Details

sample43.0ms

Algorithm

intervals

Results

14.0ms	54×	body	1280	valid
7.0ms	43×	body	640	valid
5.0ms	132×	body	80	valid
3.0ms	9×	body	160	valid
2.0ms	18×	body	320	valid

simplify646.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	35	15
1	35	15

prune4.0ms

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

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))

series90.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
27.0ms	(- 1.0 (* (tan x) (tan x)))
9.0ms	(* (tan x) (tan x))
20.0ms	(* (tan x) (tan x))

simplify54.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4960	1331
1	4960	1331

prune181.0ms

Filtered

78 candidates to 117 candidates (-50.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	105	12	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	12	118

Merged error: 0.1b

Counts

118 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin x) 2)
0.3b	(pow (sin x) 2)
0.3b	(pow (cos x) 2)
0.3b	(pow (cos 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 (sin x) 2)
2.0ms	(pow (sin x) 2)
2.0ms	(pow (cos x) 2)
3.0ms	(pow (cos x) 2)

series14.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(pow (sin x) 2)
4.0ms	(pow (sin x) 2)
3.0ms	(pow (cos x) 2)
3.0ms	(pow (cos x) 2)

simplify36.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4985	424
1	4985	424

prune156.0ms

Filtered

48 candidates to 84 candidates (-75.0%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	82	14	96

Merged error: 0.1b

Counts

96 → 14

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

rewrite27.0ms

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

series81.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
17.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
16.0ms	(/ (* (tan x) (sin x)) (cos x))
9.0ms	(* (tan x) (tan x))

simplify56.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5009	1782

prune165.0ms

Filtered

82 candidates to 116 candidates (-41.5%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	111	5	116
Fresh	4	8	12
Picked	1	0	1
Done	0	1	1
Total	116	14	130

Merged error: 0.0b

Counts

130 → 14

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.3b	(cbrt (pow (- 1.0 (* (tan x) (tan x))) 3))
0.4b	(pow (- 1.0 (* (tan x) (tan x))) 3)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
19×	`pow1`
18×	`add-cube-cbrt` `*-un-lft-identity`
14×	`cbrt-prod`
9×	`add-exp-log` `add-cbrt-cube`
8×	`tan-quot` `unpow-prod-down` `cube-prod`
6×	`swap-sqr` `associate-r` `associate-l`
4×	`cube-div` `add-log-exp` `difference-of-squares`
3×	`pow-unpow`
2×	`pow2` `cube-mult` `frac-times` `cbrt-div` `flip3--` `pow-plus` `unpow3` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `unswap-sqr` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 108

Calls

4 calls:

5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
3.0ms	(cbrt (pow (- 1.0 (* (tan x) (tan x))) 3))
4.0ms	(pow (- 1.0 (* (tan x) (tan x))) 3)

series48.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (tan x) (tan x))
9.0ms	(* (tan x) (tan x))
9.0ms	(cbrt (pow (- 1.0 (* (tan x) (tan x))) 3))
21.0ms	(pow (- 1.0 (* (tan x) (tan x))) 3)

simplify33.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5276	1012

prune110.0ms

Filtered

64 candidates to 120 candidates (-87.5%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	120	14	134

Merged error: 0.0b

Counts

134 → 14

regimes301.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	23
1	12	23

end0.0ms

sample987.0ms

Algorithm

intervals

Results

373.0ms	1503×	body	1280	valid
200.0ms	1225×	body	640	valid
165.0ms	4338×	body	80	valid
73.0ms	616×	body	320	valid
26.0ms	318×	body	160	valid

Details

sample43.0ms

simplify646.0ms

prune4.0ms

localize10.0ms

rewrite25.0ms

series90.0ms

simplify54.0ms

prune181.0ms

localize13.0ms

rewrite11.0ms

series14.0ms

simplify36.0ms

prune156.0ms

localize14.0ms

rewrite27.0ms

series81.0ms

simplify56.0ms

prune165.0ms

localize11.0ms

rewrite22.0ms

series48.0ms

simplify33.0ms

prune110.0ms

regimes301.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample987.0ms

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