Details

sample78.0ms

Algorithm

intervals

Results

40.0ms	112×	body	1280	valid
13.0ms	16×	body	2560	valid
11.0ms	58×	body	640	valid
3.0ms	27×	body	320	valid
1.0ms	35×	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: 36.2b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.5b	(- (tan (+ x eps)) (tan x))
4.0b	(tan (+ x eps))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

5×	`tan-quot`
4×	`tan-sum`
3×	`frac-sub`
2×	`+-commutative`
1×	`sub-neg` `flip3--` `flip--`

Counts

2 → 10

Calls

2 calls:

4.0ms	(- (tan (+ x eps)) (tan x))
3.0ms	(tan (+ x eps))

series137.0ms

Counts

2 → 6

Calls

2 calls:

86.0ms	(- (tan (+ x eps)) (tan x))
50.0ms	(tan (+ x eps))

simplify75.0ms

Algorithm

egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 3 (21.0ms)

Iter	Nodes	Cost
0	129	138
1	284	136
2	769	136
3	2484	134
4	5002	134

prune35.0ms

Filtered

16 candidates to 10 candidates (62.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	12	4	16
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	13	4	17

Merged error: 14.9b

Counts

17 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x))))
0.2b	(+ (tan x) (tan eps))
0.2b	(* (tan eps) (tan x))
1.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x)))) (tan x))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

16×	`tan-quot`
6×	`frac-sub` `associate-/l/`
4×	`associate-/r/`
3×	`flip3--` `flip3-+` `fma-neg` `frac-add` `flip--` `flip-+`
2×	`frac-2neg` `clear-num` `div-inv`
1×	`+-commutative` `frac-times` `sub-neg` `associate-r/` `associate-l/` `*-commutative`

Counts

4 → 29

Calls

4 calls:

6.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x))))
3.0ms	(+ (tan x) (tan eps))
3.0ms	(* (tan eps) (tan x))
9.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x)))) (tan x))

series875.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x))))
211.0ms	(+ (tan x) (tan eps))
87.0ms	(* (tan eps) (tan x))
374.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x)))) (tan x))

simplify34.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	325	500
1	1162	494
2	5002	479

prune158.0ms

Filtered

41 candidates to 36 candidates (87.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	30	11	41
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	33	12	45

Merged error: 14.7b

Counts

45 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (tan eps) (sin x)) (cos x))
0.2b	(+ (tan x) (tan eps))
0.2b	(* (tan eps) (sin x))
1.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan eps) (sin x)) (cos x)))) (tan x))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

12×	`tan-quot`
6×	`frac-sub`
4×	`associate-/l/`
3×	`fma-neg`
2×	`flip3--` `frac-2neg` `flip3-+` `associate-l/` `frac-add` `clear-num` `associate-/r/` `-commutative` `flip--` `flip-+` `div-inv` `associate-/l*`
1×	`+-commutative` `sub-neg`

Counts

4 → 25

Calls

4 calls:

5.0ms	(/ (* (tan eps) (sin x)) (cos x))
3.0ms	(+ (tan x) (tan eps))
3.0ms	(* (tan eps) (sin x))
9.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan eps) (sin x)) (cos x)))) (tan x))

series605.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (* (tan eps) (sin x)) (cos x))
87.0ms	(+ (tan x) (tan eps))
67.0ms	(* (tan eps) (sin x))
361.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan eps) (sin x)) (cos x)))) (tan x))

simplify34.0ms

Algorithm

egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	322	462
1	1116	455
2	5002	438

prune148.0ms

Filtered

37 candidates to 30 candidates (81.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	29	8	37
Fresh	9	2	11
Picked	1	0	1
Done	0	0	0
Total	39	10	49

Merged error: 14.7b

Counts

49 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan eps) (sin x))
0.2b	(* (tan eps) (sin x))
0.3b	(* (/ (* (tan eps) (sin x)) (cos x)) (/ (* (tan eps) (sin x)) (cos x)))
1.4b	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (/ (* (tan eps) (sin x)) (cos x)) (/ (* (tan eps) (sin x)) (cos x))))) (+ 1 (/ (* (tan eps) (sin x)) (cos x))) (- (tan x)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

36×	`frac-times`
28×	`associate-/l*`
22×	`associate-*l/`
17×	`*-commutative`
16×	`tan-quot`
15×	`clear-num`
14×	`frac-2neg` `associate-/l/`
6×	`associate-*r/`
4×	`div-inv`
1×	`pow2` `swap-sqr` `associate-r` `associate-l` `un-div-inv` `fma-udef`

Counts

4 → 59

Calls

4 calls:

3.0ms	(* (tan eps) (sin x))
3.0ms	(* (tan eps) (sin x))
11.0ms	(* (/ (* (tan eps) (sin x)) (cos x)) (/ (* (tan eps) (sin x)) (cos x)))
1.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (/ (* (tan eps) (sin x)) (cos x)) (/ (* (tan eps) (sin x)) (cos x))))) (+ 1 (/ (* (tan eps) (sin x)) (cos x))) (- (tan x)))

series790.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (tan eps) (sin x))
62.0ms	(* (tan eps) (sin x))
112.0ms	(* (/ (* (tan eps) (sin x)) (cos x)) (/ (* (tan eps) (sin x)) (cos x)))
553.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (/ (* (tan eps) (sin x)) (cos x)) (/ (* (tan eps) (sin x)) (cos x))))) (+ 1 (/ (* (tan eps) (sin x)) (cos x))) (- (tan x)))

simplify52.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	441	742
1	2323	694
2	5001	690

prune221.0ms

Filtered

71 candidates to 41 candidates (57.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	72	9	81

Merged error: 14.7b

Counts

81 → 9

regimes192.0ms

Accuracy

85% (1.2b remaining)

Error of 15.1b against oracle of 14.0b and baseline of 21.7b

bsearch120.0ms

Steps

Iters	Range		Point
8	1.185487053096793e-108	9.185000414034106e-105	9.008897623605655e-105
9	-1.0196393039696783e-24	-9.763271116316594e-33	-2.0754543686162598e-29

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	53
1	61	53
2	62	53
3	62	53

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.3s	3361×	body	1280	valid
520.0ms	614×	body	2560	valid
374.0ms	1808×	body	640	valid
99.0ms	769×	body	320	valid
43.0ms	1093×	body	80	valid
31.0ms	355×	body	160	valid