Details

sample86.0ms

Algorithm

intervals

Results

36.0ms	94×	body	1280	valid
21.0ms	25×	body	2560	valid
14.0ms	67×	body	640	valid
4.0ms	32×	body	320	valid
1.0ms	30×	body	80	valid
1.0ms	8×	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: 36.3b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (tan (+ x eps)) (tan x))
1.9b	(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))
4.0ms	(tan (+ x eps))

series137.0ms

Counts

2 → 6

Calls

2 calls:

86.0ms	(- (tan (+ x eps)) (tan x))
51.0ms	(tan (+ x eps))

simplify76.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (22.0ms)

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

prune78.0ms

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: 15.9b

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))))
0.3b	(* (tan x) (tan eps))
2.7b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite34.0ms

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

series730.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(+ (tan x) (tan eps))
208.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
89.0ms	(* (tan x) (tan eps))
344.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify46.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	397	1050
1	1432	1005
2	5001	995

prune267.0ms

Filtered

98 candidates to 74 candidates (75.5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	84	14	98
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	90	16	106

Merged error: 15.7b

Counts

106 → 16

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan eps))
0.3b	(* (tan x) (tan eps))
0.3b	(* (tan x) (tan eps))
2.7b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
15.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series1.3s

Counts

4 → 12

Calls

4 calls:

91.0ms	(* (tan x) (tan eps))
90.0ms	(* (tan x) (tan eps))
90.0ms	(* (tan x) (tan eps))
1.1s	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify62.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	428	1131
1	1996	1040
2	5001	1040

prune301.0ms

Filtered

94 candidates to 73 candidates (77.7%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	86	8	94
Fresh	2	13	15
Picked	1	0	1
Done	0	0	0
Total	89	21	110

Merged error: 15.7b

Counts

110 → 21

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (sin eps))
0.3b	(* (tan x) (tan eps))
0.3b	(* (tan x) (tan eps))
2.7b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

5.0ms	(* (tan x) (sin eps))
5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
13.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

series1.2s

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (tan x) (sin eps))
91.0ms	(* (tan x) (tan eps))
94.0ms	(* (tan x) (tan eps))
965.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

simplify63.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	497	1219
1	2235	1103
2	5001	1103

prune264.0ms

Filtered

92 candidates to 68 candidates (73.9%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	1	19	20
Picked	1	0	1
Done	0	0	0
Total	93	20	113

Merged error: 15.7b

Counts

113 → 20

regimes189.0ms

Accuracy

87.6% (0.9b remaining)

Error of 15.3b against oracle of 14.3b and baseline of 21.8b

bsearch114.0ms

Steps

Iters	Range		Point
8	7.074457224487564e-68	3.35181569450666e-65	1.5653482556163336e-66
8	-1.5423755018950112e-54	-6.784788556987943e-59	-8.147957075904114e-55

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	55
1	50	55

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.3s	3285×	body	1280	valid
545.0ms	623×	body	2560	valid
420.0ms	1875×	body	640	valid
113.0ms	780×	body	320	valid
51.0ms	1090×	body	80	valid
33.0ms	347×	body	160	valid