Details

sample2.5s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 24.993896%

Results

39.0ms	104×	body	1280	valid
16.0ms	73×	body	640	valid
14.0ms	17×	body	2560	valid
2.0ms	15×	body	320	valid
1.0ms	32×	body	80	valid
1.0ms	15×	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

prune5.0ms

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: 37.1b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

1.4b	(- (tan (+ x eps)) (tan x))
4.2b	(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))

series44.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(- (tan (+ x eps)) (tan x))
17.0ms	(tan (+ x eps))

simplify82.0ms

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

prune65.0ms

Filtered

25 candidates to 31 candidates (-24.0%)

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: 17.9b

Counts

32 → 8

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))
2.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite34.0ms

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))
14.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series219.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
23.0ms	(+ (tan x) (tan eps))
24.0ms	(* (tan x) (tan eps))
109.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify48.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (38.0ms)

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

prune176.0ms

Filtered

74 candidates to 98 candidates (-32.4%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	85	13	98
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	89	17	106

Merged error: 17.8b

Counts

106 → 17

localize18.0ms

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)))
2.4b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
45×	`tan-quot`
21×	`frac-times`
20×	`add-exp-log` `add-cbrt-cube`
19×	`pow-prod-down`
15×	`associate-*r/`
14×	`associate-*l/`
12×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`frac-sub`
4×	`pow-sqr` `pow-prod-up`
3×	`*-commutative`
2×	`flip3-+` `pow-plus` `associate--l+` `flip-+` `unswap-sqr`
1×	`pow2` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `diff-log` `swap-sqr` `flip--`

Counts

4 → 110

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
11.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
12.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series433.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (tan x) (tan eps))
23.0ms	(* (tan x) (tan eps))
35.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
351.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify85.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	599	1352
1	3021	1220
2	5001	1220

prune186.0ms

Filtered

76 candidates to 122 candidates (-60.5%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	115	7	122
Fresh	5	11	16
Picked	1	0	1
Done	0	0	0
Total	121	18	139

Merged error: 17.8b

Counts

139 → 18

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.4b	(pow (* (tan x) (tan eps)) 6)
2.4b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 6)))) (+ 1 (* (tan x) (tan eps)))) (tan x))
15.2b	(cbrt (pow (* (tan x) (tan eps)) 6))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`tan-quot` `pow1` `add-exp-log`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-cbrt-cube` `add-log-exp`
5×	`cbrt-prod` `frac-sub`
3×	`frac-times` `pow-unpow` `associate-r/` `associate-r` `associate-l*`
2×	`unpow-prod-down` `pow-pow` `flip3-+` `pow-prod-down` `associate-*l/` `pow-exp` `prod-exp` `associate--l+` `flip-+` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `sub-neg` `flip3--` `distribute-lft-in` `pow1/3` `diff-log` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`

Counts

4 → 70

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
5.0ms	(pow (* (tan x) (tan eps)) 6)
16.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 6)))) (+ 1 (* (tan x) (tan eps)))) (tan x))
4.0ms	(cbrt (pow (* (tan x) (tan eps)) 6))

series451.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (tan x) (tan eps))
46.0ms	(pow (* (tan x) (tan eps)) 6)
346.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 6)))) (+ 1 (* (tan x) (tan eps)))) (tan x))
33.0ms	(cbrt (pow (* (tan x) (tan eps)) 6))

simplify75.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	586	1120
1	2642	1019
2	5001	1011

prune361.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	79	3	82
Fresh	3	14	17
Picked	1	0	1
Done	0	0	0
Total	83	17	100

Merged error: 17.8b

Counts

100 → 17

regimes225.0ms

Accuracy

87.1% (0.9b remaining)

Error of 16.0b against oracle of 15.1b and baseline of 22.1b

bsearch112.0ms

Steps

Iters	Range		Point
9	2.1593211035053825e-38	2.900356889188494e-31	1.6626953811672289e-37
9	-4.378614731320926e-61	-2.3207283139322119e-66	-1.5973706195668936e-61

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	73	100
1	77	100
2	84	100
3	88	100
4	94	100
5	100	100
6	100	100

end0.0ms

sample5.2s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 24.993896%

Results

1.3s	3271×	body	1280	valid
600.0ms	694×	body	2560	valid
387.0ms	1782×	body	640	valid
114.0ms	788×	body	320	valid
49.0ms	1099×	body	80	valid
35.0ms	366×	body	160	valid

Details

sample2.5s

simplify5.0ms

prune5.0ms

localize9.0ms

rewrite11.0ms

series44.0ms

simplify82.0ms

prune65.0ms

localize12.0ms

rewrite34.0ms

series219.0ms

simplify48.0ms

prune176.0ms

localize18.0ms

rewrite37.0ms

series433.0ms

simplify85.0ms

prune186.0ms

localize18.0ms

rewrite32.0ms

series451.0ms

simplify75.0ms

prune361.0ms

regimes225.0ms

bsearch112.0ms

simplify5.0ms

end0.0ms

sample5.2s

Profiling