Details

analyze719.0ms

Algorithm: search

sample42.0ms

Algorithm

intervals

Results

12.0ms	46×	body	1280	valid
11.0ms	44×	body	640	valid
6.0ms	136×	body	80	valid
3.0ms	25×	body	320	valid
0.0ms	5×	body	160	valid

simplify380.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	13	9
1	21	9
2	26	9
3	34	9
4	37	9
5	37	9

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))

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:

6.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
2.0ms	(- 1.0 (* (tan x) (tan x)))
5.0ms	(* (tan x) (tan x))
7.0ms	(* (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)))
8.0ms	(* (tan x) (tan x))
19.0ms	(* (tan x) (tan x))

simplify43.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (33.0ms)

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

prune189.0ms

Filtered

77 candidates to 117 candidates (-51.9%)

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: 0.0b

Counts

118 → 12

localize13.0ms

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)

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)

series16.0ms

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 (55.0ms)

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

prune157.0ms

Filtered

48 candidates to 84 candidates (-75.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	85	11	96

Merged error: 0.0b

Counts

96 → 11

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (+ 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))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 165

Calls

4 calls:

10.0ms	(/ 1 (/ (+ 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))
5.0ms	(* (tan x) (tan x))

series56.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
8.0ms	(- 1.0 (* (tan x) (tan x)))
8.0ms	(* (tan x) (tan x))
9.0ms	(* (tan x) (tan x))

simplify74.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	545	2148
1	2567	1966
2	5001	1864

prune183.0ms

Filtered

90 candidates to 177 candidates (-96.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	174	3	177
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	178	10	188

Merged error: 0.0b

Counts

188 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite21.0ms

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:

4.0ms	(* (tan x) (sin x))
4.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
5.0ms	(/ (* (tan x) (sin x)) (cos x))
5.0ms	(* (tan x) (tan x))

series50.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(* (tan x) (sin x))
14.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
15.0ms	(/ (* (tan x) (sin x)) (cos x))
8.0ms	(* (tan x) (tan x))

simplify43.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	291	567
1	1265	503
2	5001	497

prune87.0ms

Filtered

62 candidates to 95 candidates (-53.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	92	3	95
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	94	11	105

Merged error: 0.0b

Counts

105 → 11

regimes374.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	13
1	12	13

end0.0ms

analyze491.0ms

Algorithm: search

sample1.0s

Algorithm

intervals

Results

404.0ms	1529×	body	1280	valid
224.0ms	1285×	body	640	valid
169.0ms	4207×	body	80	valid
82.0ms	662×	body	320	valid
27.0ms	317×	body	160	valid

Details

analyze719.0ms

sample42.0ms

simplify380.0ms

prune4.0ms

localize10.0ms

rewrite24.0ms

series73.0ms

simplify43.0ms

prune189.0ms

localize13.0ms

rewrite11.0ms

series16.0ms

simplify60.0ms

prune157.0ms

localize9.0ms

rewrite28.0ms

series56.0ms

simplify74.0ms

prune183.0ms

localize14.0ms

rewrite21.0ms

series50.0ms

simplify43.0ms

prune87.0ms

regimes374.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze491.0ms

sample1.0s

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