Details

sample115.0ms

Algorithm

intervals

Results

46.0ms	100×	body	1280	valid
26.0ms	25×	body	2560	valid
16.0ms	64×	body	640	valid
4.0ms	7×	body	160	valid
4.0ms	23×	body	320	valid
2.0ms	37×	body	80	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune5.0ms

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: 43.0b

Counts

2 → 1

localize16.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (tan (+ x eps)) (tan x))
4.2b	(tan (+ x eps))

rewrite15.0ms

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:

8.0ms	(- (tan (+ x eps)) (tan x))
6.0ms	(tan (+ x eps))

series41.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(- (tan (+ x eps)) (tan x))
15.0ms	(tan (+ x eps))

simplify84.0ms

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

prune106.0ms

Filtered

31 candidates to 25 candidates (19.4%)

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: 18.3b

Counts

32 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.2b	(+ (tan x) (tan eps))
0.3b	(* (tan x) (tan eps))
3.3b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite29.0ms

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:

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

series192.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
22.0ms	(+ (tan x) (tan eps))
21.0ms	(* (tan x) (tan eps))
96.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify50.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (38.0ms)

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

prune170.0ms

Filtered

98 candidates to 74 candidates (24.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	85	13	98
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	91	15	106

Merged error: 18.1b

Counts

106 → 15

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (tan x) (tan eps))
0.2b	(* (sin x) (tan eps))
0.2b	(/ (* (sin x) (tan eps)) (cos x))
3.3b	(- (/ (+ (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))
5.0ms	(* (sin x) (tan eps))
5.0ms	(/ (* (sin x) (tan eps)) (cos x))
17.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

series160.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+ (tan x) (tan eps))
16.0ms	(* (sin x) (tan eps))
23.0ms	(/ (* (sin x) (tan eps)) (cos x))
101.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

simplify42.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (34.0ms)

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

prune117.0ms

Filtered

82 candidates to 60 candidates (26.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	1	13	14
Picked	1	0	1
Done	0	0	0
Total	83	14	97

Merged error: 18.1b

Counts

97 → 14

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x)))
0.3b	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
0.3b	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
3.3b	(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos eps)))) (/ (sin x) (cos x)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-exp-log` `add-cbrt-cube`
11×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`cbrt-undiv` `div-exp`
9×	`prod-exp` `cbrt-unprod` `add-log-exp`
6×	`add-cube-cbrt` `times-frac`
5×	`associate-/l*`
4×	`pow1` `associate-/r/`
3×	`frac-2neg` `clear-num` `associate-/r*` `frac-sub` `div-inv`
2×	`flip3--` `diff-log` `associate-*l/` `cos-mult` `flip--` `associate-/l/` `sin-mult` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `flip3-+` `frac-add` `associate--l+` `sum-log` `flip-+` `distribute-lft-out`

Counts

4 → 90

Calls

4 calls:

9.0ms	(/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x)))
7.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
7.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
22.0ms	(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos eps)))) (/ (sin x) (cos x)))

series180.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x)))
21.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
22.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
98.0ms	(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos eps)))) (/ (sin x) (cos x)))

simplify68.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	546	2112
1	2412	1871
2	5001	1871

prune111.0ms

Filtered

102 candidates to 70 candidates (31.4%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	93	9	102
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	98	18	116

Merged error: 18.1b

Counts

116 → 18

regimes278.0ms

Accuracy

86.8% (1.1b remaining)

Error of 17.1b against oracle of 16.0b and baseline of 24.6b

bsearch90.0ms

Steps

Iters	Range		Point
8	7.164138489181444e-33	2.6325156759024487e-28	1.063827061721738e-30
10	-1.1848157380742672e-82	-2.1887046899906262e-92	-1.1327425688405658e-82

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	58	58
1	58	58

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.3s	3264×	body	1280	valid
607.0ms	707×	body	2560	valid
375.0ms	1742×	body	640	valid
99.0ms	709×	body	320	valid
53.0ms	1265×	body	80	valid
29.0ms	313×	body	160	valid

Details

sample115.0ms

simplify8.0ms

prune5.0ms

localize16.0ms

rewrite15.0ms

series41.0ms

simplify84.0ms

prune106.0ms

localize11.0ms

rewrite29.0ms

series192.0ms

simplify50.0ms

prune170.0ms

localize17.0ms

rewrite34.0ms

series160.0ms

simplify42.0ms

prune117.0ms

localize24.0ms

rewrite48.0ms

series180.0ms

simplify68.0ms

prune111.0ms

regimes278.0ms

bsearch90.0ms

simplify2.0ms

end0.0ms

sample2.7s

Profiling