Details

sample147.0ms

Algorithm

intervals

Results

69.0ms	110×	body	1280	valid
40.0ms	28×	body	2560	valid
15.0ms	40×	body	640	valid
5.0ms	21×	body	320	valid
3.0ms	48×	body	80	valid
2.0ms	9×	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: 32.5b

Counts

2 → 1

localize12.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (tan (+ x eps)) (tan x))
2.4b	(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))

series136.0ms

Counts

2 → 6

Calls

2 calls:

89.0ms	(- (tan (+ x eps)) (tan x))
47.0ms	(tan (+ x eps))

simplify81.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (24.0ms)

Iter	Nodes	Cost
0	134	211
1	295	202
2	757	200
3	2482	199
4	5001	199

prune79.0ms

Filtered

31 candidates to 25 candidates (80.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	25	6	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	26	6	32

Merged error: 15.7b

Counts

32 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1 (* (tan x) (tan eps)))
0.1b	(+ (tan x) (tan eps))
0.3b	(* (tan x) (tan eps))
2.2b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite25.0ms

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

series632.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(- 1 (* (tan x) (tan eps)))
90.0ms	(+ (tan x) (tan eps))
89.0ms	(* (tan x) (tan eps))
349.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify125.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (32.0ms)

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

prune205.0ms

Filtered

74 candidates to 56 candidates (75.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	64	10	74
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	68	12	80

Merged error: 15.6b

Counts

80 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (* (tan x) (tan eps)))
0.3b	(* (tan x) (tan eps))
2.2b	(- (/ (+ (tan x) (tan eps)) (- 1 (log (exp (* (tan x) (tan eps)))))) (tan x))
2.8b	(log (exp (* (tan x) (tan eps))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-log-exp`
7×	`pow1` `add-cube-cbrt`
6×	`add-exp-log` `add-cbrt-cube`
5×	`tan-quot`
3×	`log-prod` `associate-r` `associate-l` `log-pow`
2×	`exp-prod` `exp-to-pow` `difference-of-squares`
1×	`frac-times` `sub-neg` `flip3--` `times-frac` `diff-log` `associate-r/` `rem-log-exp` `pow-prod-down` `associate-l/` `prod-exp` `*-commutative` `frac-sub` `flip--` `cbrt-unprod` `rem-exp-log` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 61

Calls

4 calls:

4.0ms	(exp (* (tan x) (tan eps)))
5.0ms	(* (tan x) (tan eps))
17.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (log (exp (* (tan x) (tan eps)))))) (tan x))
2.0ms	(log (exp (* (tan x) (tan eps))))

series651.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(exp (* (tan x) (tan eps)))
91.0ms	(* (tan x) (tan eps))
352.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (log (exp (* (tan x) (tan eps)))))) (tan x))
93.0ms	(log (exp (* (tan x) (tan eps))))

simplify77.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	271	685
1	808	627
2	2809	613
3	5001	613

prune200.0ms

Filtered

73 candidates to 55 candidates (75.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	73	12	85

Merged error: 15.6b

Counts

85 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.2b	(exp (- 1 (* (tan x) (tan eps))))
0.3b	(* (tan x) (tan eps))
2.2b	(- (/ (+ (tan x) (tan eps)) (log (exp (- 1 (* (tan x) (tan eps)))))) (tan x))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`*-un-lft-identity` `add-log-exp`
7×	`tan-quot` `add-cube-cbrt`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`exp-prod` `associate-r` `associate-l`
2×	`sub-neg` `diff-log` `exp-sum` `rem-exp-log` `difference-of-squares`
1×	`+-commutative` `frac-times` `flip3--` `flip3-+` `times-frac` `exp-diff` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `sum-log` `*-commutative` `frac-sub` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 65

Calls

4 calls:

6.0ms	(+ (tan x) (tan eps))
7.0ms	(exp (- 1 (* (tan x) (tan eps))))
5.0ms	(* (tan x) (tan eps))
16.0ms	(- (/ (+ (tan x) (tan eps)) (log (exp (- 1 (* (tan x) (tan eps)))))) (tan x))

series682.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(+ (tan x) (tan eps))
138.0ms	(exp (- 1 (* (tan x) (tan eps))))
91.0ms	(* (tan x) (tan eps))
361.0ms	(- (/ (+ (tan x) (tan eps)) (log (exp (- 1 (* (tan x) (tan eps)))))) (tan x))

simplify101.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	345	719
1	1088	666
2	3871	654
3	5001	654

prune197.0ms

Filtered

77 candidates to 59 candidates (76.6%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	77	12	89

Merged error: 15.6b

Counts

89 → 12

regimes114.0ms

Accuracy

75.1% (1.8b remaining)

Error of 15.9b against oracle of 14.1b and baseline of 21.4b

bsearch128.0ms

Steps

Iters	Range		Point
8	9.0699185804222e-63	4.453774208921603e-58	1.203511472582379e-60
8	-4.090212744229217e-170	-1.3798267575409003e-173	-4.01563370897399e-170

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	28
1	35	28

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.3s	3309×	body	1280	valid
560.0ms	645×	body	2560	valid
392.0ms	1846×	body	640	valid
112.0ms	742×	body	320	valid
48.0ms	1106×	body	80	valid
34.0ms	352×	body	160	valid

Details

sample147.0ms

simplify5.0ms

prune2.0ms

localize12.0ms

rewrite11.0ms

series136.0ms

simplify81.0ms

prune79.0ms

localize15.0ms

rewrite25.0ms

series632.0ms

simplify125.0ms

prune205.0ms

localize18.0ms

rewrite30.0ms

series651.0ms

simplify77.0ms

prune200.0ms

localize15.0ms

rewrite36.0ms

series682.0ms

simplify101.0ms

prune197.0ms

regimes114.0ms

bsearch128.0ms

simplify1.0ms

end0.0ms

sample2.6s

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