Details

sample45.0ms

Algorithm

intervals

Results

12.0ms	45×	body	1280	valid
7.0ms	39×	body	640	valid
6.0ms	150×	body	80	valid
2.0ms	19×	body	320	valid
0.0ms	3×	body	160	valid

simplify593.0ms

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

prune5.0ms

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)))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))

rewrite37.0ms

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:

6.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
3.0ms	(- 1.0 (* (tan x) (tan x)))
17.0ms	(* (tan x) (tan x))
8.0ms	(* (tan x) (tan x))

series66.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
10.0ms	(- 1.0 (* (tan x) (tan x)))
8.0ms	(* (tan x) (tan x))
18.0ms	(* (tan x) (tan x))

simplify43.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (33.0ms)

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

prune173.0ms

Filtered

77 candidates to 117 candidates (-51.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	107	10	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	10	118

Merged error: 0.1b

Counts

118 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

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:

4.0ms	(- (sqrt 1.0) (tan x))
10.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
4.0ms	(+ (sqrt 1.0) (tan x))
5.0ms	(* (tan x) (tan x))

series42.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (sqrt 1.0) (tan x))
19.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
7.0ms	(+ (sqrt 1.0) (tan x))
8.0ms	(* (tan x) (tan x))

simplify48.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (40.0ms)

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

prune160.0ms

Filtered

67 candidates to 101 candidates (-50.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	97	4	101
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	100	11	111

Merged error: 0.0b

Counts

111 → 11

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (- (tan x) (sqrt 1.0)))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))
0.3b	(pow (tan x) 3)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`pow1`
19×	`*-un-lft-identity`
17×	`add-cube-cbrt`
12×	`tan-quot` `associate-r`
11×	`add-exp-log` `add-cbrt-cube`
9×	`associate-l`
6×	`swap-sqr`
4×	`frac-times` `associate-*r/` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `cube-prod` `pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
2×	`pow2` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `pow-plus` `pow-sqr` `pow-prod-up` `flip--` `difference-of-squares`
1×	`cube-div` `cube-mult` `pow-to-exp` `pow-pow` `unpow3` `pow-exp` `sqrt-prod` `distribute-lft-out--` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 110

Calls

4 calls:

8.0ms	(* (tan x) (- (tan x) (sqrt 1.0)))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
3.0ms	(pow (tan x) 3)

series44.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* (tan x) (- (tan x) (sqrt 1.0)))
8.0ms	(* (tan x) (tan x))
10.0ms	(* (tan x) (tan x))
12.0ms	(pow (tan x) 3)

simplify67.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	326	538
1	1835	478
2	5002	462

prune241.0ms

Filtered

71 candidates to 122 candidates (-71.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	121	12	133

Merged error: 0.0b

Counts

133 → 12

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
25×	`pow1`
18×	`*-un-lft-identity`
16×	`add-cube-cbrt`
12×	`tan-quot`
10×	`add-exp-log` `add-cbrt-cube`
9×	`swap-sqr` `associate-r` `associate-l`
6×	`add-log-exp`
4×	`times-frac` `associate-/r/` `difference-of-squares`
3×	`pow2` `frac-times` `distribute-rgt-out--` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
2×	`flip3-+` `flip-+` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `distribute-lft-out--` `sub-div`

Counts

4 → 106

Calls

4 calls:

5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
12.0ms	(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

series78.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (tan x) (tan x))
8.0ms	(* (tan x) (tan x))
11.0ms	(* (tan x) (tan x))
50.0ms	(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

simplify37.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	266	869
1	914	800
2	5002	784

prune103.0ms

Filtered

69 candidates to 118 candidates (-71.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	113	5	118
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	117	13	130

Merged error: 0.0b

Counts

130 → 13

regimes298.0ms

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	16	16
1	16	16

end0.0ms

sample1.0s

Algorithm

intervals

Results

379.0ms	1463×	body	1280	valid
207.0ms	1211×	body	640	valid
170.0ms	4341×	body	80	valid
82.0ms	658×	body	320	valid
28.0ms	327×	body	160	valid

Details

sample45.0ms

simplify593.0ms

prune5.0ms

localize10.0ms

rewrite37.0ms

series66.0ms

simplify43.0ms

prune173.0ms

localize10.0ms

rewrite25.0ms

series42.0ms

simplify48.0ms

prune160.0ms

localize21.0ms

rewrite24.0ms

series44.0ms

simplify67.0ms

prune241.0ms

localize11.0ms

rewrite30.0ms

series78.0ms

simplify37.0ms

prune103.0ms

regimes298.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.0s

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