Details

sample92.0ms

Algorithm

intervals

Results

46.0ms	111×	body	1280	valid
16.0ms	19×	body	2560	valid
12.0ms	59×	body	640	valid
3.0ms	23×	body	320	valid
1.0ms	16×	body	160	valid
1.0ms	28×	body	80	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune3.0ms

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: 39.5b

Counts

2 → 1

localize12.0ms

Local error

Found 2 expressions with local error:

1.9b	(- (tan (+ x eps)) (tan x))
4.1b	(tan (+ x eps))

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 → 25

Calls

2 calls:

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

series37.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(- (tan (+ x eps)) (tan x))
14.0ms	(tan (+ x eps))

simplify76.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (21.0ms)

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

prune63.0ms

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: 14.8b

Counts

32 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.2b	(* (tan x) (tan eps))
2.5b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite32.0ms

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:

4.0ms	(+ (tan x) (tan eps))
9.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
5.0ms	(* (tan x) (tan eps))
11.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series191.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+ (tan x) (tan eps))
54.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
20.0ms	(* (tan x) (tan eps))
97.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify43.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (33.0ms)

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

prune168.0ms

Filtered

98 candidates to 74 candidates (24.5%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	82	16	98
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	88	18	106

Merged error: 14.7b

Counts

106 → 18

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))
0.2b	(* (sin x) (sin eps))
0.2b	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
2.5b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

49×	`*-un-lft-identity`
40×	`add-sqr-sqrt`
26×	`times-frac`
20×	`add-exp-log` `add-cbrt-cube`
18×	`add-cube-cbrt`
12×	`difference-of-squares`
7×	`associate-/r*` `distribute-lft-out`
6×	`pow1` `distribute-lft-out--` `add-log-exp`
5×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `associate-/l*`
4×	`associate-/l/`
3×	`tan-quot` `associate-r` `associate-l` `associate-/r/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--` `div-inv` `sin-mult`
1×	`sub-neg` `flip3-+` `diff-log` `pow-prod-down` `frac-add` `cos-mult` `*-commutative` `frac-sub` `flip-+` `unswap-sqr`

Counts

4 → 109

Calls

4 calls:

10.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))
5.0ms	(* (sin x) (sin eps))
7.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
19.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

series177.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))
9.0ms	(* (sin x) (sin eps))
20.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
95.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

simplify63.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	536	1825
1	2373	1688
2	5001	1688

prune165.0ms

Filtered

121 candidates to 81 candidates (33.1%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	117	4	121
Fresh	2	15	17
Picked	1	0	1
Done	0	0	0
Total	120	19	139

Merged error: 14.7b

Counts

139 → 19

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.3b	(pow (* (tan x) (tan eps)) 3)
2.5b	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 3)))) (tan x))
26.3b	(cbrt (pow (* (tan x) (tan eps)) 3))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`tan-quot`
10×	`*-un-lft-identity`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`cbrt-prod` `add-cube-cbrt`
6×	`cube-div` `add-log-exp`
3×	`frac-times` `pow-unpow` `cbrt-div` `associate-r/` `associate-r` `associate-l` `associate-l/`
2×	`cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `difference-of-squares` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `times-frac` `pow1/3` `diff-log` `*-commutative` `frac-sub` `flip--` `rem-cbrt-cube` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
5.0ms	(pow (* (tan x) (tan eps)) 3)
24.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 3)))) (tan x))
4.0ms	(cbrt (pow (* (tan x) (tan eps)) 3))

series171.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (tan x) (tan eps))
35.0ms	(pow (* (tan x) (tan eps)) 3)
95.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 3)))) (tan x))
21.0ms	(cbrt (pow (* (tan x) (tan eps)) 3))

simplify50.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	384	787
1	1733	744
2	5002	743

prune110.0ms

Filtered

94 candidates to 66 candidates (29.8%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	18	18
Picked	0	1	1
Done	0	0	0
Total	94	19	113

Merged error: 14.7b

Counts

113 → 19

regimes236.0ms

Accuracy

83.7% (1.2b remaining)

Error of 15.5b against oracle of 14.3b and baseline of 21.5b

bsearch41.0ms

Steps

Iters	Range		Point
0	4.567299040530162e-110	4.6641958512618205e-110	4.615747445895991e-110
10	-5.946903100628194e-57	-1.1839762205027933e-67	-2.546786933082043e-58

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	16
1	34	16

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.3s	3294×	body	1280	valid
554.0ms	642×	body	2560	valid
400.0ms	1866×	body	640	valid
103.0ms	739×	body	320	valid
47.0ms	1125×	body	80	valid
31.0ms	334×	body	160	valid

Details

sample92.0ms

simplify4.0ms

prune3.0ms

localize12.0ms

rewrite10.0ms

series37.0ms

simplify76.0ms

prune63.0ms

localize11.0ms

rewrite32.0ms

series191.0ms

simplify43.0ms

prune168.0ms

localize21.0ms

rewrite45.0ms

series177.0ms

simplify63.0ms

prune165.0ms

localize14.0ms

rewrite39.0ms

series171.0ms

simplify50.0ms

prune110.0ms

regimes236.0ms

bsearch41.0ms

simplify1.0ms

end0.0ms

sample2.7s

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