`
1×	`tan-quot` `cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `associate-/r/` `frac-sub` `flip--`

Counts

2 → 50

Calls

2 calls:

8.0ms	(/ 1.0 (tan x))
12.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series107.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(/ 1.0 (tan x))
74.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify85.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	227	342
1	635	327
2	2856	326
3	5001	326

prune162.0ms

Filtered

56 candidates to 46 candidates (82.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	53	3	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	3	57

Merged error: 1.3b

Counts

57 → 3

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* (pow x 2) (- 0.5 (* x 0.03333333333333333))) (* 0.3333333333333333 x))
0.0b	(* (pow x 2) (- 0.5 (* x 0.03333333333333333)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`associate-l`
7×	`add-exp-log`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`distribute-rgt-in` `sub-neg` `unpow-prod-down` `associate-+l+` `distribute-lft-in` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
3×	`associate-r` `prod-exp`
2×	`pow1` `associate-*r/` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `flip3--` `flip3-+` `pow-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `flip-+`

Counts

2 → 48

Calls

2 calls:

6.0ms	(+ (* (pow x 2) (- 0.5 (* x 0.03333333333333333))) (* 0.3333333333333333 x))
6.0ms	(* (pow x 2) (- 0.5 (* x 0.03333333333333333)))

series109.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(+ (* (pow x 2) (- 0.5 (* x 0.03333333333333333))) (* 0.3333333333333333 x))
72.0ms	(* (pow x 2) (- 0.5 (* x 0.03333333333333333)))

simplify40.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	245	376
1	998	331
2	5002	325

prune147.0ms

Filtered

54 candidates to 35 candidates (64.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	49	5	54
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	50	7	57

Merged error: 1.0b

Counts

57 → 7

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (log (exp (* (pow x 2) (- 0.5 (* x 0.03333333333333333))))) (* 0.3333333333333333 x))
0.0b	(* (pow x 2) (- 0.5 (* x 0.03333333333333333)))
3.0b	(log (exp (* (pow x 2) (- 0.5 (* x 0.03333333333333333)))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `log-prod`
8×	`add-exp-log` `add-cube-cbrt` `-un-lft-identity` `associate-l*` `exp-sum`
7×	`associate-+l+`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
5×	`add-cbrt-cube` `add-log-exp`
4×	`pow1` `unpow-prod-down` `unswap-sqr`
3×	`associate-r` `prod-exp` `log-pow`
2×	`associate-*r/` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `exp-prod` `flip3--` `exp-to-pow` `flip3-+` `rem-log-exp` `pow-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `flip-+`

Counts

3 → 69

Calls

3 calls:

5.0ms	(+ (log (exp (* (pow x 2) (- 0.5 (* x 0.03333333333333333))))) (* 0.3333333333333333 x))
7.0ms	(* (pow x 2) (- 0.5 (* x 0.03333333333333333)))
3.0ms	(log (exp (* (pow x 2) (- 0.5 (* x 0.03333333333333333)))))

series185.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(+ (log (exp (* (pow x 2) (- 0.5 (* x 0.03333333333333333))))) (* 0.3333333333333333 x))
75.0ms	(* (pow x 2) (- 0.5 (* x 0.03333333333333333)))
77.0ms	(log (exp (* (pow x 2) (- 0.5 (* x 0.03333333333333333)))))

simplify43.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	280	559
1	1053	479
2	5002	473

prune217.0ms

Filtered

78 candidates to 50 candidates (64.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	75	3	78
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	78	7	85

Merged error: 0.8b

Counts

85 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (pow x 2) (- 0.5 (* x 0.03333333333333333)))
0.0b	(* (pow x 2) (- 0.5 (* x 0.03333333333333333)))
2.8b	(log (sqrt (exp (* (pow x 2) (- 0.5 (* x 0.03333333333333333))))))
2.8b	(log (sqrt (exp (* (pow x 2) (- 0.5 (* x 0.03333333333333333))))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
20×	`log-prod`
16×	`add-exp-log` `associate-l`
14×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
10×	`log-pow`
8×	`pow1` `distribute-rgt-in` `sub-neg` `unpow-prod-down` `distribute-lft-in` `exp-sum` `add-cbrt-cube` `unswap-sqr`
6×	`sqrt-pow1` `associate-r` `prod-exp` `add-log-exp`
4×	`associate-*r/` `unpow2` `sqr-pow`
2×	`pow-to-exp` `exp-prod` `flip3--` `exp-to-pow` `pow1/2` `rem-log-exp` `pow-exp` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 112

Calls

4 calls:

7.0ms	(* (pow x 2) (- 0.5 (* x 0.03333333333333333)))
7.0ms	(* (pow x 2) (- 0.5 (* x 0.03333333333333333)))
3.0ms	(log (sqrt (exp (* (pow x 2) (- 0.5 (* x 0.03333333333333333))))))
4.0ms	(log (sqrt (exp (* (pow x 2) (- 0.5 (* x 0.03333333333333333))))))

series342.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(* (pow x 2) (- 0.5 (* x 0.03333333333333333)))
74.0ms	(* (pow x 2) (- 0.5 (* x 0.03333333333333333)))
94.0ms	(log (sqrt (exp (* (pow x 2) (- 0.5 (* x 0.03333333333333333))))))
100.0ms	(log (sqrt (exp (* (pow x 2) (- 0.5 (* x 0.03333333333333333))))))

simplify43.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	261	1042
1	976	934
2	5002	926

prune430.0ms

Filtered

124 candidates to 80 candidates (64.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	124	7	131

Merged error: 0.8b

Counts

131 → 7

regimes56.0ms

Accuracy

0% (0.4b remaining)

Error of 1.1b against oracle of 0.7b and baseline of 1.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	28
1	26	28

end0.0ms

sample7.3s

Algorithm

intervals

Results

5.4s	3235×	body	2560	valid
1.3s	2520×	body	1280	valid
212.0ms	1204×	body	640	valid
113.0ms	8000×	pre	80	true
74.0ms	660×	body	320	valid
26.0ms	338×	body	160	valid
2.0ms	43×	body	80	valid

Details

sample310.0ms

simplify4.0ms

prune3.0ms

localize5.0ms

rewrite21.0ms

series107.0ms

simplify85.0ms

prune162.0ms

localize8.0ms

rewrite14.0ms

series109.0ms

simplify40.0ms

prune147.0ms

localize11.0ms

rewrite16.0ms

series185.0ms

simplify43.0ms

prune217.0ms

localize13.0ms

rewrite23.0ms

series342.0ms

simplify43.0ms

prune430.0ms

regimes56.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample7.3s

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