Details

sample289.0ms

Algorithm

intervals

Results

16.0ms	56×	body	1280	valid
8.0ms	45×	body	640	valid
5.0ms	123×	body	80	valid
2.0ms	19×	body	320	valid
1.0ms	13×	body	160	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	9
1	21	9
2	26	9
3	34	9
4	37	9
5	37	9

prune3.0ms

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: 0.3b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.2b	(- 1.0 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`pow1`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`difference-of-squares`
4×	`associate-/l*`
3×	`associate-/r*`
2×	`pow2` `frac-times` `flip3--` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 105

Calls

4 calls:

7.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
3.0ms	(- 1.0 (* (tan x) (tan x)))
5.0ms	(* (tan x) (tan x))
7.0ms	(* (tan x) (tan x))

series217.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
33.0ms	(- 1.0 (* (tan x) (tan x)))
33.0ms	(* (tan x) (tan x))
58.0ms	(* (tan x) (tan x))

simplify47.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	314	909
1	1157	838
2	5001	824

prune254.0ms

Filtered

117 candidates to 77 candidates (65.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	103	14	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	104	14	118

Merged error: 0.1b

Counts

118 → 14

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.4b	(exp (* (tan x) (tan x)))
1.4b	(log (exp (* (tan x) (tan x))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

19×	`pow1`
17×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
8×	`tan-quot` `add-exp-log` `add-cbrt-cube`
7×	`add-log-exp`
6×	`swap-sqr` `associate-r` `associate-l`
3×	`log-prod` `log-pow`
2×	`pow2` `frac-times` `exp-prod` `exp-to-pow` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`rem-log-exp` `rem-exp-log`

Counts

4 → 80

Calls

4 calls:

5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
3.0ms	(exp (* (tan x) (tan x)))
2.0ms	(log (exp (* (tan x) (tan x))))

series149.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (tan x) (tan x))
31.0ms	(* (tan x) (tan x))
52.0ms	(exp (* (tan x) (tan x)))
32.0ms	(log (exp (* (tan x) (tan x))))

simplify67.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 3 (62.0ms)

Iter	Nodes	Cost
0	132	407
1	406	344
2	1778	324
3	5002	318

prune180.0ms

Filtered

92 candidates to 53 candidates (57.6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	90	2	92
Fresh	2	11	13
Picked	0	1	1
Done	0	0	0
Total	92	14	106

Merged error: 0.1b

Counts

106 → 14

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
0.2b	(- (sqrt 1.0) (tan x))
0.2b	(+ (sqrt 1.0) (tan x))
0.3b	(* (tan x) (tan x))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
13×	`pow1`
10×	`add-cube-cbrt`
9×	`associate-r`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`associate-l`
5×	`frac-times`
4×	`tan-quot` `flip3--` `flip3-+` `flip--` `flip-+` `difference-of-squares`
3×	`sub-neg` `associate-r/` `swap-sqr` `associate-l/`
2×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `sqrt-prod` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `pow2` `pow-plus` `diff-log` `sum-log` `pow-sqr` `pow-prod-up`

Counts

4 → 89

Calls

4 calls:

14.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
5.0ms	(- (sqrt 1.0) (tan x))
5.0ms	(+ (sqrt 1.0) (tan x))
5.0ms	(* (tan x) (tan x))

series204.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
39.0ms	(- (sqrt 1.0) (tan x))
32.0ms	(+ (sqrt 1.0) (tan x))
32.0ms	(* (tan x) (tan x))

simplify49.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	328	693
1	1582	618
2	5001	607

prune218.0ms

Filtered

101 candidates to 68 candidates (67.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	99	2	101
Fresh	1	11	12
Picked	1	0	1
Done	1	0	1
Total	102	13	115

Merged error: 0.1b

Counts

115 → 13

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(- 1.0 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.4b	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
19×	`pow1` `log-pow`
18×	`exp-prod`
12×	`times-frac`
8×	`tan-quot` `add-exp-log` `add-cbrt-cube`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
4×	`difference-of-squares`
3×	`log-prod`
2×	`pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `log-div` `flip3--` `flip3-+` `exp-diff` `diff-log` `div-sub` `rem-log-exp` `flip--` `flip-+` `div-inv`

Counts

4 → 100

Calls

4 calls:

3.0ms	(- 1.0 (* (tan x) (tan x)))
6.0ms	(* (tan x) (tan x))
8.0ms	(* (tan x) (tan x))
8.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

series193.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- 1.0 (* (tan x) (tan x)))
32.0ms	(* (tan x) (tan x))
32.0ms	(* (tan x) (tan x))
94.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

simplify140.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 3 (131.0ms)

Iter	Nodes	Cost
0	289	756
1	888	687
2	3990	673
3	5001	667

prune197.0ms

Filtered

112 candidates to 73 candidates (65.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	112	13	125

Merged error: 0.1b

Counts

125 → 13

regimes186.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	11
1	10	11

end0.0ms

sample982.0ms

Algorithm

intervals

Results

398.0ms	1580×	body	1280	valid
205.0ms	1221×	body	640	valid
165.0ms	4293×	body	80	valid
73.0ms	602×	body	320	valid
25.0ms	304×	body	160	valid