Details

sample204.0ms

Algorithm

intervals

Results

110.0ms	105×	body	2560	valid
50.0ms	95×	body	1280	valid
8.0ms	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

simplify101.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	40	13
1	101	13
2	258	13
3	766	13
4	3895	13
5	5001	13

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 58.7b

localize21.0ms

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)

rewrite131.0ms

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:

80.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
15.0ms	(- (exp (* b eps)) 1.0)
15.0ms	(- (exp (* a eps)) 1.0)
16.0ms	(- (exp (* (+ a b) eps)) 1.0)

series148.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
28.0ms	(- (exp (* b eps)) 1.0)
34.0ms	(- (exp (* a eps)) 1.0)
42.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify68.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (49.0ms)

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

prune472.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 55.8b

localize19.0ms

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)

rewrite132.0ms

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:

77.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
15.0ms	(- (exp (* b eps)) 1.0)
15.0ms	(- (exp (* a eps)) 1.0)
20.0ms	(- (exp (* (+ a b) eps)) 1.0)

series153.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
33.0ms	(- (exp (* b eps)) 1.0)
32.0ms	(- (exp (* a eps)) 1.0)
45.0ms	(- (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

prune560.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 55.8b

localize27.0ms

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)

rewrite307.0ms

Algorithm

rewrite-expression-head

Rules

450×	`prod-diff`
295×	`add-sqr-sqrt`
265×	`*-un-lft-identity`
243×	`unpow-prod-down` `cube-prod`
239×	`add-cube-cbrt`
146×	`distribute-rgt-in` `distribute-lft-in`
89×	`sqr-pow`
73×	`cube-mult` `unpow3`
35×	`difference-of-squares`
25×	`associate-r`
18×	`fma-neg`
13×	`distribute-lft-out--`
10×	`add-log-exp`
9×	`flip3--` `flip--`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`sub-neg` `associate-l`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u`
3×	`diff-log`
2×	`difference-cubes` `associate-r/` `associate-l/`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 592

Calls

4 calls:

177.0ms	(* (- (exp (* a eps)) 1.0) (- (pow (exp (* b eps)) 3) (pow 1.0 3)))
50.0ms	(- (pow (exp (* b eps)) 3) (pow 1.0 3))
15.0ms	(- (exp (* a eps)) 1.0)
17.0ms	(- (exp (* (+ a b) eps)) 1.0)

series189.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (- (exp (* a eps)) 1.0) (- (pow (exp (* b eps)) 3) (pow 1.0 3)))
48.0ms	(- (pow (exp (* b eps)) 3) (pow 1.0 3))
37.0ms	(- (exp (* a eps)) 1.0)
44.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify230.0ms

Algorithm

egg-herbie

Counts

604 → 604

Iterations

Useful iterations: 2 (131.0ms)

Iter	Nodes	Cost
0	1034	9996
1	3942	7595
2	5001	7590

prune789.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 55.8b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
52×	`add-sqr-sqrt`
41×	`add-cube-cbrt`
36×	`prod-diff`
18×	`associate-l`
13×	`times-frac`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`fma-neg`
5×	`associate-r`
4×	`expm1-log1p-u` `sub-neg` `flip3--` `pow-pow` `flip--` `log1p-expm1-u`
3×	`unpow-prod-down` `exp-prod` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
2×	`frac-times` `diff-log` `associate-*r/` `prod-exp` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `pow-to-exp` `pow-unpow` `flip3-+` `div-exp` `pow-prod-down` `associate-l/` `pow-exp` `-commutative` `flip-+` `div-inv` `sqr-pow`

Counts

4 → 143

Calls

4 calls:

5.0ms	(pow (exp a) (* 2 eps))
78.0ms	(* (/ (fma (- 1.0) 1.0 (pow (exp a) (* 2 eps))) (+ (exp (* a eps)) 1.0)) (- (exp (* b eps)) 1.0))
15.0ms	(- (exp (* b eps)) 1.0)
20.0ms	(- (exp (* (+ a b) eps)) 1.0)

series270.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(pow (exp a) (* 2 eps))
149.0ms	(* (/ (fma (- 1.0) 1.0 (pow (exp a) (* 2 eps))) (+ (exp (* a eps)) 1.0)) (- (exp (* b eps)) 1.0))
28.0ms	(- (exp (* b eps)) 1.0)
46.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify83.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	698	2167
1	3039	1774
2	5002	1763

prune722.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 55.5b

regimes272.0ms

Accuracy

23.6% (3.3b remaining)

Error of 59.5b against oracle of 56.3b and baseline of 60.5b

bsearch259.0ms

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	62	59
1	64	59
2	64	59

end0.0ms

sample6.2s

Algorithm

intervals

Results

3.1s	2916×	body	2560	valid
1.8s	3363×	body	1280	valid
292.0ms	921×	body	640	valid
242.0ms	4223×	body	80	overflowed
188.0ms	12226×	pre	80	true
41.0ms	191×	body	320	valid
32.0ms	570×	body	80	valid
6.0ms	42×	body	160	valid