Details

sample220.0ms

Algorithm

intervals

Results

68.0ms	67×	body	2560	valid
60.0ms	116×	body	1280	valid
53.0ms	55×	body	10240	exit
12.0ms	42×	body	640	valid
5.0ms	311×	pre	80	true
2.0ms	11×	body	320	valid
1.0ms	17×	body	80	valid
0.0ms	3×	body	160	valid

simplify103.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
3.0b	(- (exp (* b eps)) 1.0)
3.0b	(- (exp (* a eps)) 1.0)
5.1b	(- (exp (* (+ a b) eps)) 1.0)

rewrite123.0ms

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:

75.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
14.0ms	(- (exp (* b eps)) 1.0)
14.0ms	(- (exp (* a eps)) 1.0)
15.0ms	(- (exp (* (+ a b) eps)) 1.0)

series149.0ms

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)
35.0ms	(- (exp (* a eps)) 1.0)
42.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify67.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (48.0ms)

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

prune715.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 47.0b

localize27.0ms

Local error

Found 4 expressions with local error:

3.6b	(fma 1/6 (* (pow a 3) (pow eps 3)) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps)))
5.1b	(- (exp (* (+ a b) eps)) 1.0)
16.0b	(* (pow a 2) (pow eps 2))
17.2b	(* (pow a 3) (pow eps 3))

rewrite58.0ms

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:

0.0ms	(fma 1/6 (* (pow a 3) (pow eps 3)) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps)))
15.0ms	(- (exp (* (+ a b) eps)) 1.0)
18.0ms	(* (pow a 2) (pow eps 2))
19.0ms	(* (pow a 3) (pow eps 3))

series226.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(fma 1/6 (* (pow a 3) (pow eps 3)) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps)))
41.0ms	(- (exp (* (+ a b) eps)) 1.0)
29.0ms	(* (pow a 2) (pow eps 2))
62.0ms	(* (pow a 3) (pow eps 3))

simplify93.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (76.0ms)

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

prune1.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 46.5b

localize20.0ms

Local error

Found 4 expressions with local error:

2.6b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps)) (- (exp (* b eps)) 1.0)))
3.0b	(- (exp (* b eps)) 1.0)
5.1b	(- (exp (* (+ a b) eps)) 1.0)
16.0b	(* (pow a 2) (pow eps 2))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
28×	`add-exp-log`
26×	`*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`prod-diff` `add-cbrt-cube`
16×	`unswap-sqr`
14×	`unpow-prod-down`
13×	`prod-exp`
10×	`unpow2` `sqr-pow`
8×	`associate-r` `associate-l` `add-log-exp`
6×	`pow-to-exp` `fma-neg` `pow-exp`
5×	`cbrt-unprod`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `flip3--` `associate-*r/` `div-exp` `flip--` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`frac-2neg` `times-frac` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l*`

Counts

4 → 136

Calls

4 calls:

43.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps)) (- (exp (* b eps)) 1.0)))
16.0ms	(- (exp (* b eps)) 1.0)
15.0ms	(- (exp (* (+ a b) eps)) 1.0)
17.0ms	(* (pow a 2) (pow eps 2))

series670.0ms

Counts

4 → 12

Calls

4 calls:

564.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps)) (- (exp (* b eps)) 1.0)))
34.0ms	(- (exp (* b eps)) 1.0)
42.0ms	(- (exp (* (+ a b) eps)) 1.0)
30.0ms	(* (pow a 2) (pow eps 2))

simplify95.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	725	1617
1	3666	1202
2	5003	1193

prune842.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ (/ 1 b) (/ 1 a))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
15×	`times-frac`
13×	`fma-def`
10×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`distribute-lft-out`
5×	`div-inv`
3×	`add-log-exp`
1×	`pow1` `add-exp-log` `+-commutative` `expm1-log1p-u` `flip3-+` `frac-add` `sum-log` `add-cbrt-cube` `flip-+` `log1p-expm1-u`

Counts

1 → 34

Calls

1 calls:

23.0ms

(+ (/ 1 b) (/ 1 a))

series10.0ms

Counts

1 → 3

Calls

1 calls:

10.0ms

(+ (/ 1 b) (/ 1 a))

simplify68.0ms

Algorithm

egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	107	112
1	368	101
2	1274	98
3	3144	98
4	5001	98

prune81.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes86.0ms

Accuracy

0% (3.6b remaining)

Error of 3.7b against oracle of 0.1b and baseline of 3.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	3
1	9	3

end0.0ms

sample7.2s

Algorithm

intervals

Results

2.5s	2488×	body	2560	valid
1.9s	2030×	body	10240	exit
1.9s	3499×	body	1280	valid
311.0ms	1030×	body	640	valid
160.0ms	10034×	pre	80	true
74.0ms	369×	body	320	valid
30.0ms	496×	body	80	valid
16.0ms	122×	body	160	valid