Details

sample227.0ms

Algorithm

intervals

Results

70.0ms	70×	body	2560	valid
67.0ms	125×	body	1280	valid
53.0ms	58×	body	10240	exit
10.0ms	37×	body	640	valid
6.0ms	314×	pre	80	true
3.0ms	14×	body	320	valid
1.0ms	10×	body	80	valid

simplify99.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 61.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.0b	(- (exp (* b eps)) 1.0)
3.6b	(- (exp (* a eps)) 1.0)
5.1b	(- (exp (* (+ a b) eps)) 1.0)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
45×	`prod-diff`
39×	`add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`add-log-exp`
9×	`flip3--` `fma-neg` `flip--`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`sub-neg` `associate-r` `associate-l` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u`
3×	`diff-log`
2×	`associate-r/` `associate-l/`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 138

Calls

4 calls:

26.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
5.0ms	(- (exp (* b eps)) 1.0)
5.0ms	(- (exp (* a eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)

series164.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
36.0ms	(- (exp (* b eps)) 1.0)
33.0ms	(- (exp (* a eps)) 1.0)
48.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify64.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	488	1660
1	2051	1241
2	5003	1216

prune459.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 49.7b

localize26.0ms

Local error

Found 4 expressions with local error:

2.7b	(* (fma 1/6 (* (pow a 3) (pow eps 3)) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0))
5.1b	(- (exp (* (+ a b) eps)) 1.0)
14.5b	(* (pow a 2) (pow eps 2))
15.7b	(* (pow a 3) (pow eps 3))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
35×	`add-cube-cbrt`
33×	`unswap-sqr`
30×	`add-exp-log`
28×	`unpow-prod-down`
27×	`prod-diff`
25×	`associate-r`
23×	`associate-l`
20×	`sqr-pow`
19×	`prod-exp`
14×	`cube-prod`
12×	`pow-to-exp` `pow-exp`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`add-cbrt-cube` `unpow2`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `fma-neg` `pow-prod-down` `*-commutative` `cbrt-unprod`
2×	`cube-mult` `flip3--` `unpow3` `associate-*r/` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log`

Counts

4 → 188

Calls

4 calls:

14.0ms	(* (fma 1/6 (* (pow a 3) (pow eps 3)) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0))
5.0ms	(- (exp (* (+ a b) eps)) 1.0)
11.0ms	(* (pow a 2) (pow eps 2))
12.0ms	(* (pow a 3) (pow eps 3))

series266.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(* (fma 1/6 (* (pow a 3) (pow eps 3)) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0))
50.0ms	(- (exp (* (+ a b) eps)) 1.0)
31.0ms	(* (pow a 2) (pow eps 2))
65.0ms	(* (pow a 3) (pow eps 3))

simplify113.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 2 (93.0ms)

Iter	Nodes	Cost
0	651	2054
1	3019	1718
2	5002	1708

prune745.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 49.3b

localize24.0ms

Local error

Found 4 expressions with local error:

2.6b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma 1/6 (pow (* eps a) 3) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0)))
2.7b	(* (fma 1/6 (pow (* eps a) 3) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0))
5.1b	(- (exp (* (+ a b) eps)) 1.0)
14.5b	(* (pow a 2) (pow eps 2))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
30×	`add-exp-log`
29×	`add-cube-cbrt`
27×	`prod-diff`
20×	`add-cbrt-cube`
17×	`unswap-sqr`
14×	`unpow-prod-down` `prod-exp`
13×	`associate-r`
11×	`distribute-rgt-in` `distribute-lft-in` `associate-l`
10×	`unpow2` `sqr-pow`
6×	`pow1` `pow-to-exp` `associate-*r/` `pow-exp` `cbrt-unprod` `add-log-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `flip3--` `div-exp` `flip--` `log1p-expm1-u`
3×	`sub-neg` `fma-neg`
2×	`pow-prod-down` `associate-/r/` `*-commutative` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`frac-2neg` `times-frac` `diff-log` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 154

Calls

4 calls:

17.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma 1/6 (pow (* eps a) 3) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0)))
14.0ms	(* (fma 1/6 (pow (* eps a) 3) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0))
8.0ms	(- (exp (* (+ a b) eps)) 1.0)
9.0ms	(* (pow a 2) (pow eps 2))

series1.1s

Counts

4 → 12

Calls

4 calls:

942.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma 1/6 (pow (* eps a) 3) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0)))
104.0ms	(* (fma 1/6 (pow (* eps a) 3) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0))
48.0ms	(- (exp (* (+ a b) eps)) 1.0)
31.0ms	(* (pow a 2) (pow eps 2))

simplify118.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	785	2568
1	4065	2039
2	5001	2030

prune590.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize4.0ms

Local error

Found 1 expressions with local error:

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

rewrite17.0ms

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:

16.0ms

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

series10.0ms

Counts

1 → 3

Calls

1 calls:

10.0ms

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

simplify68.0ms

Algorithm

egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 2 (11.0ms)

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

prune66.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes61.0ms

Accuracy

0% (2.9b remaining)

Error of 3.3b against oracle of 0.4b 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

sample6.8s

Algorithm

intervals

Results

2.5s	2566×	body	2560	valid
1.7s	1920×	body	10240	exit
1.7s	3422×	body	1280	valid
294.0ms	1040×	body	640	valid
174.0ms	9920×	pre	80	true
70.0ms	373×	body	320	valid
24.0ms	445×	body	80	valid
18.0ms	154×	body	160	valid