Details

sample482.0ms

Algorithm

intervals

Results

167.0ms	57×	body	2560	valid
42.0ms	75×	body	1280	valid
20.0ms	72×	body	640	valid
4.0ms	26×	body	320	valid
2.0ms	12×	body	160	valid
1.0ms	14×	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: 31.3b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite37.0ms

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:

23.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series174.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(/ (- x (sin x)) (- x (tan x)))
58.0ms	(- x (tan x))
40.0ms	(- x (sin x))

simplify147.0ms

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

prune179.0ms

Filtered

89 candidates to 63 candidates (70.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	86	3	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	3	90

Merged error: 0.0b

Counts

90 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
0.9b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.2b	(- x (tan x))
1.2b	(- x (tan x))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
44×	`add-sqr-sqrt`
33×	`times-frac`
18×	`distribute-lft-out--`
16×	`add-cube-cbrt`
12×	`difference-of-squares`
10×	`add-log-exp`
6×	`add-exp-log` `flip3--` `associate-/r/` `add-cbrt-cube` `flip--`
5×	`associate-/r*`
4×	`pow1`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `div-inv` `associate-/l*`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `frac-sub` `sub-div`

Counts

4 → 94

Calls

4 calls:

6.0ms	(/ (sin x) (- x (tan x)))
29.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
3.0ms	(- x (tan x))
3.0ms	(- x (tan x))

series331.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ (sin x) (- x (tan x)))
172.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
49.0ms	(- x (tan x))
53.0ms	(- x (tan x))

simplify40.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	376	909
1	1205	872
2	5001	872

prune203.0ms

Filtered

106 candidates to 80 candidates (75.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	106	3	109

Merged error: 0.0b

Counts

109 → 3

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.2b	(* 9/40 (pow x 2))
16.1b	(- (* 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))

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

prune125.0ms

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: 0.0b

Counts

78 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.2b	(* 9/40 (pow x 2))
0.7b	(log (exp (* 27/2800 (pow x 4))))
16.1b	(- (* 9/40 (pow x 2)) (+ (log (exp (* 27/2800 (pow x 4)))) 1/2))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

5.0ms	(* 27/2800 (pow x 4))
5.0ms	(* 9/40 (pow x 2))
2.0ms	(log (exp (* 27/2800 (pow x 4))))
7.0ms	(- (* 9/40 (pow x 2)) (+ (log (exp (* 27/2800 (pow x 4)))) 1/2))

series143.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* 27/2800 (pow x 4))
24.0ms	(* 9/40 (pow x 2))
35.0ms	(log (exp (* 27/2800 (pow x 4))))
46.0ms	(- (* 9/40 (pow x 2)) (+ (log (exp (* 27/2800 (pow x 4)))) 1/2))

simplify43.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	300	448
1	1183	390
2	5001	385

prune177.0ms

Filtered

92 candidates to 58 candidates (63.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	91	4	95

Merged error: 0.0b

Counts

95 → 4

regimes35.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.7b

bsearch67.0ms

Steps

Iters	Range		Point
6	0.011261476250181132	0.06406876111163662	0.028659494739821132
9	-3.7752751361666412	-2.6386627092684764e-08	-0.0300477054894042

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	16
1	32	16

end0.0ms

sample6.3s

Algorithm

intervals

Results

3.9s	1609×	body	2560	valid
1.6s	2707×	body	1280	valid
488.0ms	1922×	body	640	valid
164.0ms	912×	body	320	valid
58.0ms	490×	body	160	valid
26.0ms	360×	body	80	valid