Details

sample86.0ms

Algorithm

intervals

Results

39.0ms	100×	body	1280	valid
20.0ms	23×	body	2560	valid
12.0ms	58×	body	640	valid
3.0ms	24×	body	320	valid
2.0ms	21×	body	160	valid
1.0ms	30×	body	80	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: 40.0b

Counts

2 → 1

localize11.0ms

Local error

Found 2 expressions with local error:

2.7b	(- (tan (+ x eps)) (tan x))
3.9b	(tan (+ x eps))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`tan-quot` `add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `tan-sum` `frac-sub` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 41

Calls

2 calls:

7.0ms	(- (tan (+ x eps)) (tan x))
4.0ms	(tan (+ x eps))

series139.0ms

Counts

2 → 6

Calls

2 calls:

91.0ms	(- (tan (+ x eps)) (tan x))
47.0ms	(tan (+ x eps))

simplify74.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	192	420
1	538	319
2	2593	310
3	5001	255

prune117.0ms

Filtered

47 candidates to 33 candidates (70.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	37	10	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	10	48

Merged error: 16.7b

Counts

48 → 10

localize11.0ms

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))
4.1b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

102×	`*-un-lft-identity`
73×	`add-sqr-sqrt`
66×	`add-cube-cbrt`
61×	`times-frac`
54×	`prod-diff`
18×	`fma-neg`
17×	`distribute-lft-out`
10×	`associate-/r/`
9×	`tan-quot`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1` `flip3--` `flip--`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-def` `associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`flip3-+` `frac-add` `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` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 169

Calls

4 calls:

12.0ms	(/ (+ (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))

series739.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
90.0ms	(+ (tan x) (tan eps))
90.0ms	(* (tan x) (tan eps))
353.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify71.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	559	2915
1	2054	2366
2	5001	2345

prune357.0ms

Filtered

181 candidates to 110 candidates (60.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	169	12	181
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	174	17	191

Merged error: 16.6b

Counts

191 → 17

localize12.0ms

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))
4.1b	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`add-cube-cbrt`
10×	`add-exp-log`
9×	`times-frac`
8×	`add-cbrt-cube`
7×	`pow1`
6×	`tan-quot` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `associate-r` `associate-l` `associate-/r` `associate-/l`
2×	`div-exp` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `frac-times` `rec-exp` `flip3--` `pow-flip` `frac-2neg` `flip3-+` `1-exp` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `clear-num` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `fma-udef` `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))
1.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

series764.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ 1 (- 1 (* (tan x) (tan eps))))
265.0ms	(+ (tan x) (tan eps))
89.0ms	(* (tan x) (tan eps))
283.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

simplify40.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	367	754
1	1426	679
2	5001	679

prune249.0ms

Filtered

98 candidates to 70 candidates (71.4%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	94	4	98
Fresh	3	13	16
Picked	1	0	1
Done	0	0	0
Total	98	17	115

Merged error: 16.6b

Counts

115 → 17

localize16.0ms

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)))
4.1b	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
40×	`tan-quot`
20×	`add-exp-log` `add-cbrt-cube`
19×	`frac-times` `pow-prod-down`
13×	`associate-r/` `associate-l/`
12×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `pow-sqr` `pow-prod-up` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`pow-plus` `unswap-sqr`
1×	`pow2` `swap-sqr` `fma-udef`

Counts

4 → 107

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
10.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
1.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

series856.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(* (tan x) (tan eps))
89.0ms	(* (tan x) (tan eps))
114.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
564.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

simplify55.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	432	1098
1	1952	917
2	5001	864

prune261.0ms

Filtered

119 candidates to 74 candidates (62.2%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	16	16
Picked	0	1	1
Done	0	0	0
Total	119	17	136

Merged error: 16.6b

Counts

136 → 17

regimes191.0ms

Accuracy

87.1% (1.0b remaining)

Error of 14.7b against oracle of 13.7b and baseline of 21.4b

bsearch73.0ms

Steps

Iters	Range		Point
3	2.5991813791586212e-73	3.261569682107855e-73	3.205750517362607e-73
7	-7.384108184269461e-38	-3.3964121804544714e-40	-6.332442401033257e-40

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	42
1	41	42

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.3s	3331×	body	1280	valid
526.0ms	608×	body	2560	valid
406.0ms	1878×	body	640	valid
104.0ms	738×	body	320	valid
49.0ms	1100×	body	80	valid
32.0ms	345×	body	160	valid