Details

analyze705.0ms

Algorithm: search

sample43.0ms

Algorithm

intervals

Results

12.0ms	45×	body	1280	valid
9.0ms	141×	body	80	valid
8.0ms	41×	body	640	valid
3.0ms	19×	body	320	valid
1.0ms	10×	body	160	valid

simplify362.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

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

prune4.0ms

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: 0.4b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 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))

rewrite25.0ms

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)))
5.0ms	(* (tan x) (tan x))
7.0ms	(* (tan x) (tan x))

series73.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
9.0ms	(- 1.0 (* (tan x) (tan x)))
9.0ms	(* (tan x) (tan x))
18.0ms	(* (tan x) (tan x))

simplify42.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (32.0ms)

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

prune189.0ms

Filtered

77 candidates to 117 candidates (-51.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	105	12	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	12	118

Merged error: 0.0b

Counts

118 → 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))
0.3b	(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

rewrite32.0ms

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))
14.0ms	(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

series79.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (tan x) (tan x))
8.0ms	(* (tan x) (tan x))
11.0ms	(* (tan x) (tan x))
51.0ms	(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

simplify36.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (27.0ms)

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

prune154.0ms

Filtered

69 candidates to 118 candidates (-71.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	111	7	118
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	116	14	130

Merged error: 0.0b

Counts

130 → 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))
0.2b	(* (tan x) (tan x))

rewrite27.0ms

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:

11.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
4.0ms	(- (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:

19.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
7.0ms	(- (sqrt 1.0) (tan x))
7.0ms	(+ (sqrt 1.0) (tan x))
9.0ms	(* (tan x) (tan x))

simplify47.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (39.0ms)

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

prune173.0ms

Filtered

68 candidates to 101 candidates (-48.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

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

Merged error: 0.0b

Counts

115 → 13

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan x))
0.2b	(* (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ 1.0 (+ 1.0 (* (tan x) (tan x)))))
0.3b	(pow (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) 3)
0.4b	(pow (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))) 3)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
64×	`times-frac`
56×	`add-cube-cbrt` `*-un-lft-identity`
27×	`add-exp-log` `add-cbrt-cube`
24×	`unpow-prod-down` `cube-prod`
20×	`pow1`
18×	`swap-sqr` `associate-r` `associate-l`
16×	`associate-/r/`
8×	`flip3-+` `flip-+` `div-inv`
7×	`cbrt-undiv` `div-exp`
6×	`pow-unpow` `prod-exp` `cbrt-unprod`
5×	`pow-exp` `rem-cube-cbrt` `unswap-sqr`
4×	`tan-quot` `add-log-exp`
2×	`cube-div` `pow2` `cube-mult` `frac-times` `pow-to-exp` `pow-pow` `pow-plus` `unpow3` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `sqr-pow`

Counts

4 → 191

Calls

4 calls:

5.0ms	(* (tan x) (tan x))
14.0ms	(* (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ 1.0 (+ 1.0 (* (tan x) (tan x)))))
6.0ms	(pow (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) 3)
7.0ms	(pow (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))) 3)

series120.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (tan x) (tan x))
30.0ms	(* (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ 1.0 (+ 1.0 (* (tan x) (tan x)))))
31.0ms	(pow (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) 3)
51.0ms	(pow (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))) 3)

simplify44.0ms

Algorithm

egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	899	2310
1	5001	2043

prune457.0ms

Filtered

119 candidates to 203 candidates (-70.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	202	1	203
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	203	13	216

Merged error: 0b

Counts

216 → 13

regimes210.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	52
1	20	52

end0.0ms

analyze491.0ms

Algorithm: search

sample1.0s

Algorithm

intervals

Results

400.0ms	1531×	body	1280	valid
209.0ms	1211×	body	640	valid
166.0ms	4286×	body	80	valid
83.0ms	686×	body	320	valid
26.0ms	286×	body	160	valid

Details

analyze705.0ms

sample43.0ms

simplify362.0ms

prune4.0ms

localize10.0ms

rewrite25.0ms

series73.0ms

simplify42.0ms

prune189.0ms

localize11.0ms

rewrite32.0ms

series79.0ms

simplify36.0ms

prune154.0ms

localize11.0ms

rewrite27.0ms

series42.0ms

simplify47.0ms

prune173.0ms

localize20.0ms

rewrite39.0ms

series120.0ms

simplify44.0ms

prune457.0ms

regimes210.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze491.0ms

sample1.0s

Profiling