Details

sample235.0ms

Algorithm

intervals

Results

161.0ms	108×	body	2560	valid
49.0ms	74×	body	1280	valid
8.0ms	38×	body	640	valid
4.0ms	256×	pre	80	true
3.0ms	23×	body	320	valid
1.0ms	11×	body	160	valid
0.0ms	2×	body	80	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	11	8
1	11	8

prune3.0ms

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: 59.9b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
3.3b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite18.0ms

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:

3.0ms	(/ 1.0 (tan x))
13.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series30.0ms

Counts

2 → 6

Calls

2 calls:

11.0ms	(/ 1.0 (tan x))
20.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify56.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5145	561

prune91.0ms

Filtered

45 candidates to 56 candidates (-24.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	54	2	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	2	57

Merged error: 0.4b

Counts

57 → 2

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.0021164021164021165 (pow x 5))
0.1b	(* 0.022222222222222223 (pow x 3))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`associate-r`
12×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp` `add-cbrt-cube`
4×	`cube-prod` `sqr-pow`
2×	`pow1` `pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `add-log-exp`
1×	`cube-mult` `unpow3`

Counts

2 → 56

Calls

2 calls:

5.0ms	(* 0.0021164021164021165 (pow x 5))
6.0ms	(* 0.022222222222222223 (pow x 3))

series9.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(* 0.0021164021164021165 (pow x 5))
4.0ms	(* 0.022222222222222223 (pow x 3))

simplify51.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4909	393
1	4909	393

prune93.0ms

Filtered

38 candidates to 62 candidates (-63.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	62	2	64

Merged error: 0.4b

Counts

64 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* 1.0 (- (/ 1.0 (* x x)) (/ 1.0 (* (tan x) (tan x))))) (+ (/ 1.0 x) (/ 1.0 (tan x))))
0.1b	(/ 1.0 (* x x))
0.1b	(/ 1.0 (* (tan x) (tan x)))
36.6b	(- (/ 1.0 (* x x)) (/ 1.0 (* (tan x) (tan x))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
30×	`times-frac`
22×	`add-sqr-sqrt`
19×	`add-exp-log` `add-cbrt-cube`
14×	`add-cube-cbrt`
10×	`associate-/r*` `distribute-lft-out`
9×	`div-inv`
7×	`associate-/l*`
6×	`cbrt-undiv` `div-exp` `associate-/r/` `add-log-exp`
4×	`tan-quot` `pow1` `associate-*r/` `difference-of-squares`
3×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `associate-/l/`
2×	`flip3--` `frac-sub` `flip--` `distribute-lft-out--`
1×	`frac-times` `sub-neg` `flip3-+` `diff-log` `associate-*l/` `frac-add` `flip-+`

Counts

4 → 101

Calls

4 calls:

26.0ms	(/ (* 1.0 (- (/ 1.0 (* x x)) (/ 1.0 (* (tan x) (tan x))))) (+ (/ 1.0 x) (/ 1.0 (tan x))))
4.0ms	(/ 1.0 (* x x))
6.0ms	(/ 1.0 (* (tan x) (tan x)))
12.0ms	(- (/ 1.0 (* x x)) (/ 1.0 (* (tan x) (tan x))))

series112.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ (* 1.0 (- (/ 1.0 (* x x)) (/ 1.0 (* (tan x) (tan x))))) (+ (/ 1.0 x) (/ 1.0 (tan x))))
3.0ms	(/ 1.0 (* x x))
18.0ms	(/ 1.0 (* (tan x) (tan x)))
34.0ms	(- (/ 1.0 (* x x)) (/ 1.0 (* (tan x) (tan x))))

simplify47.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5001	1756

prune156.0ms

Filtered

83 candidates to 113 candidates (-36.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	111	2	113
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	112	3	115

Merged error: 0.3b

Counts

115 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1.0 x) (/ 1.0 (tan x)))
0.1b	(* (pow x 4) 0.010582010582010581)
0.1b	(* x (* x 0.06666666666666667))
0.3b	(/ (* 1.0 (- 0.6666666666666666 (+ (* x (* x 0.06666666666666667)) (* (pow x 4) 0.010582010582010581)))) (+ (/ 1.0 x) (/ 1.0 (tan x))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

40×	`*-un-lft-identity`
26×	`times-frac`
21×	`add-sqr-sqrt`
19×	`add-exp-log`
16×	`add-cube-cbrt` `add-cbrt-cube`
15×	`distribute-lft-out`
10×	`associate-l`
9×	`pow1`
8×	`associate-/r*`
7×	`prod-exp` `div-inv`
6×	`add-log-exp`
5×	`cbrt-unprod`
4×	`unpow-prod-down` `associate-r`
3×	`pow-prod-down` `associate-/r/` `unswap-sqr`
2×	`cbrt-undiv` `flip3-+` `associate-r/` `div-exp` `frac-add` `-commutative` `flip-+` `associate-/l/` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `flip3--` `frac-2neg` `pow-exp` `clear-num` `sum-log` `flip--` `associate-/l*`

Counts

4 → 96

Calls

4 calls:

12.0ms	(+ (/ 1.0 x) (/ 1.0 (tan x)))
5.0ms	(* (pow x 4) 0.010582010582010581)
5.0ms	(* x (* x 0.06666666666666667))
20.0ms	(/ (* 1.0 (- 0.6666666666666666 (+ (* x (* x 0.06666666666666667)) (* (pow x 4) 0.010582010582010581)))) (+ (/ 1.0 x) (/ 1.0 (tan x))))

series44.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+ (/ 1.0 x) (/ 1.0 (tan x)))
4.0ms	(* (pow x 4) 0.010582010582010581)
3.0ms	(* x (* x 0.06666666666666667))
21.0ms	(/ (* 1.0 (- 0.6666666666666666 (+ (* x (* x 0.06666666666666667)) (* (pow x 4) 0.010582010582010581)))) (+ (/ 1.0 x) (/ 1.0 (tan x))))

simplify46.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4966	1563
1	4966	1563

prune183.0ms

Filtered

75 candidates to 108 candidates (-44.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	99	9	108
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	100	11	111

Merged error: 0.0b

Counts

111 → 11

regimes71.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	52
1	30	52

end0.0ms

sample7.1s

Algorithm

intervals

Results

5.1s	3290×	body	2560	valid
1.3s	2476×	body	1280	valid
230.0ms	1232×	body	640	valid
132.0ms	8000×	pre	80	true
73.0ms	646×	body	320	valid
26.0ms	302×	body	160	valid
2.0ms	54×	body	80	valid

Details

sample235.0ms

simplify3.0ms

prune3.0ms

localize5.0ms

rewrite18.0ms

series30.0ms

simplify56.0ms

prune91.0ms

localize10.0ms

rewrite13.0ms

series9.0ms

simplify51.0ms

prune93.0ms

localize13.0ms

rewrite54.0ms

series112.0ms

simplify47.0ms

prune156.0ms

localize15.0ms

rewrite46.0ms

series44.0ms

simplify46.0ms

prune183.0ms

regimes71.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample7.1s

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