Details

sample88.0ms

Algorithm

intervals

Results

45.0ms	116×	body	1280	valid
16.0ms	72×	body	640	valid
13.0ms	15×	body	2560	valid
2.0ms	16×	body	320	valid
1.0ms	30×	body	80	valid
1.0ms	7×	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: 37.2b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.6b	(- (tan (+ x eps)) (tan x))
2.9b	(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))

series146.0ms

Counts

2 → 6

Calls

2 calls:

92.0ms	(- (tan (+ x eps)) (tan x))
54.0ms	(tan (+ x eps))

simplify81.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (24.0ms)

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

prune83.0ms

Filtered

31 candidates to 25 candidates (80.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	24	7	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	25	7	32

Merged error: 14.8b

Counts

32 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
1.7b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite35.0ms

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:

8.0ms	(/ (+ (tan x) (tan eps)) (- 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))

series764.0ms

Counts

4 → 12

Calls

4 calls:

215.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
95.0ms	(+ (tan x) (tan eps))
94.0ms	(* (tan x) (tan eps))
359.0ms	(- (/ (+ (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	995

prune252.0ms

Filtered

98 candidates to 74 candidates (75.5%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	84	14	98
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	88	17	105

Merged error: 14.8b

Counts

105 → 17

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.1b	(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
0.2b	(* (tan x) (tan eps))
1.7b	(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
22×	`tan-quot`
19×	`*-un-lft-identity`
18×	`associate-r`
15×	`add-exp-log`
14×	`add-cube-cbrt`
11×	`times-frac` `add-cbrt-cube`
8×	`pow1` `frac-sub` `add-log-exp`
7×	`frac-times` `associate-l` `associate-*l/`
5×	`flip3-+` `frac-add` `prod-exp` `flip-+`
4×	`unswap-sqr`
3×	`associate-*r/` `cbrt-unprod`
2×	`flip3--` `div-exp` `pow-prod-down` `associate-/r/` `un-div-inv` `*-commutative` `flip--` `distribute-lft-out`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rec-exp` `diff-log` `1-exp` `sum-log` `div-inv`

Counts

4 → 99

Calls

4 calls:

4.0ms	(+ (tan x) (tan eps))
13.0ms	(* (+ (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))

series763.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(+ (tan x) (tan eps))
216.0ms	(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
93.0ms	(* (tan x) (tan eps))
361.0ms	(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

simplify66.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	561	1286
1	2547	1185
2	5001	1184

prune284.0ms

Filtered

111 candidates to 82 candidates (73.9%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	107	4	111
Fresh	2	14	16
Picked	1	0	1
Done	0	0	0
Total	110	18	128

Merged error: 14.7b

Counts

128 → 18

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.3b	(pow (* (tan x) (tan eps)) 3)
1.7b	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 3)))) (tan x))
23.9b	(cbrt (pow (* (tan x) (tan eps)) 3))

rewrite43.0ms

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)
26.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 3)))) (tan x))
4.0ms	(cbrt (pow (* (tan x) (tan eps)) 3))

series691.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (tan x) (tan eps))
128.0ms	(pow (* (tan x) (tan eps)) 3)
371.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 3)))) (tan x))
96.0ms	(cbrt (pow (* (tan x) (tan eps)) 3))

simplify55.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (46.0ms)

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

prune221.0ms

Filtered

94 candidates to 66 candidates (70.2%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	0	17	17
Picked	0	1	1
Done	0	0	0
Total	93	19	112

Merged error: 14.7b

Counts

112 → 19

regimes186.0ms

Accuracy

83.7% (1.2b remaining)

Error of 15.3b against oracle of 14.2b and baseline of 21.2b

bsearch143.0ms

Steps

Iters	Range		Point
10	1.601655691670321e-121	8.465412832341177e-111	8.349705234817486e-111
7	-8.55212409334588e-51	-3.3886585713584866e-52	-5.1774237133732126e-51

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	43
1	49	43

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.4s	3327×	body	1280	valid
513.0ms	575×	body	2560	valid
436.0ms	1859×	body	640	valid
116.0ms	765×	body	320	valid
55.0ms	1114×	body	80	valid
38.0ms	360×	body	160	valid

Details

sample88.0ms

simplify5.0ms

prune2.0ms

localize9.0ms

rewrite11.0ms

series146.0ms

simplify81.0ms

prune83.0ms

localize12.0ms

rewrite35.0ms

series764.0ms

simplify47.0ms

prune252.0ms

localize13.0ms

rewrite37.0ms

series763.0ms

simplify66.0ms

prune284.0ms

localize15.0ms

rewrite43.0ms

series691.0ms

simplify55.0ms

prune221.0ms

regimes186.0ms

bsearch143.0ms

simplify2.0ms

end0.0ms

sample2.7s

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