Details

analyze962.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.2%	0.1%	6
21.9%	78%	0.1%	7
23.4%	76.5%	0.1%	8
24.2%	75.7%	0.1%	9
24.6%	75.3%	0.1%	10
24.8%	75.1%	0.1%	11
24.9%	75%	0.1%	12
24.9%	75%	0.1%	13
25%	75%	0.1%	14

sample447.0ms

Algorithm

intervals

Results

37.0ms	104×	body	1280	valid
18.0ms	21×	body	2560	valid
11.0ms	58×	body	640	valid
3.0ms	24×	body	320	valid
2.0ms	41×	body	80	valid
1.0ms	8×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune3.0ms

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: 36.8b

Counts

2 → 1

localize109.0ms

Local error

Found 2 expressions with local error:

14.8b	(tan (+ x eps))
21.9b	(- (tan (+ x eps)) (tan x))

rewrite10.0ms

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 → 24

Calls

2 calls:

3.0ms	(tan (+ x eps))
6.0ms	(- (tan (+ x eps)) (tan x))

series44.0ms

Counts

2 → 6

Calls

2 calls:

15.0ms	(tan (+ x eps))
29.0ms	(- (tan (+ x eps)) (tan x))

simplify46.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4924	332
1	4924	332

prune69.0ms

Filtered

25 candidates to 30 candidates (-20.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	22	8	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	23	8	31

Merged error: 13.6b

Counts

31 → 8

localize141.0ms

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))
21.9b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite31.0ms

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 → 85

Calls

4 calls:

8.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
4.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
12.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series212.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
22.0ms	(+ (tan x) (tan eps))
24.0ms	(* (tan x) (tan eps))
105.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify48.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5109	1560

prune190.0ms

Filtered

75 candidates to 97 candidates (-29.3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	84	13	97
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	89	16	105

Merged error: 13.5b

Counts

105 → 16

localize200.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.2b	(/ (* (tan x) (sin eps)) (cos eps))
0.2b	(* (tan x) (sin eps))
21.9b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

rewrite33.0ms

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` `div-exp` `associate-*l/` `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 → 69

Calls

4 calls:

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

series171.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(+ (tan x) (tan eps))
25.0ms	(/ (* (tan x) (sin eps)) (cos eps))
16.0ms	(* (tan x) (sin eps))
108.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

simplify59.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4943	1093
1	4943	1093

prune140.0ms

Filtered

64 candidates to 81 candidates (-26.6%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	80	1	81
Fresh	1	14	15
Picked	0	1	1
Done	0	0	0
Total	81	16	97

Merged error: 13.5b

Counts

97 → 16

localize145.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
21.9b	(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

4.0ms	(/ 1 (- 1 (* (tan x) (tan eps))))
4.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
12.0ms	(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

series191.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ 1 (- 1 (* (tan x) (tan eps))))
24.0ms	(+ (tan x) (tan eps))
23.0ms	(* (tan x) (tan eps))
109.0ms	(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

simplify54.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5468	1478

prune140.0ms

Filtered

70 candidates to 98 candidates (-40.0%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	93	5	98
Fresh	4	10	14
Picked	0	1	1
Done	0	1	1
Total	97	17	114

Merged error: 13.4b

Counts

114 → 17

regimes259.0ms

Accuracy

86.2% (1.0b remaining)

Error of 15.4b against oracle of 14.3b and baseline of 21.7b

bsearch168.0ms

Steps

Iters	Range		Point
7	1.3864940151086299e-74	2.6892834944430032e-73	2.6174394417726606e-73
6	-6.766515725646146e-55	-5.892739767685502e-56	-6.583395804010651e-55

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	100	64
1	100	64

end0.0ms

sample10.2s

Algorithm

intervals

Results

1.2s	3280×	body	1280	valid
523.0ms	614×	body	2560	valid
393.0ms	1905×	body	640	valid
102.0ms	751×	body	320	valid
44.0ms	1092×	body	80	valid
33.0ms	358×	body	160	valid

Details

analyze962.0ms

sample447.0ms

simplify4.0ms

prune3.0ms

localize109.0ms

rewrite10.0ms

series44.0ms

simplify46.0ms

prune69.0ms

localize141.0ms

rewrite31.0ms

series212.0ms

simplify48.0ms

prune190.0ms

localize200.0ms

rewrite33.0ms

series171.0ms

simplify59.0ms

prune140.0ms

localize145.0ms

rewrite27.0ms

series191.0ms

simplify54.0ms

prune140.0ms

regimes259.0ms

bsearch168.0ms

simplify2.0ms

end0.0ms

sample10.2s

Profiling