Details

sample289.0ms

Algorithm

intervals

Results

16.0ms	56×	body	1280	valid
8.0ms	45×	body	640	valid
5.0ms	123×	body	80	valid
2.0ms	19×	body	320	valid
1.0ms	13×	body	160	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	9
1	22	9
2	29	9
3	37	9
4	43	9
5	45	9
6	45	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))) (+ 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))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
23×	`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×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-neg` `prod-diff` `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 → 119

Calls

4 calls:

7.0ms	(/ (- 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))

series220.0ms

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)))
31.0ms	(* (tan x) (tan x))
61.0ms	(* (tan x) (tan x))

simplify51.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	338	1007
1	1243	918
2	5001	882

prune290.0ms

Filtered

131 candidates to 91 candidates (69.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	118	13	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	13	132

Merged error: 0.1b

Counts

132 → 13

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.4b	(exp (* (tan x) (tan x)))
1.4b	(log (exp (* (tan x) (tan x))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

19×	`pow1`
17×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
8×	`tan-quot` `add-exp-log` `add-cbrt-cube`
7×	`add-log-exp`
6×	`swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`log-prod` `log-pow`
2×	`pow2` `frac-times` `exp-prod` `exp-to-pow` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`rem-log-exp` `rem-exp-log`

Counts

4 → 88

Calls

4 calls:

8.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
3.0ms	(exp (* (tan x) (tan x)))
2.0ms	(log (exp (* (tan x) (tan x))))

series147.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (tan x) (tan x))
31.0ms	(* (tan x) (tan x))
53.0ms	(exp (* (tan x) (tan x)))
32.0ms	(log (exp (* (tan x) (tan x))))

simplify69.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	140	437
1	429	370
2	1869	350
3	5001	344

prune196.0ms

Filtered

100 candidates to 61 candidates (61.0%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	100	13	113

Merged error: 0.1b

Counts

113 → 13

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(- 1.0 (* (tan x) (tan x)))
0.2b	(log1p (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
18×	`pow1`
14×	`add-cube-cbrt` `*-un-lft-identity`
8×	`tan-quot` `add-exp-log` `add-cbrt-cube`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`expm1-log1p-u`
4×	`log1p-expm1-u`
3×	`fma-neg` `prod-diff`
2×	`pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `log1p-udef` `flip3--` `diff-log` `log1p-expm1` `flip--` `difference-of-squares`

Counts

4 → 92

Calls

4 calls:

3.0ms	(- 1.0 (* (tan x) (tan x)))
1.0ms	(log1p (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))

series323.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- 1.0 (* (tan x) (tan x)))
218.0ms	(log1p (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))
31.0ms	(* (tan x) (tan x))
37.0ms	(* (tan x) (tan x))

simplify136.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 3 (128.0ms)

Iter	Nodes	Cost
0	246	612
1	827	546
2	3958	530
3	5002	525

prune223.0ms

Filtered

104 candidates to 66 candidates (63.5%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	103	14	117

Merged error: 0.1b

Counts

117 → 14

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (tan x) (sin x)) (cos x))
0.2b	(* (tan x) (sin x))
0.2b	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
0.3b	(* (tan x) (tan x))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`add-cube-cbrt`
21×	`prod-diff`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`times-frac`
6×	`tan-quot` `associate-r` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`fma-neg` `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--` `associate-/l/` `associate-/l` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 115

Calls

4 calls:

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

series196.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ (* (tan x) (sin x)) (cos x))
47.0ms	(* (tan x) (sin x))
50.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
36.0ms	(* (tan x) (tan x))

simplify70.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	432	1314
1	1873	967
2	5001	929

prune229.0ms

Filtered

127 candidates to 77 candidates (60.6%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	0	11	11
Picked	0	1	1
Done	1	1	2
Total	127	14	141

Merged error: 0.1b

Counts

141 → 14

regimes199.0ms

Accuracy

0% (1.0b remaining)

Error of 1.1b against oracle of 0.1b and baseline of 1.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	11
1	10	11

end0.0ms

sample1.0s

Algorithm

intervals

Results

410.0ms	1580×	body	1280	valid
205.0ms	1221×	body	640	valid
172.0ms	4293×	body	80	valid
72.0ms	602×	body	320	valid
26.0ms	304×	body	160	valid