Details

sample199.0ms

Algorithm

intervals

Results

107.0ms	105×	body	2560	valid
50.0ms	95×	body	1280	valid
7.0ms	24×	body	640	valid
6.0ms	113×	body	80	overflowed
5.0ms	369×	pre	80	true
2.0ms	8×	body	320	valid
1.0ms	21×	body	80	valid
0.0ms	3×	body	160	valid

simplify96.0ms

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: 58.7b

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
4.8b	(- (exp (* b eps)) 1.0)
5.7b	(- (exp (* a eps)) 1.0)
9.6b	(- (exp (* (+ a b) eps)) 1.0)

rewrite114.0ms

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:

72.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
12.0ms	(- (exp (* b eps)) 1.0)
12.0ms	(- (exp (* a eps)) 1.0)
16.0ms	(- (exp (* (+ a b) eps)) 1.0)

series151.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
29.0ms	(- (exp (* b eps)) 1.0)
30.0ms	(- (exp (* a eps)) 1.0)
44.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify43.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (9.0ms)

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

prune347.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 55.8b

localize18.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
4.8b	(- (exp (* b eps)) 1.0)
5.7b	(- (exp (* a eps)) 1.0)
9.6b	(- (exp (* (+ a b) eps)) 1.0)

rewrite114.0ms

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:

71.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
12.0ms	(- (exp (* b eps)) 1.0)
12.0ms	(- (exp (* a eps)) 1.0)
15.0ms	(- (exp (* (+ a b) eps)) 1.0)

series150.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
28.0ms	(- (exp (* b eps)) 1.0)
30.0ms	(- (exp (* a eps)) 1.0)
44.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify43.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (9.0ms)

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

prune401.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 55.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (exp (* a eps)) 1.0) (- (pow (exp (* b eps)) 3) (pow 1.0 3)))
4.7b	(- (pow (exp (* b eps)) 3) (pow 1.0 3))
5.7b	(- (exp (* a eps)) 1.0)
9.6b	(- (exp (* (+ a b) eps)) 1.0)

rewrite214.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 116

Calls

4 calls:

145.0ms	(* (- (exp (* a eps)) 1.0) (- (pow (exp (* b eps)) 3) (pow 1.0 3)))
35.0ms	(- (pow (exp (* b eps)) 3) (pow 1.0 3))
14.0ms	(- (exp (* a eps)) 1.0)
14.0ms	(- (exp (* (+ a b) eps)) 1.0)

series185.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (- (exp (* a eps)) 1.0) (- (pow (exp (* b eps)) 3) (pow 1.0 3)))
51.0ms	(- (pow (exp (* b eps)) 3) (pow 1.0 3))
31.0ms	(- (exp (* a eps)) 1.0)
44.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify67.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	497	1256
1	2224	1185
2	5002	1185

prune580.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 55.8b

localize27.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (exp a) (* 2 eps))
1.0b	(* (+ (- (* 1.0 1.0)) (pow (exp a) (* 2 eps))) (- (exp (* eps b)) 1.0))
4.8b	(- (exp (* eps b)) 1.0)
9.6b	(- (exp (* (+ a b) eps)) 1.0)

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

5.0ms	(pow (exp a) (* 2 eps))
88.0ms	(* (+ (- (* 1.0 1.0)) (pow (exp a) (* 2 eps))) (- (exp (* eps b)) 1.0))
12.0ms	(- (exp (* eps b)) 1.0)
14.0ms	(- (exp (* (+ a b) eps)) 1.0)

series194.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(pow (exp a) (* 2 eps))
66.0ms	(* (+ (- (* 1.0 1.0)) (pow (exp a) (* 2 eps))) (- (exp (* eps b)) 1.0))
33.0ms	(- (exp (* eps b)) 1.0)
43.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify55.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	435	855
1	1842	790
2	5001	782

prune476.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 55.7b

regimes249.0ms

Accuracy

24.8% (3.1b remaining)

Error of 59.5b against oracle of 56.5b and baseline of 60.5b

bsearch261.0ms

Steps

Iters	Range		Point
8	1.8818656835680947e+85	2.4781081934878466e+89	1.923558896871724e+85
7	-1.6294062058398697e+69	-1.8540113648454134e+67	-1.888307926688869e+67

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	60
1	68	60
2	68	60

end0.0ms

sample5.9s

Algorithm

intervals

Results

3.0s	2916×	body	2560	valid
1.7s	3363×	body	1280	valid
279.0ms	921×	body	640	valid
221.0ms	4223×	body	80	overflowed
176.0ms	12226×	pre	80	true
40.0ms	191×	body	320	valid
30.0ms	570×	body	80	valid
6.0ms	42×	body	160	valid