Details

sample229.0ms

Algorithm

intervals

Results

79.0ms	84×	body	2560	valid
62.0ms	70×	body	10240	exit
51.0ms	105×	body	1280	valid
8.0ms	29×	body	640	valid
6.0ms	326×	pre	80	true
3.0ms	15×	body	320	valid
1.0ms	7×	body	160	valid
1.0ms	16×	body	80	valid

simplify94.0ms

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: 59.9b

localize21.0ms

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)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

25.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
4.0ms	(- (exp (* b eps)) 1.0)
4.0ms	(- (exp (* a eps)) 1.0)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)

series164.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
31.0ms	(- (exp (* b eps)) 1.0)
33.0ms	(- (exp (* a eps)) 1.0)
50.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify42.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	346	733
1	1449	673
2	5001	673

prune339.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 48.0b

localize30.0ms

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))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 138

Calls

4 calls:

4.0ms	(- (exp (* a eps)) 1.0)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)
9.0ms	(* (pow eps 2) (pow b 2))
14.0ms	(* (pow eps 3) (pow b 3))

series177.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (exp (* a eps)) 1.0)
49.0ms	(- (exp (* (+ a b) eps)) 1.0)
30.0ms	(* (pow eps 2) (pow b 2))
64.0ms	(* (pow eps 3) (pow b 3))

simplify79.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	460	772
1	2092	679
2	5001	636

prune578.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 47.3b

localize34.0ms

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))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 115

Calls

4 calls:

7.0ms	(* (pow eps 3) b)
10.0ms	(* (* (pow eps 3) b) b)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)
9.0ms	(* (pow eps 2) (pow b 2))

series144.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (pow eps 3) b)
42.0ms	(* (* (pow eps 3) b) b)
45.0ms	(- (exp (* (+ a b) eps)) 1.0)
35.0ms	(* (pow eps 2) (pow b 2))

simplify70.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	390	576
1	1829	484
2	5001	472

prune503.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 47.3b

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 171

Calls

4 calls:

4.0ms	(- (exp (* (+ a b) eps)) 1.0)
160.0ms	(* (/ (+ (- (* 1.0 1.0)) (pow (exp a) (* 2 eps))) (+ (exp (* a eps)) 1.0)) (+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b))))
9.0ms	(* (pow eps 2) (pow b 2))
12.0ms	(* (pow eps 3) (pow b 3))

series518.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(- (exp (* (+ a b) eps)) 1.0)
370.0ms	(* (/ (+ (- (* 1.0 1.0)) (pow (exp a) (* 2 eps))) (+ (exp (* a eps)) 1.0)) (+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b))))
33.0ms	(* (pow eps 2) (pow b 2))
65.0ms	(* (pow eps 3) (pow b 3))

simplify159.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	933	2133
1	4867	1913
2	5002	1913

prune952.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 45.3b

regimes280.0ms

Accuracy

38.6% (5.7b remaining)

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

bsearch354.0ms

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	102	79
1	102	79

end0.0ms

sample6.8s

Algorithm

intervals

Results

2.5s	2597×	body	2560	valid
1.7s	2020×	body	10240	exit
1.6s	3413×	body	1280	valid
302.0ms	1102×	body	640	valid
182.0ms	10025×	pre	80	true
65.0ms	349×	body	320	valid
25.0ms	422×	body	80	valid
14.0ms	122×	body	160	valid