Details

sample470.0ms

Algorithm

intervals

Results

124.0ms	53×	body	2560	valid
61.0ms	87×	body	1280	valid
15.0ms	54×	body	640	valid
9.0ms	36×	body	320	valid
2.0ms	17×	body	160	valid
1.0ms	9×	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: 30.5b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.3b	(- x (tan x))
1.3b	(- 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)))
4.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series174.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(/ (- x (sin x)) (- x (tan x)))
57.0ms	(- x (tan x))
41.0ms	(- x (sin x))

simplify151.0ms

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

prune184.0ms

Filtered

89 candidates to 63 candidates (70.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	87	3	90

Merged error: 0.0b

Counts

90 → 3

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.3b	(* 9/40 (pow x 2))
16.8b	(- (* 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:

38.0ms	(* 27/2800 (pow x 4))
24.0ms	(* 9/40 (pow x 2))
47.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify42.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (36.0ms)

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

prune128.0ms

Filtered

75 candidates to 46 candidates (61.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	75	3	78

Merged error: 0b

Counts

78 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4))) 1/2)
0.1b	(* 27/2800 (pow x 4))
0.3b	(* 9/40 (pow x 2))
16.8b	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
15×	`associate-r`
14×	`add-exp-log`
12×	`*-un-lft-identity`
11×	`add-log-exp`
10×	`add-cube-cbrt`
8×	`unpow-prod-down` `add-cbrt-cube`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`pow1` `diff-log` `sqr-pow`
3×	`sub-neg`
2×	`pow-to-exp` `flip3--` `pow-exp` `associate--l+` `*-commutative` `flip--` `cbrt-unprod` `unpow2`
1×	`associate--l-` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 82

Calls

4 calls:

7.0ms	(- (- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4))) 1/2)
6.0ms	(* 27/2800 (pow x 4))
6.0ms	(* 9/40 (pow x 2))
4.0ms	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

series210.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4))) 1/2)
35.0ms	(* 27/2800 (pow x 4))
26.0ms	(* 9/40 (pow x 2))
103.0ms	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

simplify48.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	308	480
1	1219	449
2	5001	437

prune159.0ms

Filtered

94 candidates to 59 candidates (62.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	94	3	97

Merged error: 0b

Counts

97 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan x))
1.3b	(- (* x x) (* (tan x) (tan x)))
1.3b	(- x (sin x))
16.0b	(/ (- x (sin x)) (- (* x x) (* (tan x) (tan x))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
20×	`times-frac`
19×	`add-cube-cbrt`
13×	`difference-of-squares`
11×	`pow1`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`distribute-lft-out--`
5×	`associate-/l*`
4×	`tan-quot` `flip3--` `associate-/r*` `flip--`
3×	`swap-sqr` `associate-r` `associate-l`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-times` `frac-2neg` `pow-plus` `div-sub` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 101

Calls

4 calls:

5.0ms	(* (tan x) (tan x))
3.0ms	(- (* x x) (* (tan x) (tan x)))
4.0ms	(- x (sin x))
9.0ms	(/ (- x (sin x)) (- (* x x) (* (tan x) (tan x))))

series237.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (tan x) (tan x))
82.0ms	(- (* x x) (* (tan x) (tan x)))
33.0ms	(- x (sin x))
90.0ms	(/ (- x (sin x)) (- (* x x) (* (tan x) (tan x))))

simplify54.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	437	985
1	1743	918
2	5001	910

prune226.0ms

Filtered

113 candidates to 79 candidates (69.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	113	3	116

Merged error: 0b

Counts

116 → 3

regimes50.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.5b

bsearch84.0ms

Steps

Iters	Range		Point
10	0.005370866090842012	4.21737757242384e+15	0.030633531225492793
10	-3.4402871636077537	-5.738045557766166e-18	-0.028549322719814054

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	11
1	28	11

end0.0ms

sample6.3s

Algorithm

intervals

Results

3.8s	1592×	body	2560	valid
1.6s	2767×	body	1280	valid
495.0ms	1847×	body	640	valid
177.0ms	957×	body	320	valid
59.0ms	471×	body	160	valid
28.0ms	366×	body	80	valid