Details

sample175.0ms

Algorithm

intervals

Results

84.0ms	118×	body	1280	valid
47.0ms	28×	body	2560	valid
24.0ms	51×	body	640	valid
5.0ms	19×	body	320	valid
3.0ms	15×	body	160	valid
2.0ms	25×	body	80	valid

simplify6.0ms

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: 40.5b

localize9.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (tan (+ x eps)) (tan x))
2.5b	(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))
3.0ms	(tan (+ x eps))

series140.0ms

Counts

2 → 6

Calls

2 calls:

85.0ms	(- (tan (+ x eps)) (tan x))
55.0ms	(tan (+ x eps))

simplify77.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (22.0ms)

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

prune87.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 17.6b

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))))
0.3b	(* (tan x) (tan eps))
3.6b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite63.0ms

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:

5.0ms	(+ (tan x) (tan eps))
11.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
5.0ms	(* (tan x) (tan eps))
40.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series740.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(+ (tan x) (tan eps))
210.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
89.0ms	(* (tan x) (tan eps))
352.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify46.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	397	1050
1	1432	1005
2	5001	995

prune286.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 17.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
0.3b	(* (tan x) (tan eps))
0.3b	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
7.0b	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

123×	`times-frac`
104×	`*-un-lft-identity`
83×	`add-sqr-sqrt`
67×	`add-cube-cbrt`
23×	`associate-/r*`
19×	`add-exp-log`
16×	`associate-/r/` `distribute-lft-out`
15×	`tan-quot`
13×	`add-cbrt-cube`
8×	`div-exp`
7×	`pow1` `div-inv`
6×	`associate-/l*` `add-log-exp`
5×	`flip3-+` `frac-add` `flip-+` `difference-of-squares`
4×	`cbrt-undiv`
3×	`associate-r` `associate-l`
2×	`rec-exp` `flip3--` `frac-2neg` `1-exp` `clear-num` `flip--` `associate-/l/` `distribute-lft-out--`
1×	`frac-times` `sub-neg` `pow-flip` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `*-commutative` `frac-sub` `cbrt-unprod` `inv-pow` `unswap-sqr`

Counts

4 → 178

Calls

4 calls:

10.0ms	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
5.0ms	(* (tan x) (tan eps))
13.0ms	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
83.0ms	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

series931.0ms

Counts

4 → 12

Calls

4 calls:

268.0ms	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
91.0ms	(* (tan x) (tan eps))
218.0ms	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
354.0ms	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

simplify83.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	703	2793
1	3290	2509
2	5001	2506

prune398.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 17.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan eps))
0.3b	(/ 1 (/ (- (pow 1 3) (pow (* (tan x) (tan eps)) 3)) (* (+ (* (* (tan x) (tan eps)) (+ (* (tan x) (tan eps)) 1)) 1) (+ (tan x) (tan eps)))))
0.3b	(pow (* (tan x) (tan eps)) 3)
7.0b	(- (/ 1 (/ (- (pow 1 3) (pow (* (tan x) (tan eps)) 3)) (* (+ (* (* (tan x) (tan eps)) (+ (* (tan x) (tan eps)) 1)) 1) (+ (tan x) (tan eps))))) (tan x))

rewrite542.0ms

Algorithm

rewrite-expression-head

Rules

173×	`times-frac`
106×	`add-sqr-sqrt`
81×	`*-un-lft-identity`
51×	`difference-of-squares`
49×	`add-cube-cbrt`
45×	`associate-/r/`
33×	`tan-quot` `associate-/r*` `sqr-pow`
30×	`add-exp-log`
28×	`flip3-+` `flip-+`
26×	`frac-times`
18×	`add-cbrt-cube`
17×	`unpow-prod-down` `cube-prod`
14×	`associate-*r/`
12×	`div-exp` `frac-add`
10×	`pow1` `associate-*l/` `distribute-lft-out--`
6×	`div-inv` `add-log-exp`
5×	`cbrt-undiv` `cube-mult` `prod-exp`
4×	`difference-cubes`
3×	`cube-div` `rec-exp` `pow-unpow` `1-exp` `associate-r` `associate-l` `cbrt-unprod` `associate-/l*`
2×	`pow-pow` `pow-prod-down` `pow-exp` `rem-cube-cbrt`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-flip` `frac-2neg` `diff-log` `unpow3` `clear-num` `*-commutative` `frac-sub` `flip--` `inv-pow` `unswap-sqr`

Counts

4 → 224

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
95.0ms	(/ 1 (/ (- (pow 1 3) (pow (* (tan x) (tan eps)) 3)) (* (+ (* (* (tan x) (tan eps)) (+ (* (tan x) (tan eps)) 1)) 1) (+ (tan x) (tan eps)))))
4.0ms	(pow (* (tan x) (tan eps)) 3)
425.0ms	(- (/ 1 (/ (- (pow 1 3) (pow (* (tan x) (tan eps)) 3)) (* (+ (* (* (tan x) (tan eps)) (+ (* (tan x) (tan eps)) 1)) 1) (+ (tan x) (tan eps))))) (tan x))

series2.2s

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (tan x) (tan eps))
488.0ms	(/ 1 (/ (- (pow 1 3) (pow (* (tan x) (tan eps)) 3)) (* (+ (* (* (tan x) (tan eps)) (+ (* (tan x) (tan eps)) 1)) 1) (+ (tan x) (tan eps)))))
124.0ms	(pow (* (tan x) (tan eps)) 3)
1.5s	(- (/ 1 (/ (- (pow 1 3) (pow (* (tan x) (tan eps)) 3)) (* (+ (* (* (tan x) (tan eps)) (+ (* (tan x) (tan eps)) 1)) 1) (+ (tan x) (tan eps))))) (tan x))

simplify84.0ms

Algorithm

egg-herbie

Counts

236 → 236

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1483	6238
1	5002	5708

prune552.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 17.4b

regimes199.0ms

Accuracy

80.2% (1.4b remaining)

Error of 15.7b against oracle of 14.3b and baseline of 21.6b

bsearch234.0ms

Steps

Iters	Range		Point
11	3.909725892130977e-164	8.040031359683334e-132	7.892404413523218e-132
8	-3.398414508756592e-20	-5.474676979875971e-25	-7.404911580597804e-25

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	72
1	64	72

end0.0ms

sample5.0s

Algorithm

intervals

Results

2.5s	3207×	body	1280	valid
1.1s	668×	body	2560	valid
781.0ms	1848×	body	640	valid
219.0ms	777×	body	320	valid
104.0ms	1128×	body	80	valid
69.0ms	372×	body	160	valid