Details

sample42.0ms

Algorithm

intervals

Results

11.0ms	41×	body	1280	valid
8.0ms	138×	body	80	valid
7.0ms	41×	body	640	valid
3.0ms	28×	body	320	valid
1.0ms	8×	body	160	valid

simplify15.0ms

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

prune189.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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)))
0.2b	(* (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))))
2.0ms	(- 1.0 (* (tan x) (tan x)))
5.0ms	(* (tan x) (tan x))
8.0ms	(* (tan x) (tan x))

series71.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
9.0ms	(- 1.0 (* (tan x) (tan x)))
8.0ms	(* (tan x) (tan x))
18.0ms	(* (tan x) (tan x))

simplify44.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (33.0ms)

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

prune207.0ms

Filtered

117 candidates to 77 candidates (34.2%)

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: 0.0b

Counts

118 → 14

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (sqrt 1.0) (tan x))
0.2b	(- (sqrt 1.0) (tan x))
0.2b	(* (+ (sqrt 1.0) (tan x)) (- (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))
4.0ms	(- (sqrt 1.0) (tan x))
10.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
5.0ms	(* (tan x) (tan x))

series39.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (sqrt 1.0) (tan x))
7.0ms	(- (sqrt 1.0) (tan x))
17.0ms	(* (+ (sqrt 1.0) (tan x)) (- (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

prune190.0ms

Filtered

101 candidates to 67 candidates (33.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	97	4	101
Fresh	5	8	13
Picked	0	1	1
Done	0	0	0
Total	102	13	115

Merged error: 0.0b

Counts

115 → 13

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 104

Calls

4 calls:

8.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(/ (* (tan x) (sin x)) (cos x))
4.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
5.0ms	(* (tan x) (tan x))

series74.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
15.0ms	(/ (* (tan x) (sin x)) (cos x))
14.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
8.0ms	(* (tan x) (tan x))

simplify58.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	432	1210
1	1837	1122
2	5003	1116

prune156.0ms

Filtered

116 candidates to 79 candidates (31.9%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	2	9	11
Picked	0	1	1
Done	0	1	1
Total	117	12	129

Merged error: 0.0b

Counts

129 → 12

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite22.0ms

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

series57.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(- 1.0 (* (tan x) (tan x)))
8.0ms	(* (tan x) (tan x))
8.0ms	(* (tan x) (tan x))
30.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

simplify136.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 3 (128.0ms)

Iter	Nodes	Cost
0	289	756
1	888	687
2	3990	673
3	5001	669

prune134.0ms

Filtered

112 candidates to 73 candidates (34.8%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	112	12	124

Merged error: 0.0b

Counts

124 → 12

regimes345.0ms

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	13	12
1	13	12

end0.0ms

sample1.0s

Algorithm

intervals

Results

395.0ms	1522×	body	1280	valid
218.0ms	1266×	body	640	valid
169.0ms	4326×	body	80	valid
70.0ms	574×	body	320	valid
26.0ms	312×	body	160	valid

Details

sample42.0ms

simplify15.0ms

prune189.0ms

localize10.0ms

rewrite25.0ms

series71.0ms

simplify44.0ms

prune207.0ms

localize13.0ms

rewrite25.0ms

series39.0ms

simplify48.0ms

prune190.0ms

localize14.0ms

rewrite25.0ms

series74.0ms

simplify58.0ms

prune156.0ms

localize11.0ms

rewrite22.0ms

series57.0ms

simplify136.0ms

prune134.0ms

regimes345.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.0s

Profiling