Details

sample92.0ms

Algorithm

intervals

Results

45.0ms	111×	body	1280	valid
20.0ms	22×	body	2560	valid
13.0ms	61×	body	640	valid
4.0ms	25×	body	320	valid
1.0ms	31×	body	80	valid
1.0ms	6×	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: 37.8b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.2b	(- (tan (+ x eps)) (tan x))
3.1b	(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:

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

series134.0ms

Counts

2 → 6

Calls

2 calls:

86.0ms	(- (tan (+ x eps)) (tan x))
48.0ms	(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

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: 14.5b

Counts

32 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1 (* (tan x) (tan eps)))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
1.9b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite24.0ms

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

series616.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(- 1 (* (tan x) (tan eps)))
87.0ms	(+ (tan x) (tan eps))
86.0ms	(* (tan x) (tan eps))
339.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify128.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (35.0ms)

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

prune211.0ms

Filtered

74 candidates to 56 candidates (75.7%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	60	14	74
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	65	17	82

Merged error: 14.4b

Counts

82 → 17

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.2b	(/ (* (sin x) (tan eps)) (cos x))
0.2b	(* (sin x) (tan eps))
1.9b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

4.0ms	(+ (tan x) (tan eps))
6.0ms	(/ (* (sin x) (tan eps)) (cos x))
5.0ms	(* (sin x) (tan eps))
17.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

series623.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(+ (tan x) (tan eps))
98.0ms	(/ (* (sin x) (tan eps)) (cos x))
76.0ms	(* (sin x) (tan eps))
362.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

simplify45.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	389	785
1	1406	711
2	5001	699

prune241.0ms

Filtered

82 candidates to 61 candidates (74.4%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	79	3	82
Fresh	2	14	16
Picked	0	1	1
Done	0	0	0
Total	81	18	99

Merged error: 14.4b

Counts

99 → 18

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.3b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
1.9b	(- (/ (+ (tan x) (tan eps)) (/ (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (+ 1 (* (tan x) (tan eps))))) (tan x))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
41×	`tan-quot`
21×	`add-sqr-sqrt`
20×	`add-exp-log` `add-cbrt-cube`
19×	`frac-times` `pow-prod-down`
13×	`associate-r/` `associate-l/`
10×	`*-un-lft-identity` `prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt`
7×	`associate-r` `associate-l`
6×	`add-log-exp`
4×	`pow-sqr` `pow-prod-up`
3×	`times-frac` `*-commutative` `difference-of-squares`
2×	`pow-plus` `unswap-sqr`
1×	`pow2` `sub-neg` `flip3--` `diff-log` `swap-sqr` `frac-sub` `flip--` `distribute-lft-out--`

Counts

4 → 108

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
6.0ms	(* (tan x) (tan eps))
11.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
35.0ms	(- (/ (+ (tan x) (tan eps)) (/ (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (+ 1 (* (tan x) (tan eps))))) (tan x))

series1.2s

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (tan x) (tan eps))
87.0ms	(* (tan x) (tan eps))
112.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
869.0ms	(- (/ (+ (tan x) (tan eps)) (/ (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (+ 1 (* (tan x) (tan eps))))) (tan x))

simplify60.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	487	1344
1	2155	1184
2	5002	1111

prune238.0ms

Filtered

120 candidates to 73 candidates (60.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	117	3	120
Fresh	2	14	16
Picked	1	0	1
Done	1	0	1
Total	121	17	138

Merged error: 14.4b

Counts

138 → 17

regimes183.0ms

Accuracy

89.1% (0.8b remaining)

Error of 15.2b against oracle of 14.4b and baseline of 21.7b

bsearch109.0ms

Steps

Iters	Range		Point
8	2.255896759856785e-46	1.8629716801109002e-42	1.2660897646861507e-42
7	-6.796277293523942e-28	-1.1064465835999565e-29	-1.4477006368600308e-29

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	62
1	53	62

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.3s	3281×	body	1280	valid
547.0ms	622×	body	2560	valid
418.0ms	1859×	body	640	valid
123.0ms	834×	body	320	valid
50.0ms	1057×	body	80	valid
34.0ms	347×	body	160	valid

Details

sample92.0ms

simplify5.0ms

prune2.0ms

localize9.0ms

rewrite11.0ms

series134.0ms

simplify79.0ms

prune78.0ms

localize11.0ms

rewrite24.0ms

series616.0ms

simplify128.0ms

prune211.0ms

localize17.0ms

rewrite34.0ms

series623.0ms

simplify45.0ms

prune241.0ms

localize16.0ms

rewrite60.0ms

series1.2s

simplify60.0ms

prune238.0ms

regimes183.0ms

bsearch109.0ms

simplify2.0ms

end0.0ms

sample2.7s

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