Details

sample248.0ms

Algorithm

intervals

Results

84.0ms	85×	body	2560	valid
70.0ms	71×	body	10240	exit
59.0ms	116×	body	1280	valid
8.0ms	327×	pre	80	true
7.0ms	25×	body	640	valid
2.0ms	8×	body	320	valid
1.0ms	17×	body	80	valid
1.0ms	5×	body	160	valid

simplify99.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
1.9b	(- (exp (* a eps)) 1.0)
3.4b	(- (exp (* b eps)) 1.0)
4.0b	(- (exp (* (+ a b) eps)) 1.0)

rewrite30.0ms

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:

11.0ms	(* (- (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)

series164.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
36.0ms	(- (exp (* a eps)) 1.0)
31.0ms	(- (exp (* b eps)) 1.0)
49.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify66.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (52.0ms)

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

prune459.0ms

Filtered

150 candidates to 91 candidates (60.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 48.0b

localize28.0ms

Local error

Found 4 expressions with local error:

4.0b	(- (exp (* (+ a b) eps)) 1.0)
4.3b	(fma 1/6 (* (pow a 3) (pow eps 3)) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps)))
13.1b	(* (pow a 2) (pow eps 2))
13.7b	(* (pow a 3) (pow eps 3))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
32×	`unswap-sqr`
28×	`add-exp-log` `unpow-prod-down`
23×	`*-un-lft-identity`
21×	`add-cube-cbrt`
20×	`associate-r` `associate-l` `sqr-pow`
18×	`prod-exp`
14×	`cube-prod`
12×	`pow-to-exp` `pow-exp`
10×	`unpow2`
9×	`prod-diff`
8×	`add-cbrt-cube`
6×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg`
2×	`cube-mult` `unpow3` `pow-prod-down` `*-commutative` `cbrt-unprod`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `fma-udef` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 152

Calls

4 calls:

5.0ms	(- (exp (* (+ a b) eps)) 1.0)
1.0ms	(fma 1/6 (* (pow a 3) (pow eps 3)) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps)))
7.0ms	(* (pow a 2) (pow eps 2))
9.0ms	(* (pow a 3) (pow eps 3))

series242.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (exp (* (+ a b) eps)) 1.0)
100.0ms	(fma 1/6 (* (pow a 3) (pow eps 3)) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps)))
35.0ms	(* (pow a 2) (pow eps 2))
61.0ms	(* (pow a 3) (pow eps 3))

simplify89.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	484	1008
1	2207	829
2	5001	783

prune628.0ms

Filtered

164 candidates to 89 candidates (54.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 48.0b

localize29.0ms

Local error

Found 4 expressions with local error:

3.9b	(* (- (exp (* a eps)) 1.0) (fma 1/6 (* (pow eps 3) (pow b 3)) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b))))
4.0b	(- (exp (* (+ a b) eps)) 1.0)
16.8b	(* (pow eps 2) (pow b 2))
17.5b	(* (pow eps 3) (pow b 3))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-sqr-sqrt`
33×	`unswap-sqr`
30×	`add-exp-log`
28×	`unpow-prod-down`
27×	`*-un-lft-identity`
25×	`associate-l`
23×	`add-cube-cbrt` `associate-r`
20×	`sqr-pow`
19×	`prod-exp`
14×	`cube-prod`
12×	`pow-to-exp` `pow-exp`
10×	`add-cbrt-cube` `unpow2`
9×	`prod-diff`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `pow-prod-down` `*-commutative` `cbrt-unprod`
2×	`cube-mult` `flip3--` `unpow3` `associate-*l/` `flip--` `fma-udef` `distribute-lft-out--` `difference-of-squares`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `diff-log`

Counts

4 → 168

Calls

4 calls:

7.0ms	(* (- (exp (* a eps)) 1.0) (fma 1/6 (* (pow eps 3) (pow b 3)) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b))))
5.0ms	(- (exp (* (+ a b) eps)) 1.0)
7.0ms	(* (pow eps 2) (pow b 2))
9.0ms	(* (pow eps 3) (pow b 3))

series361.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(* (- (exp (* a eps)) 1.0) (fma 1/6 (* (pow eps 3) (pow b 3)) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b))))
50.0ms	(- (exp (* (+ a b) eps)) 1.0)
31.0ms	(* (pow eps 2) (pow b 2))
67.0ms	(* (pow eps 3) (pow b 3))

simplify107.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	623	1418
1	3157	1159
2	5001	1149

prune739.0ms

Filtered

180 candidates to 98 candidates (54.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 47.2b

localize33.0ms

Local error

Found 4 expressions with local error:

4.0b	(- (exp (* (+ a b) eps)) 1.0)
4.5b	(* (pow eps 3) b)
5.0b	(* (* (pow eps 3) b) b)
16.8b	(* (pow eps 2) (pow b 2))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
31×	`add-exp-log`
22×	`*-un-lft-identity`
21×	`associate-l`
20×	`add-cube-cbrt` `unswap-sqr`
19×	`prod-exp`
18×	`unpow-prod-down`
14×	`associate-r`
13×	`add-cbrt-cube`
12×	`sqr-pow`
10×	`unpow2`
9×	`prod-diff`
8×	`pow-to-exp` `pow-exp`
6×	`pow1` `add-log-exp`
5×	`cbrt-unprod`
4×	`expm1-log1p-u` `cube-prod` `log1p-expm1-u`
3×	`fma-neg` `*-commutative`
2×	`pow-prod-down`
1×	`cube-mult` `sub-neg` `flip3--` `diff-log` `unpow3` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 135

Calls

4 calls:

5.0ms	(- (exp (* (+ a b) eps)) 1.0)
6.0ms	(* (pow eps 3) b)
6.0ms	(* (* (pow eps 3) b) b)
8.0ms	(* (pow eps 2) (pow b 2))

series148.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (exp (* (+ a b) eps)) 1.0)
27.0ms	(* (pow eps 3) b)
40.0ms	(* (* (pow eps 3) b) b)
35.0ms	(* (pow eps 2) (pow b 2))

simplify76.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	455	771
1	2073	604
2	5002	589

prune607.0ms

Filtered

147 candidates to 82 candidates (55.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 46.8b

regimes251.0ms

Accuracy

54.9% (4.0b remaining)

Error of 52.2b against oracle of 48.3b and baseline of 57.1b

bsearch316.0ms

Steps

Iters	Range		Point
9	6.938439791906156e+55	1.079661997625702e+62	1.3999991042422356e+60
8	-9.35438154110346e+67	-2.1954737652864763e+65	-2.8033747794466244e+65

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	41
1	60	41

end0.0ms

sample6.8s

Algorithm

intervals

Results

2.5s	2563×	body	2560	valid
1.7s	1983×	body	10240	exit
1.7s	3429×	body	1280	valid
292.0ms	1070×	body	640	valid
169.0ms	9984×	pre	80	true
65.0ms	351×	body	320	valid
24.0ms	457×	body	80	valid
15.0ms	131×	body	160	valid