Details

sample147.0ms

Algorithm

intervals

Results

66.0ms	95×	body	1280	valid
37.0ms	22×	body	2560	valid
23.0ms	58×	body	640	valid
6.0ms	25×	body	320	valid
3.0ms	18×	body	160	valid
3.0ms	38×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize13.0ms

Local error

Found 2 expressions with local error:

2.6b	(- (tan (+ x eps)) (tan x))
3.9b	(tan (+ x eps))

rewrite12.0ms

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))

series138.0ms

Counts

2 → 6

Calls

2 calls:

89.0ms	(- (tan (+ x eps)) (tan x))
48.0ms	(tan (+ x eps))

simplify80.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (23.0ms)

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

prune91.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.4b

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))
4.0b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite64.0ms

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:

13.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
3.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
40.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series755.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
92.0ms	(+ (tan x) (tan eps))
92.0ms	(* (tan x) (tan eps))
359.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify48.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (38.0ms)

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

prune295.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
0.2b	(* (tan x) (tan eps))
0.3b	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
7.1b	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

rewrite119.0ms

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:

15.0ms	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
5.0ms	(* (tan x) (tan eps))
10.0ms	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
81.0ms	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

series934.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
93.0ms	(* (tan x) (tan eps))
266.0ms	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
363.0ms	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

simplify83.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	703	2793
1	3294	2509
2	5001	2506

prune420.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(/ (- (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)
7.1b	(- (/ 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))

rewrite505.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
27×	`*-un-lft-identity` `difference-of-squares`
20×	`times-frac`
18×	`associate-/l*`
17×	`sqr-pow`
15×	`tan-quot`
14×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/r/`
9×	`pow1` `add-cube-cbrt` `unpow-prod-down` `cube-prod`
8×	`frac-times`
7×	`flip3-+` `flip-+`
6×	`distribute-lft-out--` `add-log-exp`
5×	`associate-*r/`
4×	`associate-*l/`
3×	`cube-div` `cube-mult` `pow-unpow` `associate-r` `associate-l` `frac-add` `prod-exp` `cbrt-unprod`
2×	`difference-cubes` `cbrt-undiv` `flip3--` `pow-pow` `div-exp` `pow-prod-down` `pow-exp` `flip--` `div-inv` `associate-/l/` `rem-cube-cbrt`
1×	`pow-to-exp` `sub-neg` `frac-2neg` `diff-log` `unpow3` `div-sub` `clear-num` `associate-/r` `-commutative` `frac-sub` `unswap-sqr`

Counts

4 → 129

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
68.0ms	(/ (- (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)
423.0ms	(- (/ 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))

series2.3s

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (tan x) (tan eps))
561.0ms	(/ (- (pow 1 3) (pow (* (tan x) (tan eps)) 3)) (* (+ (* (* (tan x) (tan eps)) (+ (* (tan x) (tan eps)) 1)) 1) (+ (tan x) (tan eps))))
126.0ms	(pow (* (tan x) (tan eps)) 3)
1.6s	(- (/ 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))

simplify50.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1029	3005
1	5002	2737

prune495.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

regimes108.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	114
1	63	114

end0.0ms

sample4.9s

Algorithm

intervals

Results

2.4s	3289×	body	1280	valid
1.2s	686×	body	2560	valid
761.0ms	1815×	body	640	valid
218.0ms	736×	body	320	valid
98.0ms	1115×	body	80	valid
64.0ms	359×	body	160	valid