Details

sample81.0ms

Algorithm

intervals

Results

37.0ms	103×	body	1280	valid
18.0ms	22×	body	2560	valid
11.0ms	51×	body	640	valid
4.0ms	26×	body	320	valid
2.0ms	39×	body	80	valid
1.0ms	15×	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: 36.2b

localize12.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (tan (+ x eps)) (tan x))
3.5b	(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:

6.0ms	(- (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))
49.0ms	(tan (+ x eps))

simplify78.0ms

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

prune93.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.4b

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))))
0.2b	(* (tan x) (tan eps))
1.8b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite32.0ms

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:

4.0ms	(+ (tan x) (tan eps))
8.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
5.0ms	(* (tan x) (tan eps))
12.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series947.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(+ (tan x) (tan eps))
410.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
91.0ms	(* (tan x) (tan eps))
356.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify45.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (36.0ms)

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

prune277.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 16.3b

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)))
1.8b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite36.0ms

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:

5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
11.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
12.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series1.2s

Counts

4 → 12

Calls

4 calls:

90.0ms	(* (tan x) (tan eps))
91.0ms	(* (tan x) (tan eps))
112.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
901.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify83.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	599	1352
1	3021	1220
2	5001	1220

prune354.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 16.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (* (tan x) (tan eps)))
0.3b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
1.8b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (log (exp (* (tan x) (tan eps)))))) (tan x))
2.4b	(log (exp (* (tan x) (tan eps))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

44×	`pow1`
37×	`tan-quot`
19×	`frac-times`
17×	`pow-prod-down`
16×	`add-exp-log` `add-cbrt-cube`
13×	`associate-*r/`
12×	`associate-*l/`
9×	`add-log-exp`
8×	`prod-exp` `cbrt-unprod`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `frac-sub`
4×	`pow-sqr` `pow-prod-up`
3×	`log-prod` `log-pow`
2×	`exp-prod` `exp-to-pow` `flip3-+` `pow-plus` `associate--l+` `flip-+`
1×	`pow2` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `diff-log` `swap-sqr` `rem-log-exp` `associate-r` `associate-l` `*-commutative` `flip--` `rem-exp-log`

Counts

4 → 92

Calls

4 calls:

3.0ms	(exp (* (tan x) (tan eps)))
11.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
13.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (log (exp (* (tan x) (tan eps)))))) (tan x))
2.0ms	(log (exp (* (tan x) (tan eps))))

series1.2s

Counts

4 → 12

Calls

4 calls:

122.0ms	(exp (* (tan x) (tan eps)))
110.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
893.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (log (exp (* (tan x) (tan eps)))))) (tan x))
96.0ms	(log (exp (* (tan x) (tan eps))))

simplify76.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	599	1410
1	2861	1191
2	5002	1189

prune272.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 16.2b

regimes159.0ms

Accuracy

77.1% (1.7b remaining)

Error of 15.9b against oracle of 14.2b and baseline of 21.4b

bsearch94.0ms

Steps

Iters	Range		Point
4	2.1678204836809376e-60	3.3511168341522894e-60	3.304095522341824e-60
7	-3.5343660131329102e-152	-6.77721693477311e-154	-3.4917397134065755e-152

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	27
1	41	27

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.2s	3228×	body	1280	valid
544.0ms	632×	body	2560	valid
387.0ms	1863×	body	640	valid
112.0ms	801×	body	320	valid
48.0ms	1103×	body	80	valid
34.0ms	373×	body	160	valid