Details

sample226.0ms

Algorithm

intervals

Results

82.0ms	87×	body	2560	valid
55.0ms	110×	body	1280	valid
55.0ms	65×	body	10240	exit
9.0ms	36×	body	640	valid
5.0ms	321×	pre	80	true
1.0ms	6×	body	320	valid
1.0ms	6×	body	160	valid
1.0ms	11×	body	80	valid

simplify92.0ms

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

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:

0.2b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.4b	(- (exp (* b eps)) 1.0)
2.7b	(- (exp (* a eps)) 1.0)
3.8b	(- (exp (* (+ a b) eps)) 1.0)

rewrite108.0ms

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:

67.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
15.0ms	(- (exp (* b eps)) 1.0)
11.0ms	(- (exp (* a eps)) 1.0)
13.0ms	(- (exp (* (+ a b) eps)) 1.0)

series148.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
27.0ms	(- (exp (* b eps)) 1.0)
33.0ms	(- (exp (* a eps)) 1.0)
41.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify42.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (8.0ms)

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

prune336.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 49.7b

localize30.0ms

Local error

Found 4 expressions with local error:

2.7b	(- (exp (* a eps)) 1.0)
3.8b	(- (exp (* (+ a b) eps)) 1.0)
13.0b	(* (pow eps 2) (pow b 2))
14.7b	(* (pow eps 3) (pow b 3))

rewrite69.0ms

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:

12.0ms	(- (exp (* a eps)) 1.0)
13.0ms	(- (exp (* (+ a b) eps)) 1.0)
20.0ms	(* (pow eps 2) (pow b 2))
19.0ms	(* (pow eps 3) (pow b 3))

series162.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(- (exp (* a eps)) 1.0)
46.0ms	(- (exp (* (+ a b) eps)) 1.0)
28.0ms	(* (pow eps 2) (pow b 2))
59.0ms	(* (pow eps 3) (pow b 3))

simplify80.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (70.0ms)

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

prune583.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 49.2b

localize29.0ms

Local error

Found 4 expressions with local error:

3.2b	(* (pow eps 3) b)
3.8b	(- (exp (* (+ a b) eps)) 1.0)
5.1b	(* (* (* (pow eps 3) b) b) b)
13.0b	(* (pow eps 2) (pow b 2))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

12.0ms	(* (pow eps 3) b)
13.0ms	(- (exp (* (+ a b) eps)) 1.0)
68.0ms	(* (* (* (pow eps 3) b) b) b)
17.0ms	(* (pow eps 2) (pow b 2))

series157.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (pow eps 3) b)
47.0ms	(- (exp (* (+ a b) eps)) 1.0)
60.0ms	(* (* (* (pow eps 3) b) b) b)
30.0ms	(* (pow eps 2) (pow b 2))

simplify80.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	436	616
1	2133	512
2	5001	488

prune522.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 49.2b

localize36.0ms

Local error

Found 4 expressions with local error:

3.2b	(* (pow eps 3) b)
3.8b	(- (exp (* (+ a b) eps)) 1.0)
5.1b	(* (* (* (pow eps 3) b) b) b)
13.0b	(* (pow eps 2) (pow b 2))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

14.0ms	(* (pow eps 3) b)
13.0ms	(- (exp (* (+ a b) eps)) 1.0)
66.0ms	(* (* (* (pow eps 3) b) b) b)
16.0ms	(* (pow eps 2) (pow b 2))

series150.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (pow eps 3) b)
41.0ms	(- (exp (* (+ a b) eps)) 1.0)
60.0ms	(* (* (* (pow eps 3) b) b) b)
29.0ms	(* (pow eps 2) (pow b 2))

simplify73.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	436	655
1	2161	515
2	5002	500

prune539.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 49.2b

regimes187.0ms

Accuracy

50.5% (4.2b remaining)

Error of 53.5b against oracle of 49.3b and baseline of 57.8b

bsearch316.0ms

Steps

Iters	Range		Point
7	8.712263967736246e+126	3.260842031768285e+128	9.716140837926457e+126
9	-3.889995037463458e+74	-1.693162129245245e+66	-1.9693375139914443e+72

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	45
1	76	45

end0.0ms

sample6.8s

Algorithm

intervals

Results

2.5s	2587×	body	2560	valid
1.8s	2040×	body	10240	exit
1.7s	3506×	body	1280	valid
264.0ms	989×	body	640	valid
146.0ms	10043×	pre	80	true
58.0ms	320×	body	320	valid
23.0ms	458×	body	80	valid
16.0ms	143×	body	160	valid