Details

sample231.0ms

Algorithm

intervals

Results

84.0ms	86×	body	2560	valid
60.0ms	70×	body	10240	exit
49.0ms	109×	body	1280	valid
8.0ms	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

simplify93.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	13
1	101	13
2	245	13
3	697	13
4	3463	13
5	5001	13

prune4.0ms

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)

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `flip3--` `*-un-lft-identity` `flip--` `add-log-exp`
8×	`associate-/r/`
4×	`pow1` `cbrt-undiv` `frac-times` `add-cube-cbrt` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod`
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 → 73

Calls

4 calls:

52.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
15.0ms	(- (exp (* a eps)) 1.0)
12.0ms	(- (exp (* b eps)) 1.0)
14.0ms	(- (exp (* (+ a b) eps)) 1.0)

series286.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
34.0ms	(- (exp (* a eps)) 1.0)
28.0ms	(- (exp (* b eps)) 1.0)
42.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify57.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	488	957
1	2299	794
2	5001	789

prune306.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 1 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
7×	`distribute-lft-out`
6×	`times-frac`
4×	`div-inv`
3×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
1×	`pow1` `add-exp-log` `+-commutative` `flip3-+` `frac-add` `sum-log` `add-cbrt-cube` `flip-+`

Counts

1 → 19

Calls

1 calls:

23.0ms

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

series9.0ms

Counts

1 → 3

Calls

1 calls:

9.0ms

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

simplify65.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 3 (26.0ms)

Iter	Nodes	Cost
0	101	104
1	345	94
2	1153	91
3	2775	90
4	5001	90

prune38.0ms

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))))

rewrite266.0ms

Algorithm

rewrite-expression-head

Rules

138×	`*-un-lft-identity`
106×	`sqrt-prod`
81×	`distribute-lft-out`
60×	`div-inv`
42×	`add-sqr-sqrt` `times-frac`
35×	`swap-sqr`
30×	`sqrt-div`
28×	`add-cube-cbrt`
21×	`pow1`
13×	`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×	`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 → 170

Calls

4 calls:

23.0ms	(+ (/ 1 b) (/ 1 a))
36.0ms	(sqrt (+ (/ 1 b) (/ 1 a)))
36.0ms	(sqrt (+ (/ 1 b) (/ 1 a)))
161.0ms	(* (sqrt (+ (/ 1 b) (/ 1 a))) (sqrt (+ (/ 1 b) (/ 1 a))))

series149.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ (/ 1 b) (/ 1 a))
62.0ms	(sqrt (+ (/ 1 b) (/ 1 a)))
57.0ms	(sqrt (+ (/ 1 b) (/ 1 a)))
21.0ms	(* (sqrt (+ (/ 1 b) (/ 1 a))) (sqrt (+ (/ 1 b) (/ 1 a))))

simplify60.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	321	1208
1	1520	1045
2	5001	1029

prune239.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

158×	`times-frac`
147×	`*-un-lft-identity`
105×	`add-sqr-sqrt`
71×	`add-cube-cbrt`
26×	`associate-/r*`
21×	`distribute-lft-out`
17×	`distribute-lft-out--` `difference-of-squares`
13×	`add-log-exp`
9×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
6×	`flip3--` `flip--`
5×	`div-inv`
4×	`pow1`
3×	`cbrt-undiv` `sub-neg` `diff-log` `div-exp` `associate-/l*`
2×	`associate-+r+` `sum-log` `associate--r+`
1×	`+-commutative` `distribute-rgt-in` `associate-+r-` `frac-2neg` `distribute-lft-in` `flip3-+` `clear-num` `flip-+`

Counts

4 → 166

Calls

4 calls:

88.0ms	(/ eps (/ (+ (exp (+ (* a eps) (* eps b))) (- 1.0 (* 1.0 (+ (exp (* eps b)) (exp (* a eps)))))) (- (exp (* (+ a b) eps)) 1.0)))
5.0ms	(- 1.0 (* 1.0 (+ (exp (* eps b)) (exp (* a eps)))))
47.0ms	(+ (exp (+ (* a eps) (* eps b))) (- 1.0 (* 1.0 (+ (exp (* eps b)) (exp (* a eps))))))
14.0ms	(- (exp (* (+ a b) eps)) 1.0)

series374.0ms

Counts

4 → 12

Calls

4 calls:

215.0ms	(/ eps (/ (+ (exp (+ (* a eps) (* eps b))) (- 1.0 (* 1.0 (+ (exp (* eps b)) (exp (* a eps)))))) (- (exp (* (+ a b) eps)) 1.0)))
52.0ms	(- 1.0 (* 1.0 (+ (exp (* eps b)) (exp (* a eps)))))
60.0ms	(+ (exp (+ (* a eps) (* eps b))) (- 1.0 (* 1.0 (+ (exp (* eps b)) (exp (* a eps))))))
47.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify106.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	663	4317
1	3186	4146
2	5001	4140

prune594.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes51.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	9	3
1	9	3

end0.0ms

sample6.8s

Algorithm

intervals

Results

2.5s	2647×	body	2560	valid
1.7s	1974×	body	10240	exit
1.6s	3398×	body	1280	valid
278.0ms	1054×	body	640	valid
153.0ms	9976×	pre	80	true
59.0ms	342×	body	320	valid
22.0ms	441×	body	80	valid
13.0ms	120×	body	160	valid