Details

sample229.0ms

Algorithm

intervals

Results

82.0ms	84×	body	2560	valid
58.0ms	70×	body	10240	exit
55.0ms	105×	body	1280	valid
8.0ms	29×	body	640	valid
6.0ms	326×	pre	80	true
3.0ms	15×	body	320	valid
1.0ms	16×	body	80	valid
1.0ms	7×	body	160	valid

simplify98.0ms

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: 59.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
3.0b	(- (exp (* b eps)) 1.0)
3.4b	(- (exp (* a eps)) 1.0)
4.7b	(- (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))
4.0ms	(- (exp (* b eps)) 1.0)
4.0ms	(- (exp (* a eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)

series163.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
35.0ms	(- (exp (* b eps)) 1.0)
32.0ms	(- (exp (* a eps)) 1.0)
49.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify64.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (50.0ms)

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

prune461.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 48.0b

localize28.0ms

Local error

Found 4 expressions with local error:

3.4b	(- (exp (* a eps)) 1.0)
4.7b	(- (exp (* (+ a b) eps)) 1.0)
13.6b	(* (pow eps 2) (pow b 2))
16.0b	(* (pow eps 3) (pow b 3))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt`
32×	`*-un-lft-identity` `unswap-sqr`
28×	`add-exp-log` `add-cube-cbrt` `unpow-prod-down`
20×	`associate-r` `associate-l` `sqr-pow`
18×	`prod-diff` `prod-exp`
14×	`cube-prod`
12×	`pow-to-exp` `pow-exp`
10×	`unpow2`
8×	`add-cbrt-cube` `add-log-exp`
6×	`fma-neg`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cube-mult` `sub-neg` `flip3--` `diff-log` `unpow3` `pow-prod-down` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 170

Calls

4 calls:

5.0ms	(- (exp (* a eps)) 1.0)
8.0ms	(- (exp (* (+ a b) eps)) 1.0)
9.0ms	(* (pow eps 2) (pow b 2))
12.0ms	(* (pow eps 3) (pow b 3))

series182.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (exp (* a eps)) 1.0)
45.0ms	(- (exp (* (+ a b) eps)) 1.0)
36.0ms	(* (pow eps 2) (pow b 2))
61.0ms	(* (pow eps 3) (pow b 3))

simplify89.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	554	1168
1	2622	884
2	5001	872

prune683.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 47.3b

localize27.0ms

Local error

Found 4 expressions with local error:

4.5b	(* (pow eps 3) b)
4.6b	(* (* (pow eps 3) b) b)
4.7b	(- (exp (* (+ a b) eps)) 1.0)
13.6b	(* (pow eps 2) (pow b 2))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
31×	`add-exp-log`
22×	`*-un-lft-identity`
21×	`associate-l`
20×	`add-cube-cbrt` `unswap-sqr`
19×	`prod-exp`
18×	`unpow-prod-down`
14×	`associate-r`
13×	`add-cbrt-cube`
12×	`sqr-pow`
10×	`unpow2`
9×	`prod-diff`
8×	`pow-to-exp` `pow-exp`
6×	`pow1` `add-log-exp`
5×	`cbrt-unprod`
4×	`expm1-log1p-u` `cube-prod` `log1p-expm1-u`
3×	`fma-neg` `*-commutative`
2×	`pow-prod-down`
1×	`cube-mult` `sub-neg` `flip3--` `diff-log` `unpow3` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 135

Calls

4 calls:

6.0ms	(* (pow eps 3) b)
9.0ms	(* (* (pow eps 3) b) b)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)
9.0ms	(* (pow eps 2) (pow b 2))

series141.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (pow eps 3) b)
43.0ms	(* (* (pow eps 3) b) b)
44.0ms	(- (exp (* (+ a b) eps)) 1.0)
31.0ms	(* (pow eps 2) (pow b 2))

simplify72.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	455	810
1	2136	607
2	5001	600

prune561.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 47.3b

localize35.0ms

Local error

Found 4 expressions with local error:

4.7b	(- (exp (* (+ a b) eps)) 1.0)
4.8b	(* (/ (fma (- 1.0) 1.0 (pow (exp a) (* 2 eps))) (+ (exp (* a eps)) 1.0)) (fma 1/6 (* (pow eps 3) (pow b 3)) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b))))
13.6b	(* (pow eps 2) (pow b 2))
16.0b	(* (pow eps 3) (pow b 3))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-sqr-sqrt`
38×	`-un-lft-identity` `associate-l*`
34×	`unswap-sqr`
33×	`add-exp-log`
30×	`add-cube-cbrt`
28×	`unpow-prod-down`
23×	`associate-r`
20×	`prod-exp` `sqr-pow`
14×	`cube-prod`
13×	`times-frac` `add-cbrt-cube`
12×	`pow-to-exp` `pow-exp`
10×	`unpow2`
9×	`prod-diff`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u`
3×	`fma-neg` `pow-prod-down` `*-commutative` `distribute-lft-out`
2×	`cube-mult` `unpow3` `associate-/r/` `fma-udef`
1×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `flip3-+` `diff-log` `div-exp` `associate-*l/` `flip--` `flip-+` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 183

Calls

4 calls:

5.0ms	(- (exp (* (+ a b) eps)) 1.0)
18.0ms	(* (/ (fma (- 1.0) 1.0 (pow (exp a) (* 2 eps))) (+ (exp (* a eps)) 1.0)) (fma 1/6 (* (pow eps 3) (pow b 3)) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b))))
8.0ms	(* (pow eps 2) (pow b 2))
15.0ms	(* (pow eps 3) (pow b 3))

series526.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (exp (* (+ a b) eps)) 1.0)
385.0ms	(* (/ (fma (- 1.0) 1.0 (pow (exp a) (* 2 eps))) (+ (exp (* a eps)) 1.0)) (fma 1/6 (* (pow eps 3) (pow b 3)) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b))))
30.0ms	(* (pow eps 2) (pow b 2))
66.0ms	(* (pow eps 3) (pow b 3))

simplify133.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 2 (113.0ms)

Iter	Nodes	Cost
0	800	1972
1	3846	1693
2	5001	1654

prune932.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 45.3b

regimes263.0ms

Accuracy

38.4% (5.7b remaining)

Error of 52.4b against oracle of 46.7b and baseline of 55.9b

bsearch346.0ms

Steps

Iters	Range		Point
10	4.410176380362178e+58	1.1829225377078756e+70	3.545917895875284e+64
7	-513705451564942.06	-3513425960593.053	-346828314544410.56

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	81	71
1	81	71

end0.0ms

sample6.8s

Algorithm

intervals

Results

2.5s	2597×	body	2560	valid
1.7s	2020×	body	10240	exit
1.7s	3413×	body	1280	valid
303.0ms	1102×	body	640	valid
167.0ms	10025×	pre	80	true
62.0ms	349×	body	320	valid
22.0ms	422×	body	80	valid
14.0ms	122×	body	160	valid