Details

sample238.0ms

Algorithm

intervals

Results

87.0ms	86×	body	2560	valid
60.0ms	70×	body	10240	exit
54.0ms	109×	body	1280	valid
9.0ms	33×	body	640	valid
5.0ms	326×	pre	80	true
2.0ms	10×	body	320	valid
1.0ms	6×	body	160	valid
1.0ms	12×	body	80	valid

simplify103.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	40	13
1	101	13
2	258	13
3	766	13
4	3895	13
5	5001	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
3.8b	(- (exp (* a eps)) 1.0)
3.9b	(- (exp (* b eps)) 1.0)
5.6b	(- (exp (* (+ a b) eps)) 1.0)

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt` `*-un-lft-identity`
27×	`prod-diff`
25×	`add-cube-cbrt`
16×	`add-exp-log` `add-cbrt-cube`
10×	`flip3--` `flip--` `add-log-exp`
9×	`fma-neg`
8×	`associate-/r/`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `frac-times` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`sub-neg` `diff-log` `distribute-lft-out--` `difference-of-squares`
2×	`associate-*l/` `associate-/l/`
1×	`frac-2neg` `times-frac` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 117

Calls

4 calls:

57.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
14.0ms	(- (exp (* a eps)) 1.0)
17.0ms	(- (exp (* b eps)) 1.0)
15.0ms	(- (exp (* (+ a b) eps)) 1.0)

series299.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
30.0ms	(- (exp (* a eps)) 1.0)
35.0ms	(- (exp (* b eps)) 1.0)
46.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify76.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	608	1462
1	2778	1079
2	5002	1072

prune430.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ (/ 1 b) (/ 1 a))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
15×	`times-frac`
13×	`fma-def`
10×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`distribute-lft-out`
5×	`div-inv`
3×	`add-log-exp`
1×	`pow1` `add-exp-log` `+-commutative` `expm1-log1p-u` `flip3-+` `frac-add` `sum-log` `add-cbrt-cube` `flip-+` `log1p-expm1-u`

Counts

1 → 34

Calls

1 calls:

24.0ms

(+ (/ 1 b) (/ 1 a))

series14.0ms

Counts

1 → 3

Calls

1 calls:

13.0ms

(+ (/ 1 b) (/ 1 a))

simplify69.0ms

Algorithm

egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	107	112
1	368	101
2	1274	98
3	3144	98
4	5001	98

prune73.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1 b) (/ 1 a))
0.1b	(sqrt (+ (/ 1 b) (/ 1 a)))
0.1b	(sqrt (+ (/ 1 b) (/ 1 a)))
0.3b	(* (sqrt (+ (/ 1 b) (/ 1 a))) (sqrt (+ (/ 1 b) (/ 1 a))))

rewrite264.0ms

Algorithm

rewrite-expression-head

Rules

157×	`*-un-lft-identity`
106×	`sqrt-prod`
97×	`add-sqr-sqrt`
81×	`distribute-lft-out`
75×	`times-frac`
61×	`div-inv`
35×	`add-cube-cbrt` `swap-sqr`
30×	`sqrt-div`
21×	`pow1`
18×	`hypot-def`
13×	`fma-def` `associate-r` `associate-l`
11×	`flip3-+` `frac-add` `flip-+`
10×	`sqrt-pow1` `pow1/2`
9×	`frac-times`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr`
2×	`rem-sqrt-square`
1×	`+-commutative` `pow2` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 209

Calls

4 calls:

24.0ms	(+ (/ 1 b) (/ 1 a))
37.0ms	(sqrt (+ (/ 1 b) (/ 1 a)))
37.0ms	(sqrt (+ (/ 1 b) (/ 1 a)))
154.0ms	(* (sqrt (+ (/ 1 b) (/ 1 a))) (sqrt (+ (/ 1 b) (/ 1 a))))

series156.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ (/ 1 b) (/ 1 a))
64.0ms	(sqrt (+ (/ 1 b) (/ 1 a)))
64.0ms	(sqrt (+ (/ 1 b) (/ 1 a)))
19.0ms	(* (sqrt (+ (/ 1 b) (/ 1 a))) (sqrt (+ (/ 1 b) (/ 1 a))))

simplify62.0ms

Algorithm

egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	335	1244
1	1529	1075
2	5001	1049

prune365.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ eps (/ (+ (exp (fma a eps (* eps b))) (- 1.0 (fma 1.0 (exp (* eps b)) (* 1.0 (exp (* a eps)))))) (- (exp (* (+ a b) eps)) 1.0)))
2.2b	(- 1.0 (fma 1.0 (exp (* eps b)) (* 1.0 (exp (* a eps)))))
3.9b	(+ (exp (fma a eps (* eps b))) (- 1.0 (fma 1.0 (exp (* eps b)) (* 1.0 (exp (* a eps))))))
5.6b	(- (exp (* (+ a b) eps)) 1.0)

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

250×	`*-un-lft-identity`
193×	`times-frac`
145×	`add-sqr-sqrt`
101×	`add-cube-cbrt`
43×	`distribute-lft-out--`
42×	`distribute-lft-out`
31×	`associate-/r*`
27×	`prod-diff`
22×	`difference-of-squares`
13×	`add-log-exp`
11×	`associate-+r+`
9×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
6×	`flip3--` `fma-neg` `flip--`
5×	`div-inv`
4×	`pow1` `expm1-log1p-u` `fma-def` `log1p-expm1-u`
3×	`cbrt-undiv` `sub-neg` `diff-log` `div-exp` `associate-/l*`
2×	`sum-log` `fma-udef`
1×	`+-commutative` `associate-+r-` `frac-2neg` `flip3-+` `exp-sum` `clear-num` `flip-+` `associate--r+`

Counts

4 → 233

Calls

4 calls:

55.0ms	(/ eps (/ (+ (exp (fma a eps (* eps b))) (- 1.0 (fma 1.0 (exp (* eps b)) (* 1.0 (exp (* a eps)))))) (- (exp (* (+ a b) eps)) 1.0)))
7.0ms	(- 1.0 (fma 1.0 (exp (* eps b)) (* 1.0 (exp (* a eps)))))
21.0ms	(+ (exp (fma a eps (* eps b))) (- 1.0 (fma 1.0 (exp (* eps b)) (* 1.0 (exp (* a eps))))))
19.0ms	(- (exp (* (+ a b) eps)) 1.0)

series383.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(/ eps (/ (+ (exp (fma a eps (* eps b))) (- 1.0 (fma 1.0 (exp (* eps b)) (* 1.0 (exp (* a eps)))))) (- (exp (* (+ a b) eps)) 1.0)))
54.0ms	(- 1.0 (fma 1.0 (exp (* eps b)) (* 1.0 (exp (* a eps)))))
64.0ms	(+ (exp (fma a eps (* eps b))) (- 1.0 (fma 1.0 (exp (* eps b)) (* 1.0 (exp (* a eps))))))
49.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify128.0ms

Algorithm

egg-herbie

Counts

245 → 245

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	776	5341
1	3618	4812
2	5002	4789

prune761.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes58.0ms

Accuracy

0% (3.2b remaining)

Error of 3.3b against oracle of 0.1b and baseline of 3.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	3
1	9	3

end0.0ms

sample7.0s

Algorithm

intervals

Results

2.6s	2647×	body	2560	valid
1.7s	1974×	body	10240	exit
1.7s	3398×	body	1280	valid
283.0ms	1054×	body	640	valid
156.0ms	9976×	pre	80	true
63.0ms	342×	body	320	valid
24.0ms	441×	body	80	valid
14.0ms	120×	body	160	valid