Details

sample465.0ms

Algorithm

intervals

Results

139.0ms	50×	body	2560	valid
58.0ms	95×	body	1280	valid
15.0ms	54×	body	640	valid
5.0ms	33×	body	320	valid
1.0ms	12×	body	160	valid
1.0ms	12×	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: 31.4b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.9b	(- x (tan x))
1.9b	(- 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:

22.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series175.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(/ (- x (sin x)) (- x (tan x)))
57.0ms	(- x (tan x))
41.0ms	(- x (sin x))

simplify150.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (10.0ms)

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

prune178.0ms

Filtered

89 candidates to 63 candidates (70.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	85	4	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	4	90

Merged error: 0.0b

Counts

90 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
0.1b	(pow (/ (- x (sin x)) (- x (tan x))) 3)
1.9b	(- x (tan x))
1.9b	(- x (sin x))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

134×	`add-sqr-sqrt` `*-un-lft-identity`
100×	`times-frac`
68×	`cbrt-prod`
62×	`unpow-prod-down` `cube-prod`
50×	`add-cube-cbrt`
42×	`distribute-lft-out--` `difference-of-squares`
8×	`associate-/r/` `add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
6×	`flip3--` `flip--`
5×	`pow1`
4×	`div-inv`
3×	`pow-unpow`
2×	`cube-div` `cube-mult` `sub-neg` `diff-log` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `cbrt-div` `pow-pow` `pow1/3` `div-exp` `rem-cbrt-cube`

Counts

4 → 188

Calls

4 calls:

12.0ms	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
11.0ms	(pow (/ (- x (sin x)) (- x (tan x))) 3)
3.0ms	(- x (tan x))
4.0ms	(- x (sin x))

series250.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
90.0ms	(pow (/ (- x (sin x)) (- x (tan x))) 3)
53.0ms	(- x (tan x))
31.0ms	(- x (sin x))

simplify84.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	736	2195
1	3051	2083
2	5001	2069

prune254.0ms

Filtered

200 candidates to 86 candidates (43.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	198	2	200
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	199	5	204

Merged error: 0b

Counts

204 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- x (tan x)))
0.1b	(* (- x (sin x)) (/ 1 (- x (tan x))))
1.9b	(- x (tan x))
1.9b	(- x (sin x))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
45×	`*-un-lft-identity`
32×	`times-frac`
24×	`add-cube-cbrt`
21×	`associate-r`
17×	`add-exp-log`
11×	`add-cbrt-cube`
10×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
7×	`pow1`
6×	`flip3--` `flip--`
5×	`associate-l` `associate-/r*`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `sub-neg` `rec-exp` `diff-log` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 119

Calls

4 calls:

5.0ms	(/ 1 (- x (tan x)))
13.0ms	(* (- x (sin x)) (/ 1 (- x (tan x))))
3.0ms	(- x (tan x))
4.0ms	(- x (sin x))

series207.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ 1 (- x (tan x)))
73.0ms	(* (- x (sin x)) (/ 1 (- x (tan x))))
51.0ms	(- x (tan x))
31.0ms	(- x (sin x))

simplify56.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	462	906
1	2072	813
2	5002	771

prune201.0ms

Filtered

131 candidates to 81 candidates (61.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	131	5	136

Merged error: 0b

Counts

136 → 5

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.3b	(* 9/40 (pow x 2))
15.8b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite19.0ms

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

series111.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(* 27/2800 (pow x 4))
24.0ms	(* 9/40 (pow x 2))
48.0ms	(- (* 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

prune116.0ms

Filtered

75 candidates to 46 candidates (61.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	76	4	80

Merged error: 0b

Counts

80 → 4

regimes55.0ms

Accuracy

100% (0.0b remaining)

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

bsearch76.0ms

Steps

Iters	Range		Point
9	0.0002199982819353488	137964.03928948785	0.02902705871059986
9	-0.41295360884021565	-1.1902930357079885e-07	-0.02453727723232867

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	13
1	31	13

end0.0ms

sample6.4s

Algorithm

intervals

Results

4.0s	1645×	body	2560	valid
1.6s	2727×	body	1280	valid
471.0ms	1858×	body	640	valid
153.0ms	928×	body	320	valid
55.0ms	477×	body	160	valid
25.0ms	365×	body	80	valid