Details

sample277.0ms

Algorithm

intervals

Results

12.0ms	47×	body	1280	valid
9.0ms	46×	body	640	valid
5.0ms	141×	body	80	valid
2.0ms	14×	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

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:

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

3.0ms	(- 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))
7.0ms	(* (tan x) (tan x))

series220.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- 1.0 (* (tan x) (tan x)))
96.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 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 (33.0ms)

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

prune229.0ms

Filtered

117 candidates to 77 candidates (65.8%)

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

localize10.0ms

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

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 135

Calls

4 calls:

8.0ms	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(- (sqrt 1.0) (tan x))
16.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
5.0ms	(* (tan x) (tan x))

series355.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
36.0ms	(- (sqrt 1.0) (tan x))
194.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
32.0ms	(* (tan x) (tan x))

simplify81.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	561	1675
1	2800	1512
2	5001	1496

prune292.0ms

Filtered

147 candidates to 99 candidates (67.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	144	3	147
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	147	10	157

Merged error: 0.0b

Counts

157 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (cos x) 2)
0.2b	(pow (cos x) 2)
0.3b	(pow (sin x) 2)
0.3b	(pow (sin x) 2)

rewrite12.0ms

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

series78.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(pow (cos x) 2)
17.0ms	(pow (cos x) 2)
19.0ms	(pow (sin x) 2)
19.0ms	(pow (sin x) 2)

simplify60.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (54.0ms)

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

prune177.0ms

Filtered

84 candidates to 48 candidates (57.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	84	10	94

Merged error: 0.0b

Counts

94 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
39×	`-un-lft-identity` `associate-r*`
31×	`times-frac`
27×	`add-cube-cbrt`
24×	`exp-prod`
21×	`log-pow`
16×	`pow1`
11×	`add-exp-log` `add-cbrt-cube`
10×	`difference-of-squares`
9×	`add-log-exp`
7×	`associate-l`
5×	`sqrt-prod` `distribute-lft-out--`
4×	`tan-quot`
3×	`frac-times` `flip3-+` `swap-sqr` `associate-*l/` `prod-exp` `cbrt-unprod` `flip-+` `unswap-sqr`
2×	`sub-neg` `diff-log` `associate-r/` `exp-sum` `pow-prod-down` `associate-/r/` `-commutative` `rem-exp-log`
1×	`cbrt-undiv` `pow2` `flip3--` `pow-plus` `exp-diff` `div-exp` `pow-sqr` `pow-prod-up` `flip--` `div-inv` `distribute-lft-out`

Counts

4 → 121

Calls

4 calls:

5.0ms	(- (sqrt 1.0) (tan x))
23.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (log (exp (- (sqrt 1.0) (tan x)))) (+ 1.0 (* (tan x) (tan x)))))
6.0ms	(exp (- (sqrt 1.0) (tan x)))
5.0ms	(* (tan x) (tan x))

series348.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (sqrt 1.0) (tan x))
200.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (log (exp (- (sqrt 1.0) (tan x)))) (+ 1.0 (* (tan x) (tan x)))))
73.0ms	(exp (- (sqrt 1.0) (tan x)))
34.0ms	(* (tan x) (tan x))

simplify77.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	583	1347
1	2951	1159
2	5002	1136

prune275.0ms

Filtered

133 candidates to 88 candidates (66.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	132	1	133
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	132	11	143

Merged error: 0b

Counts

143 → 11

regimes240.0ms

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

sample931.0ms

Algorithm

intervals

Results

360.0ms	1465×	body	1280	valid
207.0ms	1264×	body	640	valid
152.0ms	4355×	body	80	valid
67.0ms	600×	body	320	valid
25.0ms	316×	body	160	valid