Details

sample96.0ms

Algorithm

intervals

Results

43.0ms	116×	body	1280	valid
21.0ms	25×	body	2560	valid
11.0ms	50×	body	640	valid
3.0ms	21×	body	320	valid
2.0ms	34×	body	80	valid
1.0ms	10×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	7
1	10	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: 38.8b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (tan (+ x eps)) (tan x))
3.8b	(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 → 25

Calls

2 calls:

6.0ms	(- (tan (+ x eps)) (tan x))
3.0ms	(tan (+ x eps))

series39.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(- (tan (+ x eps)) (tan x))
15.0ms	(tan (+ x eps))

simplify62.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4947	335
1	4947	335

prune62.0ms

Filtered

25 candidates to 31 candidates (-24.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	23	8	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	24	8	32

Merged error: 18.0b

Counts

32 → 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))
4.0b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite31.0ms

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 → 86

Calls

4 calls:

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

series192.0ms

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))
96.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify48.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5281	1555

prune160.0ms

Filtered

74 candidates to 98 candidates (-32.4%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	88	10	98
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	89	17	106

Merged error: 17.9b

Counts

106 → 17

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (- 1 (* (tan x) (tan eps))))
0.1b	(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
0.2b	(* (tan x) (tan eps))
4.0b	(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 119

Calls

4 calls:

4.0ms	(/ 1 (- 1 (* (tan x) (tan eps))))
14.0ms	(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
5.0ms	(* (tan x) (tan eps))
11.0ms	(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

series210.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ 1 (- 1 (* (tan x) (tan eps))))
57.0ms	(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
21.0ms	(* (tan x) (tan eps))
98.0ms	(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

simplify61.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5204	2124

prune183.0ms

Filtered

88 candidates to 131 candidates (-48.9%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	128	3	131
Fresh	2	14	16
Picked	1	0	1
Done	0	0	0
Total	131	17	148

Merged error: 17.9b

Counts

148 → 17

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
0.2b	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
6.4b	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 178

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
10.0ms	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
8.0ms	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
25.0ms	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

series240.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (tan x) (tan eps))
57.0ms	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
63.0ms	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
99.0ms	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

simplify77.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4962	3973
1	4962	3973

prune181.0ms

Filtered

120 candidates to 190 candidates (-58.3%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	186	4	190
Fresh	1	15	16
Picked	1	0	1
Done	0	0	0
Total	188	19	207

Merged error: 17.9b

Counts

207 → 19

regimes258.0ms

Accuracy

86.4% (1.0b remaining)

Error of 15.9b against oracle of 14.9b and baseline of 22.4b

bsearch86.0ms

Steps

Iters	Range		Point
10	1.5101440346174218e-71	5.441273749041422e-53	6.452399184890276e-56
9	-2.416489573684541e-69	-2.731503935588759e-77	-7.298803022704687e-70

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	83
1	47	83

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.3s	3231×	body	1280	valid
623.0ms	707×	body	2560	valid
423.0ms	1849×	body	640	valid
120.0ms	786×	body	320	valid
51.0ms	1102×	body	80	valid
33.0ms	325×	body	160	valid

Details

sample96.0ms

simplify3.0ms

prune3.0ms

localize9.0ms

rewrite10.0ms

series39.0ms

simplify62.0ms

prune62.0ms

localize11.0ms

rewrite31.0ms

series192.0ms

simplify48.0ms

prune160.0ms

localize13.0ms

rewrite38.0ms

series210.0ms

simplify61.0ms

prune183.0ms

localize14.0ms

rewrite55.0ms

series240.0ms

simplify77.0ms

prune181.0ms

regimes258.0ms

bsearch86.0ms

simplify1.0ms

end0.0ms

sample2.8s

Profiling