Details

sample278.0ms

Algorithm

intervals

Results

11.0ms	42×	body	1280	valid
7.0ms	150×	body	80	valid
6.0ms	33×	body	640	valid
2.0ms	18×	body	320	valid
1.0ms	13×	body	160	valid

simplify15.0ms

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

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 0.3b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (* (tan x) (tan x)))
0.1b	(/ (- 1.0 (* (tan x) (tan x))) (+ 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:

3.0ms	(- 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))
7.0ms	(* (tan x) (tan x))

series221.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- 1.0 (* (tan x) (tan x)))
96.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
33.0ms	(* (tan x) (tan x))
58.0ms	(* (tan x) (tan x))

simplify48.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (34.0ms)

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

prune241.0ms

Filtered

117 candidates to 77 candidates (65.8%)

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

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (cbrt (pow (tan x) 6))))
0.3b	(* (tan x) (tan x))
0.7b	(pow (tan x) 6)
9.2b	(cbrt (pow (tan x) 6))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
29×	`add-sqr-sqrt`
22×	`add-cube-cbrt`
16×	`times-frac`
12×	`pow1`
9×	`add-exp-log`
8×	`add-cbrt-cube`
7×	`cbrt-prod`
6×	`unpow-prod-down`
5×	`distribute-lft-out` `difference-of-squares`
4×	`tan-quot` `associate-/r` `associate-/l` `add-log-exp`
3×	`pow-unpow` `swap-sqr` `associate-r` `associate-l`
2×	`associate-/r/` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `pow2` `frac-times` `pow-to-exp` `flip3--` `pow-pow` `frac-2neg` `flip3-+` `pow-plus` `pow1/3` `div-sub` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `pow-exp` `prod-exp` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `flip-+` `div-inv` `unswap-sqr`

Counts

4 → 101

Calls

4 calls:

9.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (cbrt (pow (tan x) 6))))
5.0ms	(* (tan x) (tan x))
3.0ms	(pow (tan x) 6)
3.0ms	(cbrt (pow (tan x) 6))

series224.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (cbrt (pow (tan x) 6))))
32.0ms	(* (tan x) (tan x))
65.0ms	(pow (tan x) 6)
33.0ms	(cbrt (pow (tan x) 6))

simplify61.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	401	916
1	1610	848
2	5001	806

prune222.0ms

Filtered

113 candidates to 73 candidates (64.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	113	13	126

Merged error: 0.0b

Counts

126 → 13

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
13×	`pow1`
10×	`add-cube-cbrt`
9×	`associate-r`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`associate-l`
5×	`frac-times`
4×	`tan-quot` `flip3--` `flip3-+` `flip--` `flip-+` `difference-of-squares`
3×	`sub-neg` `associate-r/` `swap-sqr` `associate-l/`
2×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `sqrt-prod` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `pow2` `pow-plus` `diff-log` `sum-log` `pow-sqr` `pow-prod-up`

Counts

4 → 89

Calls

4 calls:

4.0ms	(+ (sqrt 1.0) (tan x))
4.0ms	(- (sqrt 1.0) (tan x))
11.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
5.0ms	(* (tan x) (tan x))

series218.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(+ (sqrt 1.0) (tan x))
37.0ms	(- (sqrt 1.0) (tan x))
105.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
37.0ms	(* (tan x) (tan x))

simplify49.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	328	693
1	1582	618
2	5001	607

prune186.0ms

Filtered

101 candidates to 67 candidates (66.3%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	1	10	11
Picked	0	1	1
Done	0	1	1
Total	101	13	114

Merged error: 0.0b

Counts

114 → 13

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (* (tan x) (tan x)))
0.2b	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite29.0ms

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:

3.0ms	(- 1.0 (* (tan x) (tan x)))
9.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))

series198.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- 1.0 (* (tan x) (tan x)))
95.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
37.0ms	(* (tan x) (tan x))
33.0ms	(* (tan x) (tan x))

simplify74.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	545	2150
1	2567	1968
2	5001	1866

prune190.0ms

Filtered

177 candidates to 88 candidates (49.7%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	177	0	177
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	177	13	190

Merged error: 0.0b

Counts

190 → 13

regimes143.0ms

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	11	9
1	11	9

end0.0ms

sample960.0ms

Algorithm

intervals

Results

374.0ms	1468×	body	1280	valid
211.0ms	1258×	body	640	valid
156.0ms	4314×	body	80	valid
80.0ms	639×	body	320	valid
26.0ms	321×	body	160	valid

Details

sample278.0ms

simplify15.0ms

prune3.0ms

localize10.0ms

rewrite25.0ms

series221.0ms

simplify48.0ms

prune241.0ms

localize12.0ms

rewrite23.0ms

series224.0ms

simplify61.0ms

prune222.0ms

localize11.0ms

rewrite28.0ms

series218.0ms

simplify49.0ms

prune186.0ms

localize13.0ms

rewrite29.0ms

series198.0ms

simplify74.0ms

prune190.0ms

regimes143.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample960.0ms

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