Details

sample157.0ms

Algorithm

intervals

Results

81.0ms	111×	body	1280	valid
32.0ms	19×	body	2560	valid
22.0ms	56×	body	640	valid
5.0ms	19×	body	320	valid
3.0ms	39×	body	80	valid
2.0ms	12×	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: 34.3b

localize9.0ms

Local error

Found 2 expressions with local error:

0.4b	(- (tan (+ x eps)) (tan x))
3.7b	(tan (+ x eps))

rewrite24.0ms

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:

16.0ms	(- (tan (+ x eps)) (tan x))
7.0ms	(tan (+ x eps))

series150.0ms

Counts

2 → 6

Calls

2 calls:

92.0ms	(- (tan (+ x eps)) (tan x))
58.0ms	(tan (+ x eps))

simplify79.0ms

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

prune85.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.3b

localize14.0ms

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))
1.5b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite130.0ms

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:

28.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
8.0ms	(+ (tan x) (tan eps))
15.0ms	(* (tan x) (tan eps))
77.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series773.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
94.0ms	(+ (tan x) (tan eps))
94.0ms	(* (tan x) (tan eps))
368.0ms	(- (/ (+ (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

prune283.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 11.1b

localize14.0ms

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)))
1.5b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
45×	`tan-quot`
21×	`frac-times`
20×	`add-exp-log` `add-cbrt-cube`
19×	`pow-prod-down`
15×	`associate-*r/`
14×	`associate-*l/`
12×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`frac-sub`
4×	`pow-sqr` `pow-prod-up`
3×	`*-commutative`
2×	`flip3-+` `pow-plus` `associate--l+` `flip-+` `unswap-sqr`
1×	`pow2` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `diff-log` `swap-sqr` `flip--`

Counts

4 → 110

Calls

4 calls:

14.0ms	(* (tan x) (tan eps))
15.0ms	(* (tan x) (tan eps))
67.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
22.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series1.3s

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (tan x) (tan eps))
91.0ms	(* (tan x) (tan eps))
119.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
948.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify80.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	599	1358
1	3021	1222
2	5001	1222

prune328.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 11.1b

localize21.0ms

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)) (/ (* (sin x) (tan eps)) (cos x)))
1.5b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (/ (* (sin x) (tan eps)) (cos x))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-exp-log` `add-cbrt-cube`
21×	`tan-quot`
14×	`add-sqr-sqrt`
13×	`pow1` `associate-r` `prod-exp` `cbrt-unprod`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`frac-times`
8×	`associate-*l/`
7×	`associate-r/` `associate-l*`
6×	`add-log-exp`
5×	`pow-prod-down` `frac-sub`
4×	`cbrt-undiv` `div-exp`
3×	`times-frac` `*-commutative`
2×	`flip3-+` `associate--l+` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `diff-log` `flip--` `div-inv`

Counts

4 → 98

Calls

4 calls:

14.0ms	(* (tan x) (tan eps))
14.0ms	(* (tan x) (tan eps))
47.0ms	(* (* (tan x) (tan eps)) (/ (* (sin x) (tan eps)) (cos x)))
22.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (/ (* (sin x) (tan eps)) (cos x))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series1.4s

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (tan x) (tan eps))
94.0ms	(* (tan x) (tan eps))
165.0ms	(* (* (tan x) (tan eps)) (/ (* (sin x) (tan eps)) (cos x)))
1.1s	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (/ (* (sin x) (tan eps)) (cos x))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify88.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	683	1550
1	3689	1361
2	5001	1361

prune357.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 11.1b

regimes137.0ms

Accuracy

90.2% (0.7b remaining)

Error of 14.8b against oracle of 14.0b and baseline of 21.4b

bsearch167.0ms

Steps

Iters	Range		Point
9	4.037825100464093e-40	2.3369147687632714e-33	1.4834720524637052e-33
9	-3.0281572613723123e-41	-1.45570997499063e-47	-2.698740626985669e-41

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	50
1	63	50
2	63	50

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.4s	3293×	body	1280	valid
1.0s	615×	body	2560	valid
780.0ms	1875×	body	640	valid
197.0ms	770×	body	320	valid
92.0ms	1089×	body	80	valid
62.0ms	358×	body	160	valid