Details

sample41.0ms

Algorithm

intervals

Results

11.0ms	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

simplify13.0ms

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

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))

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:

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))

series73.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- 1.0 (* (tan x) (tan x)))
32.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
9.0ms	(* (tan x) (tan x))
18.0ms	(* (tan x) (tan x))

simplify43.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (32.0ms)

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

prune183.0ms

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: 0.0b

Counts

118 → 10

localize12.0ms

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)
2.0ms	(pow (sin x) 2)

series15.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(pow (cos x) 2)
3.0ms	(pow (cos x) 2)
3.0ms	(pow (sin x) 2)
6.0ms	(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

prune155.0ms

Filtered

48 candidates to 84 candidates (-75.0%)

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))

rewrite31.0ms

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))

series67.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ 1 (+ 1.0 (* (tan x) (tan x))))
31.0ms	(* (- 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))

simplify58.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (44.0ms)

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

prune152.0ms

Filtered

80 candidates to 144 candidates (-80.0%)

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

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

rewrite40.0ms

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))))
4.0ms	(+ (sqrt 1.0) (tan x))
7.0ms	(* (tan x) (tan x))
16.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

series87.0ms

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))
9.0ms	(* (tan x) (tan x))
41.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

simplify78.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (63.0ms)

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

prune219.0ms

Filtered

97 candidates to 144 candidates (-48.5%)

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

regimes367.0ms

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

sample1.0s

Algorithm

intervals

Results

395.0ms	1534×	body	1280	valid
212.0ms	1261×	body	640	valid
167.0ms	4311×	body	80	valid
68.0ms	575×	body	320	valid
26.0ms	319×	body	160	valid

Details

sample41.0ms

simplify13.0ms

prune189.0ms

localize10.0ms

rewrite25.0ms

series73.0ms

simplify43.0ms

prune183.0ms

localize12.0ms

rewrite11.0ms

series15.0ms

simplify60.0ms

prune155.0ms

localize8.0ms

rewrite31.0ms

series67.0ms

simplify58.0ms

prune152.0ms

localize10.0ms

rewrite40.0ms

series87.0ms

simplify78.0ms

prune219.0ms

regimes367.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.0s

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