Details

sample47.0ms

Algorithm

intervals

Results

13.0ms	46×	body	1280	valid
8.0ms	42×	body	640	valid
5.0ms	134×	body	80	valid
3.0ms	20×	body	320	valid
1.0ms	14×	body	160	valid

simplify445.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

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

prune6.0ms

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: 0.3b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 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))

series70.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
10.0ms	(- 1.0 (* (tan x) (tan x)))
9.0ms	(* (tan x) (tan x))
19.0ms	(* (tan x) (tan x))

simplify51.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (36.0ms)

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

prune183.0ms

Filtered

117 candidates to 77 candidates (34.2%)

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

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

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))
13.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
4.0ms	(- (sqrt 1.0) (tan x))
5.0ms	(* (tan x) (tan x))

series41.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ (sqrt 1.0) (tan x))
17.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
8.0ms	(- (sqrt 1.0) (tan x))
9.0ms	(* (tan x) (tan x))

simplify50.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (42.0ms)

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

prune162.0ms

Filtered

101 candidates to 68 candidates (32.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	99	2	101
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	102	11	113

Merged error: 0.0b

Counts

113 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

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

series16.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(pow (cos x) 2)
3.0ms	(pow (cos x) 2)
3.0ms	(pow (sin x) 2)
4.0ms	(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

prune143.0ms

Filtered

84 candidates to 48 candidates (42.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	83	12	95

Merged error: 0.0b

Counts

95 → 12

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

2.0ms	(- 1.0 (* (tan x) (tan x)))
4.0ms	(/ 1 (+ 1.0 (* (tan x) (tan x))))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))

series47.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- 1.0 (* (tan x) (tan x)))
19.0ms	(/ 1 (+ 1.0 (* (tan x) (tan x))))
9.0ms	(* (tan x) (tan x))
11.0ms	(* (tan x) (tan x))

simplify170.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 3 (163.0ms)

Iter	Nodes	Cost
0	263	638
1	953	577
2	4565	550
3	5001	544

prune93.0ms

Filtered

114 candidates to 63 candidates (44.7%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	110	4	114
Fresh	3	7	10
Picked	0	1	1
Done	0	1	1
Total	113	13	126

Merged error: 0.0b

Counts

126 → 13

regimes392.0ms

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	12	13
1	12	13

end0.0ms

sample1.0s

Algorithm

intervals

Results

387.0ms	1496×	body	1280	valid
214.0ms	1234×	body	640	valid
170.0ms	4274×	body	80	valid
84.0ms	654×	body	320	valid
29.0ms	342×	body	160	valid

Details

sample47.0ms

simplify445.0ms

prune6.0ms

localize24.0ms

rewrite24.0ms

series70.0ms

simplify51.0ms

prune183.0ms

localize11.0ms

rewrite29.0ms

series41.0ms

simplify50.0ms

prune162.0ms

localize13.0ms

rewrite11.0ms

series16.0ms

simplify60.0ms

prune143.0ms

localize9.0ms

rewrite19.0ms

series47.0ms

simplify170.0ms

prune93.0ms

regimes392.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.0s

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