Details

sample154.0ms

Algorithm

intervals

Results

78.0ms	110×	body	1280	valid
29.0ms	71×	body	640	valid
27.0ms	14×	body	2560	valid
6.0ms	23×	body	320	valid
3.0ms	31×	body	80	valid
1.0ms	7×	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: 37.6b

localize9.0ms

Local error

Found 2 expressions with local error:

1.6b	(- (tan (+ x eps)) (tan x))
3.7b	(tan (+ x eps))

rewrite13.0ms

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:

8.0ms	(- (tan (+ x eps)) (tan x))
3.0ms	(tan (+ x eps))

series150.0ms

Counts

2 → 6

Calls

2 calls:

90.0ms	(- (tan (+ x eps)) (tan x))
59.0ms	(tan (+ x eps))

simplify77.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (72.0ms)

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

prune122.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.2b

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

rewrite78.0ms

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:

3.0ms	(+ (tan x) (tan eps))
11.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
5.0ms	(* (tan x) (tan eps))
51.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series735.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(+ (tan x) (tan eps))
204.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
90.0ms	(* (tan x) (tan eps))
351.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify76.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	559	2923
1	2054	2373
2	5001	2349

prune429.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 14.0b

localize16.0ms

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

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
40×	`tan-quot`
20×	`add-exp-log` `add-cbrt-cube`
19×	`frac-times` `pow-prod-down`
13×	`associate-r/` `associate-l/`
12×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `pow-sqr` `pow-prod-up` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`pow-plus` `unswap-sqr`
1×	`pow2` `swap-sqr` `fma-udef`

Counts

4 → 107

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
21.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

series862.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (tan x) (tan eps))
91.0ms	(* (tan x) (tan eps))
114.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
566.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

simplify54.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	432	1098
1	1952	917
2	5001	864

prune372.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 14.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (/ (+ (tan x) (tan eps)) (fma (tan x) (tan eps) 1)) (- 1 (* (tan x) (tan eps)))) (+ 1 (* (tan x) (tan eps))))
0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
4.0b	(- (* (/ (/ (+ (tan x) (tan eps)) (fma (tan x) (tan eps) 1)) (- 1 (* (tan x) (tan eps)))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

87×	`times-frac`
69×	`*-un-lft-identity`
64×	`add-sqr-sqrt`
60×	`associate-l`
51×	`add-cube-cbrt`
17×	`add-exp-log` `add-cbrt-cube`
13×	`tan-quot`
10×	`pow1`
9×	`associate-r` `distribute-lft-out`
6×	`frac-times` `associate-*r/` `add-log-exp`
5×	`prod-exp` `frac-sub` `cbrt-unprod` `unswap-sqr`
4×	`expm1-log1p-u` `flip3-+` `associate-*l/` `flip-+` `log1p-expm1-u` `div-inv`
3×	`cbrt-undiv` `div-exp` `prod-diff` `pow-prod-down` `*-commutative`
2×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `associate--l+` `associate-/r/` `flip--`
1×	`sub-neg` `fma-neg` `diff-log`

Counts

4 → 155

Calls

4 calls:

40.0ms	(* (/ (/ (+ (tan x) (tan eps)) (fma (tan x) (tan eps) 1)) (- 1 (* (tan x) (tan eps)))) (+ 1 (* (tan x) (tan eps))))
5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
14.0ms	(- (* (/ (/ (+ (tan x) (tan eps)) (fma (tan x) (tan eps) 1)) (- 1 (* (tan x) (tan eps)))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series1.7s

Counts

4 → 12

Calls

4 calls:

361.0ms	(* (/ (/ (+ (tan x) (tan eps)) (fma (tan x) (tan eps) 1)) (- 1 (* (tan x) (tan eps)))) (+ 1 (* (tan x) (tan eps))))
90.0ms	(* (tan x) (tan eps))
90.0ms	(* (tan x) (tan eps))
1.2s	(- (* (/ (/ (+ (tan x) (tan eps)) (fma (tan x) (tan eps) 1)) (- 1 (* (tan x) (tan eps)))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify50.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1151	2879
1	5001	2649

prune561.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.5b

regimes99.0ms

Accuracy

0% (0.3b remaining)

Error of 0.7b against oracle of 0.3b and baseline of 0.7b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	101
1	48	101

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.4s	3290×	body	1280	valid
1.1s	658×	body	2560	valid
743.0ms	1818×	body	640	valid
211.0ms	784×	body	320	valid
95.0ms	1119×	body	80	valid
59.0ms	331×	body	160	valid