Details

sample91.0ms

Algorithm

intervals

Results

32.0ms	88×	body	1280	valid
20.0ms	24×	body	2560	valid
18.0ms	61×	body	640	valid
4.0ms	30×	body	320	valid
2.0ms	40×	body	80	valid
1.0ms	13×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune4.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 35.6b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (tan (+ x eps)) (tan x))
4.1b	(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:

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

series160.0ms

Counts

2 → 6

Calls

2 calls:

100.0ms	(- (tan (+ x eps)) (tan x))
60.0ms	(tan (+ x eps))

simplify78.0ms

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

prune107.0ms

Filtered

31 candidates to 25 candidates (19.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	22	9	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	23	9	32

Merged error: 15.6b

Counts

32 → 9

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))
2.4b	(- (/ (+ (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 → 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))

series871.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(+ (tan x) (tan eps))
245.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
111.0ms	(* (tan x) (tan eps))
407.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify47.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	397	1050
1	1432	1005
2	5001	994

prune529.0ms

Filtered

98 candidates to 74 candidates (24.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	87	11	98
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	92	15	107

Merged error: 15.5b

Counts

107 → 15

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x))))
0.2b	(* (sin x) (tan eps))
0.2b	(/ (* (sin x) (tan eps)) (cos x))
2.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

10.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x))))
5.0ms	(* (sin x) (tan eps))
6.0ms	(/ (* (sin x) (tan eps)) (cos x))
18.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

series909.0ms

Counts

4 → 12

Calls

4 calls:

258.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x))))
92.0ms	(* (sin x) (tan eps))
124.0ms	(/ (* (sin x) (tan eps)) (cos x))
434.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

simplify57.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	500	1555
1	1945	1463
2	5001	1462

prune943.0ms

Filtered

120 candidates to 82 candidates (31.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	115	5	120
Fresh	4	10	14
Picked	1	0	1
Done	0	0	0
Total	120	15	135

Merged error: 15.5b

Counts

135 → 15

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.3b	(pow (* (tan x) (tan eps)) 3)
2.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 3)))) (tan x))
25.8b	(cbrt (pow (* (tan x) (tan eps)) 3))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
5.0ms	(pow (* (tan x) (tan eps)) 3)
23.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 3)))) (tan x))
4.0ms	(cbrt (pow (* (tan x) (tan eps)) 3))

series750.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(* (tan x) (tan eps))
137.0ms	(pow (* (tan x) (tan eps)) 3)
400.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 3)))) (tan x))
106.0ms	(cbrt (pow (* (tan x) (tan eps)) 3))

simplify53.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	384	787
1	1733	744
2	5002	743

prune547.0ms

Filtered

94 candidates to 66 candidates (29.8%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	94	15	109

Merged error: 15.5b

Counts

109 → 15

regimes220.0ms

Accuracy

87.5% (0.9b remaining)

Error of 15.4b against oracle of 14.4b and baseline of 21.8b

bsearch111.0ms

Steps

Iters	Range		Point
7	4.8914605440667675e-73	6.934968998500573e-71	6.6299322689363935e-71
8	-1.3983785225698383e-32	-6.5967515378205915e-37	-9.865923450018125e-33

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	36
1	43	36

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.3s	3312×	body	1280	valid
544.0ms	630×	body	2560	valid
391.0ms	1829×	body	640	valid
101.0ms	748×	body	320	valid
48.0ms	1136×	body	80	valid
32.0ms	345×	body	160	valid

Details

sample91.0ms

simplify4.0ms

prune4.0ms

localize8.0ms

rewrite11.0ms

series160.0ms

simplify78.0ms

prune107.0ms

localize11.0ms

rewrite30.0ms

series871.0ms

simplify47.0ms

prune529.0ms

localize21.0ms

rewrite41.0ms

series909.0ms

simplify57.0ms

prune943.0ms

localize14.0ms

rewrite39.0ms

series750.0ms

simplify53.0ms

prune547.0ms

regimes220.0ms

bsearch111.0ms

simplify1.0ms

end0.0ms

sample2.7s

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