Details

sample466.0ms

Algorithm

intervals

Results

115.0ms	46×	body	2560	valid
61.0ms	94×	body	1280	valid
15.0ms	57×	body	640	valid
7.0ms	37×	body	320	valid
2.0ms	15×	body	160	valid
1.0ms	7×	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: 32.4b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.0b	(- x (sin x))
1.2b	(- x (tan x))

rewrite39.0ms

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:

24.0ms	(/ (- x (sin x)) (- x (tan x)))
4.0ms	(- x (sin x))
6.0ms	(- x (tan x))

series174.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(/ (- x (sin x)) (- x (tan x)))
37.0ms	(- x (sin x))
62.0ms	(- x (tan 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

prune164.0ms

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: 0b

Counts

90 → 4

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.2b	(* 9/40 (pow x 2))
15.3b	(- (* 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))

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))

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

prune119.0ms

Filtered

75 candidates to 46 candidates (61.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	75	4	79

Merged error: 0b

Counts

79 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt (- x (sin x))) (sqrt (- x (sin x))))
1.0b	(- x (sin x))
1.0b	(- x (sin x))
1.2b	(- x (tan x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
30×	`sqrt-prod`
19×	`pow1`
12×	`add-cube-cbrt` `sqrt-div` `swap-sqr`
10×	`add-log-exp`
9×	`flip3--` `flip--` `distribute-lft-out--`
8×	`sqrt-pow1` `pow1/2` `associate-r` `associate-l`
7×	`difference-of-squares`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`frac-times` `unswap-sqr`
3×	`sub-neg` `diff-log` `pow-prod-down` `pow-sqr`
2×	`associate-r/` `associate-l/`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 107

Calls

4 calls:

12.0ms	(* (sqrt (- x (sin x))) (sqrt (- x (sin x))))
4.0ms	(- x (sin x))
4.0ms	(- x (sin x))
3.0ms	(- x (tan x))

series149.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (sqrt (- x (sin x))) (sqrt (- x (sin x))))
30.0ms	(- x (sin x))
30.0ms	(- x (sin x))
52.0ms	(- x (tan x))

simplify44.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	318	644
1	1110	586
2	5001	569

prune201.0ms

Filtered

119 candidates to 67 candidates (56.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	119	4	123

Merged error: 0b

Counts

123 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan x))
1.0b	(- x (sin x))
1.2b	(- (* x x) (* (tan x) (tan x)))
14.3b	(/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
16×	`times-frac`
11×	`pow1`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`difference-of-squares`
5×	`distribute-lft-out`
4×	`tan-quot` `associate-/r` `associate-/l`
3×	`flip3--` `swap-sqr` `associate-r` `associate-l` `flip--`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-times` `frac-2neg` `flip3-+` `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` `flip-+` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 96

Calls

4 calls:

5.0ms	(* (tan x) (tan x))
4.0ms	(- x (sin x))
4.0ms	(- (* x x) (* (tan x) (tan x)))
8.0ms	(/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))

series289.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (tan x) (tan x))
30.0ms	(- x (sin x))
81.0ms	(- (* x x) (* (tan x) (tan x)))
143.0ms	(/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))

simplify60.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	425	855
1	1908	785
2	5001	770

prune194.0ms

Filtered

108 candidates to 74 candidates (68.5%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	108	4	112

Merged error: 0b

Counts

112 → 4

regimes55.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.7b

bsearch91.0ms

Steps

Iters	Range		Point
10	8.416769919470913e-17	1.2368608357549227	0.02823578267618705
11	-55383.34621353126	-7.66540900750845e-16	-0.02866916276075434

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	11
1	29	11

end0.0ms

sample6.4s

Algorithm

intervals

Results

3.9s	1565×	body	2560	valid
1.5s	2760×	body	1280	valid
489.0ms	1851×	body	640	valid
169.0ms	935×	body	320	valid
63.0ms	522×	body	160	valid
27.0ms	367×	body	80	valid