Details

sample240.0ms

Algorithm

intervals

Results

111.0ms	84×	body	2560	valid
75.0ms	106×	body	1280	valid
17.0ms	35×	body	640	valid
8.0ms	71×	body	80	overflowed
7.0ms	327×	pre	80	true
4.0ms	12×	body	320	valid
2.0ms	17×	body	80	valid
0.0ms	2×	body	160	valid

simplify102.0ms

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: 59.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.7b	(- (exp (* a eps)) 1.0)
2.8b	(- (exp (* b eps)) 1.0)
4.7b	(- (exp (* (+ a b) eps)) 1.0)

rewrite47.0ms

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:

27.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
5.0ms	(- (exp (* a eps)) 1.0)
5.0ms	(- (exp (* b eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)

series172.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
35.0ms	(- (exp (* a eps)) 1.0)
32.0ms	(- (exp (* b eps)) 1.0)
53.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify65.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (50.0ms)

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

prune452.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 48.5b

localize28.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (exp (* b eps)) 1.0)
4.7b	(- (exp (* (+ a b) eps)) 1.0)
14.9b	(* (pow a 2) (pow eps 2))
15.7b	(* (pow a 3) (pow eps 3))

rewrite36.0ms

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

series183.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (exp (* b eps)) 1.0)
46.0ms	(- (exp (* (+ a b) eps)) 1.0)
39.0ms	(* (pow a 2) (pow eps 2))
67.0ms	(* (pow a 3) (pow eps 3))

simplify92.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	564	1168
1	2652	884
2	5002	872

prune729.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 48.2b

localize31.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (exp (* b eps)) 1.0)
4.7b	(- (exp (* (+ a b) eps)) 1.0)
14.9b	(* (pow a 2) (pow eps 2))
15.7b	(* (pow a 3) (pow eps 3))

rewrite40.0ms

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

series179.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (exp (* b eps)) 1.0)
46.0ms	(- (exp (* (+ a b) eps)) 1.0)
36.0ms	(* (pow a 2) (pow eps 2))
61.0ms	(* (pow a 3) (pow eps 3))

simplify87.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	564	1168
1	2652	884
2	5002	872

prune787.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 48.2b

localize33.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (exp (* b eps)) 1.0)
4.7b	(- (exp (* (+ a b) eps)) 1.0)
14.9b	(* (pow a 2) (pow eps 2))
15.7b	(* (pow a 3) (pow eps 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 (* b eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)
9.0ms	(* (pow a 2) (pow eps 2))
15.0ms	(* (pow a 3) (pow eps 3))

series181.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (exp (* b eps)) 1.0)
46.0ms	(- (exp (* (+ a b) eps)) 1.0)
31.0ms	(* (pow a 2) (pow eps 2))
67.0ms	(* (pow a 3) (pow eps 3))

simplify91.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	564	1114
1	2481	873
2	5002	825

prune975.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 48.2b

regimes228.0ms

Accuracy

31.2% (5.8b remaining)

Error of 55.2b against oracle of 49.4b and baseline of 57.8b

bsearch341.0ms

Steps

Iters	Range		Point
8	1.0330457117747248e+62	5.0931338003169406e+64	2.3410812747991413e+62
10	-8.420347402970079e+188	-1.605931750786494e+170	-7.541287819732367e+174

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	59
1	68	59

end0.0ms

sample7.3s

Algorithm

intervals

Results

3.4s	2615×	body	2560	valid
2.5s	3449×	body	1280	valid
497.0ms	1053×	body	640	valid
225.0ms	2052×	body	80	overflowed
220.0ms	10057×	pre	80	true
114.0ms	341×	body	320	valid
46.0ms	428×	body	80	valid
28.0ms	119×	body	160	valid