Details

analyze775.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.2%	0.1%	6
21.9%	78%	0.1%	7
23.4%	76.5%	0.1%	8
24.2%	75.7%	0.1%	9
24.6%	75.3%	0.1%	10
24.8%	75.1%	0.1%	11
24.9%	75%	0.1%	12
24.9%	75%	0.1%	13
25%	75%	0.1%	14

sample92.0ms

Algorithm

intervals

Results

41.0ms	109×	body	1280	valid
23.0ms	26×	body	2560	valid
11.0ms	51×	body	640	valid
6.0ms	25×	body	320	valid
1.0ms	33×	body	80	valid
1.0ms	12×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune3.0ms

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: 39.2b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.9b	(- (tan (+ x eps)) (tan x))
3.6b	(tan (+ x eps))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

4×	`tan-quot` `add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `tan-sum` `frac-sub` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

7.0ms	(- (tan (+ x eps)) (tan x))
4.0ms	(tan (+ x eps))

series40.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(- (tan (+ x eps)) (tan x))
16.0ms	(tan (+ x eps))

simplify48.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4924	332
1	4924	332

prune62.0ms

Filtered

25 candidates to 30 candidates (-20.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	22	8	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	23	8	31

Merged error: 15.7b

Counts

31 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
3.8b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
13×	`times-frac`
9×	`tan-quot`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1`
5×	`distribute-lft-out`
4×	`associate-/l*`
3×	`associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`flip3--` `flip3-+` `frac-add` `associate-/r/` `flip--` `flip-+` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `frac-times` `sub-neg` `frac-2neg` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

8.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
4.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
11.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series190.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
21.0ms	(+ (tan x) (tan eps))
21.0ms	(* (tan x) (tan eps))
95.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify47.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5109	1560

prune168.0ms

Filtered

74 candidates to 97 candidates (-31.1%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	83	14	97
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	89	16	105

Merged error: 15.6b

Counts

105 → 16

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (exp (tan x)) (tan eps))
0.3b	(exp (tan x))
3.3b	(log (pow (exp (tan x)) (tan eps)))
3.8b	(- (/ (+ (tan x) (tan eps)) (- 1 (log (pow (exp (tan x)) (tan eps))))) (tan x))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt`
7×	`log-prod` `add-log-exp`
6×	`unpow-prod-down` `exp-prod`
5×	`pow1` `add-exp-log`
4×	`pow-pow` `add-cbrt-cube`
3×	`pow-unpow` `rem-log-exp`
2×	`pow-to-exp` `pow-exp` `difference-of-squares` `sqr-pow`
1×	`tan-quot` `sub-neg` `flip3--` `times-frac` `diff-log` `log-pow` `frac-sub` `flip--` `rem-exp-log` `distribute-lft-out--`

Counts

4 → 64

Calls

4 calls:

4.0ms	(pow (exp (tan x)) (tan eps))
2.0ms	(exp (tan x))
3.0ms	(log (pow (exp (tan x)) (tan eps)))
15.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (log (pow (exp (tan x)) (tan eps))))) (tan x))

series201.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(pow (exp (tan x)) (tan eps))
9.0ms	(exp (tan x))
37.0ms	(log (pow (exp (tan x)) (tan eps)))
122.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (log (pow (exp (tan x)) (tan eps))))) (tan x))

simplify51.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4934	920
1	4934	920

prune123.0ms

Filtered

53 candidates to 76 candidates (-43.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	73	3	76
Fresh	6	9	15
Picked	0	1	1
Done	0	0	0
Total	79	13	92

Merged error: 13.4b

Counts

92 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (* (tan x) (* (tan eps) (tan eps))))
0.2b	(* (tan x) (tan eps))
0.3b	(* (tan eps) (tan eps))
3.8b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (* (tan x) (* (tan eps) (tan eps)))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

45×	`tan-quot`
22×	`pow1`
21×	`frac-times` `associate-*r/`
17×	`add-exp-log` `add-cbrt-cube`
15×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-*l/`
9×	`associate-l`
8×	`pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`associate-r`
6×	`add-log-exp`
5×	`frac-sub`
3×	`swap-sqr` `*-commutative`
2×	`flip3-+` `associate--l+` `flip-+` `unswap-sqr`
1×	`pow2` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `pow-plus` `diff-log` `pow-sqr` `pow-prod-up` `flip--`

Counts

4 → 103

Calls

4 calls:

11.0ms	(* (tan x) (* (tan x) (* (tan eps) (tan eps))))
5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan eps) (tan eps))
12.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (* (tan x) (* (tan eps) (tan eps)))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series378.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (tan x) (* (tan x) (* (tan eps) (tan eps))))
21.0ms	(* (tan x) (tan eps))
9.0ms	(* (tan eps) (tan eps))
318.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (* (tan x) (* (tan eps) (tan eps)))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify33.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5283	1876

prune116.0ms

Filtered

75 candidates to 115 candidates (-53.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	112	3	115
Fresh	2	9	11
Picked	1	0	1
Done	0	1	1
Total	115	13	128

Merged error: 13.4b

Counts

128 → 13

regimes186.0ms

Accuracy

96.2% (0.4b remaining)

Error of 12.6b against oracle of 12.2b and baseline of 21.5b

bsearch60.0ms

Steps

Iters	Range		Point
8	9.383740477091332e-29	1.3202582201462097e-24	1.298064167888159e-24
8	-6.329236100813076e-07	-7.674978958902272e-11	-7.82287172944081e-11

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	92	66
1	92	66

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.3s	3331×	body	1280	valid
536.0ms	622×	body	2560	valid
374.0ms	1736×	body	640	valid
115.0ms	798×	body	320	valid
50.0ms	1144×	body	80	valid
35.0ms	369×	body	160	valid

Details

analyze775.0ms

sample92.0ms

simplify4.0ms

prune3.0ms

localize8.0ms

rewrite11.0ms

series40.0ms

simplify48.0ms

prune62.0ms

localize11.0ms

rewrite30.0ms

series190.0ms

simplify47.0ms

prune168.0ms

localize15.0ms

rewrite25.0ms

series201.0ms

simplify51.0ms

prune123.0ms

localize17.0ms

rewrite36.0ms

series378.0ms

simplify33.0ms

prune116.0ms

regimes186.0ms

bsearch60.0ms

simplify2.0ms

end0.0ms

sample2.6s

Profiling