Details

sample42.0ms

Algorithm

intervals

Results

12.0ms	44×	body	1280	valid
8.0ms	43×	body	640	valid
7.0ms	140×	body	80	valid
2.0ms	17×	body	320	valid
1.0ms	12×	body	160	valid

simplify20.0ms

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

prune255.0ms

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

rewrite24.0ms

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:

2.0ms	(- 1.0 (* (tan x) (tan x)))
6.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(* (tan x) (tan x))
8.0ms	(* (tan x) (tan x))

series117.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(- 1.0 (* (tan x) (tan x)))
61.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
10.0ms	(* (tan x) (tan x))
18.0ms	(* (tan x) (tan x))

simplify76.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	314	909
1	1157	838
2	5002	824

prune245.0ms

Filtered

117 candidates to 77 candidates (34.2%)

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: 0.0b

Counts

118 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (cos x) 2)
0.2b	(pow (cos x) 2)
0.2b	(pow (sin x) 2)
0.2b	(pow (sin x) 2)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `pow-unpow` `*-un-lft-identity`
8×	`pow1` `add-exp-log`
4×	`pow-to-exp` `pow-pow` `pow-exp` `add-cbrt-cube` `unpow2` `add-log-exp` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

2.0ms	(pow (cos x) 2)
2.0ms	(pow (cos x) 2)
2.0ms	(pow (sin x) 2)
3.0ms	(pow (sin x) 2)

series24.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(pow (cos x) 2)
6.0ms	(pow (cos x) 2)
7.0ms	(pow (sin x) 2)
6.0ms	(pow (sin x) 2)

simplify74.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (67.0ms)

Iter	Nodes	Cost
0	141	284
1	469	240
2	1590	240
3	5001	236

prune161.0ms

Filtered

84 candidates to 48 candidates (42.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	83	11	94

Merged error: 0.0b

Counts

94 → 11

localize8.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (+ 1.0 (* (tan x) (tan x))))
0.2b	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 132

Calls

4 calls:

4.0ms	(/ 1 (+ 1.0 (* (tan x) (tan x))))
12.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))

series88.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ 1 (+ 1.0 (* (tan x) (tan x))))
37.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
8.0ms	(* (tan x) (tan x))
9.0ms	(* (tan x) (tan x))

simplify74.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	392	1132
1	1813	1005
2	5002	948

prune255.0ms

Filtered

144 candidates to 80 candidates (44.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	144	11	155

Merged error: 0.0b

Counts

155 → 11

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 132

Calls

4 calls:

8.0ms	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
7.0ms	(+ (sqrt 1.0) (tan x))
5.0ms	(* (tan x) (tan x))
24.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

series99.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
7.0ms	(+ (sqrt 1.0) (tan x))
12.0ms	(* (tan x) (tan x))
51.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

simplify88.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	558	1651
1	2781	1488
2	5002	1472

prune304.0ms

Filtered

144 candidates to 97 candidates (32.6%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	144	11	155

Merged error: 0.0b

Counts

155 → 11

regimes473.0ms

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	12	13
1	12	13

end0.0ms

sample1.3s

Algorithm

intervals

Results

503.0ms	1534×	body	1280	valid
272.0ms	1261×	body	640	valid
212.0ms	4311×	body	80	valid
87.0ms	575×	body	320	valid
34.0ms	319×	body	160	valid

Details

sample42.0ms

simplify20.0ms

prune255.0ms

localize10.0ms

rewrite24.0ms

series117.0ms

simplify76.0ms

prune245.0ms

localize15.0ms

rewrite11.0ms

series24.0ms

simplify74.0ms

prune161.0ms

localize8.0ms

rewrite30.0ms

series88.0ms

simplify74.0ms

prune255.0ms

localize22.0ms

rewrite48.0ms

series99.0ms

simplify88.0ms

prune304.0ms

regimes473.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.3s

Profiling