Details

sample40.0ms

Algorithm

intervals

Results

11.0ms	41×	body	1280	valid
7.0ms	139×	body	80	valid
6.0ms	34×	body	640	valid
4.0ms	28×	body	320	valid
1.0ms	14×	body	160	valid

simplify14.0ms

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

prune204.0ms

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: 0.4b

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))))
0.1b	(- 1.0 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite26.0ms

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))
8.0ms	(* (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

prune194.0ms

Filtered

117 candidates to 77 candidates (34.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	104	13	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	13	118

Merged error: 0.1b

Counts

118 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
0.2b	(* (tan x) (sin x))
0.2b	(/ (* (tan x) (sin x)) (cos x))
0.3b	(* (tan x) (tan x))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

5.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
5.0ms	(* (tan x) (sin x))
6.0ms	(/ (* (tan x) (sin x)) (cos x))
5.0ms	(* (tan x) (tan x))

series48.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
10.0ms	(* (tan x) (sin x))
15.0ms	(/ (* (tan x) (sin x)) (cos x))
8.0ms	(* (tan x) (tan x))

simplify44.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	291	567
1	1265	503
2	5001	495

prune127.0ms

Filtered

95 candidates to 61 candidates (35.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	92	3	95
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	94	14	108

Merged error: 0.0b

Counts

108 → 14

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (sin x))
0.2b	(* (tan x) (sin x))
0.2b	(/ (* (tan x) (sin x)) (cos x))
0.2b	(/ (* (tan x) (sin x)) (cos x))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log` `add-cbrt-cube`
16×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`times-frac` `associate-r` `associate-l` `associate-/r*`
4×	`tan-quot` `cbrt-undiv` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `add-log-exp`
2×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l/` `associate-/l` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

5.0ms	(* (tan x) (sin x))
5.0ms	(* (tan x) (sin x))
6.0ms	(/ (* (tan x) (sin x)) (cos x))
6.0ms	(/ (* (tan x) (sin x)) (cos x))

series53.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(* (tan x) (sin x))
10.0ms	(* (tan x) (sin x))
15.0ms	(/ (* (tan x) (sin x)) (cos x))
15.0ms	(/ (* (tan x) (sin x)) (cos x))

simplify33.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	187	568
1	877	486
2	5002	486

prune120.0ms

Filtered

94 candidates to 68 candidates (27.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	95	13	108

Merged error: 0.0b

Counts

108 → 13

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

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)))))

series78.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (tan x) (tan x))
8.0ms	(* (tan x) (tan x))
9.0ms	(* (tan x) (tan x))
53.0ms	(- (/ 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

prune109.0ms

Filtered

118 candidates to 69 candidates (41.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	111	7	118
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	117	14	131

Merged error: 0.0b

Counts

131 → 14

regimes270.0ms

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	13
1	13	13

end0.0ms

sample1.0s

Algorithm

intervals

Results

390.0ms	1533×	body	1280	valid
199.0ms	1199×	body	640	valid
166.0ms	4348×	body	80	valid
72.0ms	593×	body	320	valid
29.0ms	327×	body	160	valid

Details

sample40.0ms

simplify14.0ms

prune204.0ms

localize10.0ms

rewrite26.0ms

series73.0ms

simplify42.0ms

prune194.0ms

localize16.0ms

rewrite22.0ms

series48.0ms

simplify44.0ms

prune127.0ms

localize13.0ms

rewrite23.0ms

series53.0ms

simplify33.0ms

prune120.0ms

localize9.0ms

rewrite31.0ms

series78.0ms

simplify36.0ms

prune109.0ms

regimes270.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.0s

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