Details

sample296.0ms

Algorithm

intervals

Results

11.0ms	43×	body	1280	valid
8.0ms	47×	body	640	valid
7.0ms	138×	body	80	valid
3.0ms	22×	body	320	valid
1.0ms	6×	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: 0.4b

Counts

2 → 1

localize10.0ms

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)))
0.2b	(* (tan x) (tan x))
0.2b	(* (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))
7.0ms	(* (tan x) (tan x))

series221.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
34.0ms	(- 1.0 (* (tan x) (tan x)))
32.0ms	(* (tan x) (tan x))
61.0ms	(* (tan x) (tan x))

simplify47.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (34.0ms)

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

prune236.0ms

Filtered

117 candidates to 77 candidates (65.8%)

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

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

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:

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

series208.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
32.0ms	(+ (sqrt 1.0) (tan x))
40.0ms	(- (sqrt 1.0) (tan x))
33.0ms	(* (tan x) (tan x))

simplify54.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (43.0ms)

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

prune206.0ms

Filtered

101 candidates to 67 candidates (66.3%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	98	3	101
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	98	15	113

Merged error: 0.1b

Counts

113 → 15

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite22.0ms

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:

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

series188.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (tan x) (sin x))
59.0ms	(/ (* (tan x) (sin x)) (cos x))
53.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
32.0ms	(* (tan x) (tan x))

simplify47.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	291	567
1	1265	503
2	5002	495

prune214.0ms

Filtered

95 candidates to 61 candidates (64.2%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	92	3	95
Fresh	2	11	13
Picked	1	0	1
Done	0	1	1
Total	95	15	110

Merged error: 0.0b

Counts

110 → 15

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (sqrt 1.0) (tan x))
0.2b	(log (exp (- (sqrt 1.0) (tan x))))
0.2b	(* (tan x) (tan x))
0.3b	(exp (- (sqrt 1.0) (tan x)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
12×	`pow1` `exp-prod`
11×	`add-cube-cbrt`
9×	`add-log-exp`
7×	`log-pow`
6×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
5×	`log-prod`
4×	`tan-quot` `exp-sum`
3×	`sub-neg` `swap-sqr` `associate-r` `associate-l` `sqrt-prod` `distribute-lft-out--`
2×	`exp-diff` `diff-log` `rem-exp-log`
1×	`pow2` `frac-times` `log-div` `flip3--` `pow-plus` `associate-r/` `rem-log-exp` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

5.0ms	(- (sqrt 1.0) (tan x))
6.0ms	(log (exp (- (sqrt 1.0) (tan x))))
5.0ms	(* (tan x) (tan x))
8.0ms	(exp (- (sqrt 1.0) (tan x)))

series181.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (sqrt 1.0) (tan x))
36.0ms	(log (exp (- (sqrt 1.0) (tan x))))
33.0ms	(* (tan x) (tan x))
71.0ms	(exp (- (sqrt 1.0) (tan x)))

simplify110.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 3 (103.0ms)

Iter	Nodes	Cost
0	226	453
1	744	412
2	3249	404
3	5001	398

prune180.0ms

Filtered

94 candidates to 60 candidates (63.8%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	13	13
Picked	0	1	1
Done	0	1	1
Total	94	15	109

Merged error: 0.0b

Counts

109 → 15

regimes247.0ms

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	13	12
1	13	12

end0.0ms

sample978.0ms

Algorithm

intervals

Results

391.0ms	1535×	body	1280	valid
204.0ms	1238×	body	640	valid
164.0ms	4274×	body	80	valid
79.0ms	633×	body	320	valid
26.0ms	320×	body	160	valid

Details

sample296.0ms

simplify15.0ms

prune3.0ms

localize10.0ms

rewrite25.0ms

series221.0ms

simplify47.0ms

prune236.0ms

localize11.0ms

rewrite26.0ms

series208.0ms

simplify54.0ms

prune206.0ms

localize14.0ms

rewrite22.0ms

series188.0ms

simplify47.0ms

prune214.0ms

localize14.0ms

rewrite26.0ms

series181.0ms

simplify110.0ms

prune180.0ms

regimes247.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample978.0ms

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