Details

sample42.0ms

Algorithm

intervals

Results

13.0ms	52×	body	1280	valid
8.0ms	37×	body	640	valid
5.0ms	142×	body	80	valid
2.0ms	19×	body	320	valid
1.0ms	6×	body	160	valid

simplify674.0ms

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

localize11.0ms

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))))
2.0ms	(- 1.0 (* (tan x) (tan x)))
5.0ms	(* (tan x) (tan x))
7.0ms	(* (tan x) (tan x))

series82.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
26.0ms	(- 1.0 (* (tan x) (tan x)))
9.0ms	(* (tan x) (tan x))
18.0ms	(* (tan x) (tan x))

simplify53.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4960	1331
1	4960	1331

prune192.0ms

Filtered

78 candidates to 117 candidates (-50.0%)

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: 0.0b

Counts

118 → 13

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin x) 2)
0.2b	(pow (sin x) 2)
0.2b	(pow (cos x) 2)
0.2b	(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)
2.0ms	(pow (cos x) 2)

series13.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify37.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4985	424
1	4985	424

prune160.0ms

Filtered

48 candidates to 84 candidates (-75.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	0	12	12
Picked	1	0	1
Done	0	0	0
Total	83	14	97

Merged error: 0.0b

Counts

97 → 14

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity`
18×	`pow1`
11×	`tan-quot`
10×	`add-exp-log` `add-cbrt-cube`
9×	`times-frac`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
4×	`associate-*r/`
3×	`frac-times` `associate-l/` `associate-/r` `frac-sub` `associate-/l*`
2×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `flip--` `flip-+` `div-inv` `associate-/l/` `sub-div`

Counts

4 → 102

Calls

4 calls:

8.0ms	(/ (tan x) (+ (* (tan x) (tan x)) 1.0))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
11.0ms	(- (/ 1.0 (+ (* (tan x) (tan x)) 1.0)) (* (tan x) (/ (tan x) (+ (* (tan x) (tan x)) 1.0))))

series93.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (tan x) (+ (* (tan x) (tan x)) 1.0))
8.0ms	(* (tan x) (tan x))
8.0ms	(* (tan x) (tan x))
51.0ms	(- (/ 1.0 (+ (* (tan x) (tan x)) 1.0)) (* (tan x) (/ (tan x) (+ (* (tan x) (tan x)) 1.0))))

simplify54.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4931	1266
1	4931	1266

prune190.0ms

Filtered

80 candidates to 114 candidates (-42.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	110	4	114
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	116	12	128

Merged error: 0.0b

Counts

128 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan x))
0.3b	(pow (tan x) 2)
0.3b	(- (/ 1.0 (+ (* (tan x) (tan x)) 1.0)) (* (tan x) (/ 1 (/ (+ 1.0 (pow (tan x) 2)) (tan x)))))
0.3b	(/ 1 (/ (+ 1.0 (pow (tan x) 2)) (tan x)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

99×	`times-frac`
84×	`*-un-lft-identity`
62×	`add-sqr-sqrt`
60×	`add-cube-cbrt`
18×	`add-exp-log`
17×	`associate-/r*`
13×	`pow1`
12×	`distribute-lft-out`
11×	`add-cbrt-cube`
10×	`tan-quot`
7×	`div-exp`
6×	`add-log-exp`
5×	`associate-/r/` `div-inv`
4×	`frac-sub`
3×	`cbrt-undiv` `unpow-prod-down` `pow-unpow` `swap-sqr` `associate-r` `associate-l` `associate-/l*`
2×	`frac-times` `rec-exp` `1-exp` `associate-r/` `associate-l/`
1×	`pow2` `pow-to-exp` `sub-neg` `flip3--` `pow-flip` `pow-pow` `frac-2neg` `pow-plus` `diff-log` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `pow-sqr` `un-div-inv` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `unpow2` `inv-pow` `unswap-sqr` `sqr-pow`

Counts

4 → 154

Calls

4 calls:

7.0ms	(* (tan x) (tan x))
3.0ms	(pow (tan x) 2)
11.0ms	(- (/ 1.0 (+ (* (tan x) (tan x)) 1.0)) (* (tan x) (/ 1 (/ (+ 1.0 (pow (tan x) 2)) (tan x)))))
9.0ms	(/ 1 (/ (+ 1.0 (pow (tan x) 2)) (tan x)))

series94.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (tan x) (tan x))
8.0ms	(pow (tan x) 2)
52.0ms	(- (/ 1.0 (+ (* (tan x) (tan x)) 1.0)) (* (tan x) (/ 1 (/ (+ 1.0 (pow (tan x) 2)) (tan x)))))
25.0ms	(/ 1 (/ (+ 1.0 (pow (tan x) 2)) (tan x)))

simplify74.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4947	2352
1	4947	2352

prune206.0ms

Filtered

95 candidates to 166 candidates (-74.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	166	12	178

Merged error: 0.0b

Counts

178 → 12

regimes233.0ms

Accuracy

0% (0.4b 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	18	24
1	18	24

end0.0ms

sample1.0s

Algorithm

intervals

Results

393.0ms	1524×	body	1280	valid
195.0ms	1166×	body	640	valid
164.0ms	4386×	body	80	valid
75.0ms	612×	body	320	valid
26.0ms	312×	body	160	valid

Details

sample42.0ms

simplify674.0ms

prune4.0ms

localize11.0ms

rewrite25.0ms

series82.0ms

simplify53.0ms

prune192.0ms

localize13.0ms

rewrite11.0ms

series13.0ms

simplify37.0ms

prune160.0ms

localize10.0ms

rewrite31.0ms

series93.0ms

simplify54.0ms

prune190.0ms

localize14.0ms

rewrite36.0ms

series94.0ms

simplify74.0ms

prune206.0ms

regimes233.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.0s

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