Details

sample157.0ms

Algorithm

intervals

Results

83.0ms	113×	body	1280	valid
29.0ms	59×	body	640	valid
22.0ms	13×	body	2560	valid
7.0ms	23×	body	320	valid
3.0ms	35×	body	80	valid
3.0ms	13×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.4b

localize10.0ms

Local error

Found 2 expressions with local error:

1.8b	(- (tan (+ x eps)) (tan x))
3.5b	(tan (+ x eps))

rewrite31.0ms

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:

24.0ms	(- (tan (+ x eps)) (tan x))
7.0ms	(tan (+ x eps))

series135.0ms

Counts

2 → 6

Calls

2 calls:

86.0ms	(- (tan (+ x eps)) (tan x))
49.0ms	(tan (+ x eps))

simplify72.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (68.0ms)

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

prune112.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 12.5b

localize12.0ms

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))))
0.3b	(* (tan x) (tan eps))
2.8b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite160.0ms

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:

10.0ms	(+ (tan x) (tan eps))
29.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
15.0ms	(* (tan x) (tan eps))
99.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series725.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(+ (tan x) (tan eps))
205.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
88.0ms	(* (tan x) (tan eps))
339.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify75.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (54.0ms)

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

prune431.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 12.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps))))
0.2b	(/ (* (tan x) (sin eps)) (cos eps))
0.2b	(* (tan x) (sin eps))
2.8b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

rewrite270.0ms

Algorithm

rewrite-expression-head

Rules

221×	`*-un-lft-identity`
164×	`add-sqr-sqrt`
124×	`times-frac`
94×	`add-cube-cbrt`
90×	`prod-diff`
44×	`difference-of-squares`
31×	`distribute-lft-out`
30×	`fma-neg`
22×	`distribute-lft-out--`
13×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
6×	`pow1` `flip3--` `flip--` `div-inv` `add-log-exp`
5×	`tan-quot` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l/`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l`
2×	`frac-2neg` `associate-*l/` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `flip3-+` `diff-log` `pow-prod-down` `frac-add` `*-commutative` `frac-sub` `flip-+` `unswap-sqr`

Counts

4 → 236

Calls

4 calls:

43.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps))))
15.0ms	(/ (* (tan x) (sin eps)) (cos eps))
13.0ms	(* (tan x) (sin eps))
185.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

series701.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps))))
90.0ms	(/ (* (tan x) (sin eps)) (cos eps))
61.0ms	(* (tan x) (sin eps))
345.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

simplify94.0ms

Algorithm

egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	697	4961
1	2736	4039
2	5002	4000

prune589.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.3b

localize20.0ms

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))
2.8b	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (- (tan x)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-exp-log` `add-sqr-sqrt` `*-un-lft-identity` `add-cbrt-cube`
9×	`add-cube-cbrt`
6×	`pow1` `add-log-exp`
4×	`tan-quot` `expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `times-frac` `associate-r` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod`
1×	`+-commutative` `frac-2neg` `flip3-+` `pow-prod-down` `frac-add` `clear-num` `sum-log` `-commutative` `flip-+` `fma-udef` `div-inv` `associate-/l/` `distribute-lft-out` `associate-/l` `unswap-sqr`

Counts

4 → 73

Calls

4 calls:

9.0ms	(+ (tan x) (tan eps))
15.0ms	(/ (* (tan x) (sin eps)) (cos eps))
16.0ms	(* (tan x) (sin eps))
0.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (- (tan x)))

series520.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(+ (tan x) (tan eps))
92.0ms	(/ (* (tan x) (sin eps)) (cos eps))
65.0ms	(* (tan x) (sin eps))
280.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (- (tan x)))

simplify52.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	350	661
1	1333	582
2	5001	581

prune285.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.3b

regimes192.0ms

Accuracy

87.6% (0.8b remaining)

Error of 15.5b against oracle of 14.7b and baseline of 21.5b

bsearch161.0ms

Steps

Iters	Range		Point
8	2.9004987402572773e-24	2.15302222000921e-20	2.0327729790594208e-23
8	-8.778595808142904e-29	-1.627781759631071e-31	-3.2842562690359854e-29

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	28
1	36	28

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.7s	3442×	body	1280	valid
1.1s	648×	body	2560	valid
791.0ms	1742×	body	640	valid
217.0ms	755×	body	320	valid
109.0ms	1081×	body	80	valid
69.0ms	332×	body	160	valid