Details

sample91.0ms

Algorithm

intervals

Results

48.0ms	121×	body	1280	valid
16.0ms	18×	body	2560	valid
11.0ms	49×	body	640	valid
4.0ms	31×	body	320	valid
1.0ms	28×	body	80	valid
1.0ms	9×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

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: 40.2b

Counts

2 → 1

localize12.0ms

Local error

Found 2 expressions with local error:

0.5b	(- (tan (+ x eps)) (tan x))
3.5b	(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 → 25

Calls

2 calls:

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

series139.0ms

Counts

2 → 6

Calls

2 calls:

90.0ms	(- (tan (+ x eps)) (tan x))
49.0ms	(tan (+ x eps))

simplify79.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (23.0ms)

Iter	Nodes	Cost
0	134	211
1	295	202
2	757	200
3	2482	199
4	5001	199

prune92.0ms

Filtered

31 candidates to 25 candidates (80.6%)

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: 15.1b

Counts

32 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1 (* (tan x) (tan eps)))
0.2b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
3.3b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-log-exp`
7×	`tan-quot`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`associate-r` `associate-l`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `difference-of-squares`
1×	`+-commutative` `frac-times` `flip3-+` `times-frac` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 62

Calls

4 calls:

3.0ms	(- 1 (* (tan x) (tan eps)))
5.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
12.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series644.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(- 1 (* (tan x) (tan eps)))
90.0ms	(+ (tan x) (tan eps))
91.0ms	(* (tan x) (tan eps))
359.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify120.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	343	662
1	1170	624
2	4756	614
3	5001	614

prune227.0ms

Filtered

74 candidates to 56 candidates (75.7%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	57	17	74
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	61	21	82

Merged error: 15.0b

Counts

82 → 21

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (tan x) (tan eps))
0.2b	(* (sin x) (sin eps))
0.3b	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
3.3b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

4.0ms	(+ (tan x) (tan eps))
5.0ms	(* (sin x) (sin eps))
8.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
18.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

series768.0ms

Counts

4 → 12

Calls

4 calls:

268.0ms	(+ (tan x) (tan eps))
43.0ms	(* (sin x) (sin eps))
100.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
357.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

simplify47.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	427	917
1	1787	792
2	5001	792

prune295.0ms

Filtered

83 candidates to 60 candidates (72.3%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	79	4	83
Fresh	2	18	20
Picked	1	0	1
Done	0	0	0
Total	82	22	104

Merged error: 15.0b

Counts

104 → 22

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (tan x) (tan eps))
0.2b	(pow (- 1 (* (tan x) (tan eps))) 3)
0.2b	(* (tan x) (tan eps))
3.3b	(- (/ (+ (tan x) (tan eps)) (cbrt (pow (- 1 (* (tan x) (tan eps))) 3))) (tan x))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
9×	`add-cube-cbrt`
8×	`add-log-exp`
7×	`tan-quot` `pow1` `add-exp-log` `add-cbrt-cube`
6×	`difference-of-squares`
5×	`times-frac`
4×	`cbrt-prod` `unpow-prod-down` `cube-prod`
3×	`pow-unpow` `associate-r` `associate-l`
2×	`cube-div` `flip3--` `flip--` `sqr-pow`
1×	`+-commutative` `cube-mult` `frac-times` `pow-to-exp` `sub-neg` `pow-pow` `flip3-+` `diff-log` `unpow3` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `pow-exp` `prod-exp` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `distribute-lft-out` `distribute-lft-out--` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 79

Calls

4 calls:

5.0ms	(+ (tan x) (tan eps))
4.0ms	(pow (- 1 (* (tan x) (tan eps))) 3)
6.0ms	(* (tan x) (tan eps))
28.0ms	(- (/ (+ (tan x) (tan eps)) (cbrt (pow (- 1 (* (tan x) (tan eps))) 3))) (tan x))

series657.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(+ (tan x) (tan eps))
134.0ms	(pow (- 1 (* (tan x) (tan eps))) 3)
88.0ms	(* (tan x) (tan eps))
347.0ms	(- (/ (+ (tan x) (tan eps)) (cbrt (pow (- 1 (* (tan x) (tan eps))) 3))) (tan x))

simplify55.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	445	938
1	1736	873
2	5001	863

prune212.0ms

Filtered

91 candidates to 61 candidates (67.0%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	88	3	91
Fresh	3	18	21
Picked	1	0	1
Done	0	0	0
Total	92	21	113

Merged error: 15.0b

Counts

113 → 21

regimes237.0ms

Accuracy

86.5% (1.0b remaining)

Error of 15.6b against oracle of 14.7b and baseline of 21.8b

bsearch158.0ms

Steps

Iters	Range		Point
10	4.9601884090646844e-27	2.767658890006075e-15	6.821703138672794e-19
9	-1.0002863198165765e-75	-3.669787644181221e-84	-7.666889808720746e-78

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	63
1	51	63

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.3s	3290×	body	1280	valid
588.0ms	677×	body	2560	valid
411.0ms	1826×	body	640	valid
109.0ms	773×	body	320	valid
47.0ms	1063×	body	80	valid
35.0ms	371×	body	160	valid

Details

sample91.0ms

simplify5.0ms

prune2.0ms

localize12.0ms

rewrite11.0ms

series139.0ms

simplify79.0ms

prune92.0ms

localize11.0ms

rewrite27.0ms

series644.0ms

simplify120.0ms

prune227.0ms

localize22.0ms

rewrite36.0ms

series768.0ms

simplify47.0ms

prune295.0ms

localize15.0ms

rewrite45.0ms

series657.0ms

simplify55.0ms

prune212.0ms

regimes237.0ms

bsearch158.0ms

simplify2.0ms

end0.0ms

sample2.7s

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