Details

sample472.0ms

Algorithm

intervals

Results

131.0ms	64×	body	2560	valid
49.0ms	91×	body	1280	valid
13.0ms	50×	body	640	valid
5.0ms	26×	body	320	valid
2.0ms	15×	body	160	valid
1.0ms	10×	body	80	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	5
1	17	5
2	19	5
3	19	5

prune4.0ms

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: 33.5b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.9b	(- x (tan x))
0.9b	(- x (sin x))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
15×	`add-cube-cbrt`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 80

Calls

3 calls:

8.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (tan x))
7.0ms	(- x (sin x))

series178.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(/ (- x (sin x)) (- x (tan x)))
59.0ms	(- x (tan x))
41.0ms	(- x (sin x))

simplify152.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	363	718
1	1148	685
2	4795	685
3	5001	685

prune212.0ms

Filtered

89 candidates to 63 candidates (70.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	86	3	89
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	86	4	90

Merged error: 0.1b

Counts

90 → 4

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.1b	(* 9/40 (pow x 2))
16.1b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `sum-log` `flip--` `associate--r+`

Counts

3 → 66

Calls

3 calls:

5.0ms	(* 27/2800 (pow x 4))
6.0ms	(* 9/40 (pow x 2))
7.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series109.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(* 27/2800 (pow x 4))
29.0ms	(* 9/40 (pow x 2))
44.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify43.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	273	349
1	1123	318
2	5001	315

prune151.0ms

Filtered

75 candidates to 46 candidates (61.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	74	5	79

Merged error: 0.1b

Counts

79 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

12.0b	(cbrt (- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2)))
16.1b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
16.1b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
16.1b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-log-exp`
6×	`diff-log`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`cbrt-prod` `sub-neg` `sum-log` `associate--r+`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 55

Calls

4 calls:

7.0ms	(cbrt (- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2)))
7.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
7.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
7.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series277.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(cbrt (- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2)))
46.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
43.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
46.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify104.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	223	719
1	715	659
2	3152	657
3	5001	657

prune195.0ms

Filtered

67 candidates to 48 candidates (71.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	67	5	72

Merged error: 0.1b

Counts

72 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

16.1b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
16.1b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
16.1b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
17.9b	(cbrt (* (cbrt (- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))) (cbrt (- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2)))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

20×	`cbrt-div`
19×	`add-log-exp`
9×	`flip3--` `flip--`
6×	`diff-log`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `frac-times` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`sub-neg` `sum-log` `associate--r+`
2×	`associate-r/` `associate-l/`
1×	`cbrt-prod` `pow1/3`

Counts

4 → 59

Calls

4 calls:

7.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
7.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
7.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
16.0ms	(cbrt (* (cbrt (- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))) (cbrt (- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2)))))

series294.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
43.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
49.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
153.0ms	(cbrt (* (cbrt (- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))) (cbrt (- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2)))))

simplify104.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	249	1088
1	737	1010
2	3117	1008
3	5002	1008

prune235.0ms

Filtered

71 candidates to 49 candidates (69.0%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	71	5	76

Merged error: 0.1b

Counts

76 → 5

regimes67.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.2b

bsearch67.0ms

Steps

Iters	Range		Point
6	0.018000635171863108	0.09117784756913819	0.027293184248221757
10	-1421.6155834850151	-1.485944467815708e-07	-0.026678702825547893

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	11
1	29	11

end0.0ms

sample6.3s

Algorithm

intervals

Results

3.9s	1643×	body	2560	valid
1.5s	2762×	body	1280	valid
468.0ms	1826×	body	640	valid
157.0ms	912×	body	320	valid
63.0ms	483×	body	160	valid
27.0ms	374×	body	80	valid