Details

analyze791.0ms

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

sample87.0ms

Algorithm

intervals

Results

36.0ms	97×	body	1280	valid
22.0ms	26×	body	2560	valid
13.0ms	59×	body	640	valid
3.0ms	24×	body	320	valid
2.0ms	48×	body	80	valid
0.0ms	2×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune7.0ms

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: 36.3b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (tan (+ x eps)) (tan x))
1.5b	(tan (+ x eps))

rewrite10.0ms

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:

6.0ms	(- (tan (+ x eps)) (tan x))
4.0ms	(tan (+ x eps))

series41.0ms

Counts

2 → 6

Calls

2 calls:

25.0ms	(- (tan (+ x eps)) (tan x))
16.0ms	(tan (+ x eps))

simplify49.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4924	332
1	4924	332

prune63.0ms

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: 14.1b

Counts

31 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.2b	(* (tan x) (tan eps))
1.9b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite32.0ms

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:

4.0ms	(+ (tan x) (tan eps))
8.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
5.0ms	(* (tan x) (tan eps))
13.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series193.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+ (tan x) (tan eps))
55.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
21.0ms	(* (tan x) (tan eps))
97.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify49.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5109	1560

prune194.0ms

Filtered

74 candidates to 97 candidates (-31.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	85	12	97
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	90	15	105

Merged error: 14.0b

Counts

105 → 15

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (* (tan x) (* (tan eps) (tan eps))))
0.2b	(* (tan x) (* (tan eps) (tan eps)))
0.2b	(* (tan eps) (tan eps))
1.9b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (* (tan x) (* (tan eps) (tan eps)))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

53×	`tan-quot`
25×	`pow1` `frac-times` `associate-*r/`
20×	`add-exp-log` `add-cbrt-cube`
13×	`add-sqr-sqrt`
12×	`associate-*l/`
10×	`add-cube-cbrt` `*-un-lft-identity` `pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`associate-l`
6×	`add-log-exp`
5×	`associate-r` `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 → 108

Calls

4 calls:

11.0ms	(* (tan x) (* (tan x) (* (tan eps) (tan eps))))
7.0ms	(* (tan x) (* (tan eps) (tan eps)))
5.0ms	(* (tan eps) (tan eps))
13.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (* (tan x) (* (tan eps) (tan eps)))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series377.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (tan x) (* (tan x) (* (tan eps) (tan eps))))
27.0ms	(* (tan x) (* (tan eps) (tan eps)))
8.0ms	(* (tan eps) (tan eps))
312.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (* (tan x) (* (tan eps) (tan eps)))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify32.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5179	1990

prune176.0ms

Filtered

76 candidates to 120 candidates (-57.9%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	116	4	120
Fresh	1	13	14
Picked	1	0	1
Done	0	0	0
Total	118	17	135

Merged error: 14.0b

Counts

135 → 17

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (cbrt (pow (tan eps) 6)))
0.5b	(pow (tan eps) 6)
1.9b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (* (tan x) (cbrt (pow (tan eps) 6)))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
10.9b	(cbrt (pow (tan eps) 6))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
17×	`cbrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
10×	`unpow-prod-down` `associate-r`
7×	`pow1` `add-exp-log`
6×	`tan-quot` `add-log-exp`
5×	`frac-sub` `add-cbrt-cube`
4×	`unswap-sqr` `sqr-pow`
3×	`pow-unpow` `associate-l`
2×	`frac-times` `flip3-+` `associate-r/` `associate-l/` `associate--l+` `flip-+`
1×	`distribute-rgt-in` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `distribute-lft-in` `pow1/3` `diff-log` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 79

Calls

4 calls:

7.0ms	(* (tan x) (cbrt (pow (tan eps) 6)))
3.0ms	(pow (tan eps) 6)
11.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (* (tan x) (cbrt (pow (tan eps) 6)))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
3.0ms	(cbrt (pow (tan eps) 6))

series379.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (tan x) (cbrt (pow (tan eps) 6)))
16.0ms	(pow (tan eps) 6)
328.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (* (tan x) (cbrt (pow (tan eps) 6)))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
8.0ms	(cbrt (pow (tan eps) 6))

simplify42.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5006	1632

prune155.0ms

Filtered

72 candidates to 91 candidates (-26.4%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	2	14	16
Picked	0	1	1
Done	0	0	0
Total	92	16	108

Merged error: 14.0b

Counts

108 → 16

regimes216.0ms

Accuracy

87% (1.0b remaining)

Error of 15.5b against oracle of 14.6b and baseline of 21.9b

bsearch77.0ms

Steps

Iters	Range		Point
8	6.32796364755843e-67	5.155107912446368e-64	5.09795473738253e-64
9	-1.5749952387852392e-60	-5.9185889057344995e-67	-4.9252008008844826e-61

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	123	139
1	123	139

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.3s	3298×	body	1280	valid
553.0ms	634×	body	2560	valid
412.0ms	1862×	body	640	valid
103.0ms	730×	body	320	valid
47.0ms	1098×	body	80	valid
37.0ms	378×	body	160	valid

Details

analyze791.0ms

sample87.0ms

simplify5.0ms

prune7.0ms

localize9.0ms

rewrite10.0ms

series41.0ms

simplify49.0ms

prune63.0ms

localize11.0ms

rewrite32.0ms

series193.0ms

simplify49.0ms

prune194.0ms

localize16.0ms

rewrite40.0ms

series377.0ms

simplify32.0ms

prune176.0ms

localize21.0ms

rewrite26.0ms

series379.0ms

simplify42.0ms

prune155.0ms

regimes216.0ms

bsearch77.0ms

simplify2.0ms

end0.0ms

sample2.6s

Profiling