Details

sample211.0ms

Algorithm

intervals

Results

64.0ms	72×	body	2560	valid
58.0ms	69×	body	10240	exit
55.0ms	114×	body	1280	valid
10.0ms	41×	body	640	valid
5.0ms	325×	pre	80	true
2.0ms	9×	body	320	valid
1.0ms	16×	body	80	valid
0.0ms	4×	body	160	valid

simplify102.0ms

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: 59.9b

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
3.4b	(- (exp (* b eps)) 1.0)
4.0b	(- (exp (* a eps)) 1.0)
6.0b	(- (exp (* (+ a b) eps)) 1.0)

rewrite29.0ms

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:

10.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
4.0ms	(- (exp (* b eps)) 1.0)
5.0ms	(- (exp (* a eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)

series166.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
30.0ms	(- (exp (* b eps)) 1.0)
33.0ms	(- (exp (* a eps)) 1.0)
51.0ms	(- (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

prune474.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 48.2b

localize27.0ms

Local error

Found 4 expressions with local error:

3.4b	(- (exp (* b eps)) 1.0)
6.0b	(- (exp (* (+ a b) eps)) 1.0)
15.9b	(* (pow a 2) (pow eps 2))
16.0b	(* (pow a 3) (pow eps 3))

rewrite31.0ms

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:

4.0ms	(- (exp (* b eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)
7.0ms	(* (pow a 2) (pow eps 2))
9.0ms	(* (pow a 3) (pow eps 3))

series179.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (exp (* b eps)) 1.0)
45.0ms	(- (exp (* (+ a b) eps)) 1.0)
37.0ms	(* (pow a 2) (pow eps 2))
66.0ms	(* (pow a 3) (pow eps 3))

simplify96.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (78.0ms)

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

prune922.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 47.7b

localize26.0ms

Local error

Found 4 expressions with local error:

3.1b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma 1/6 (pow (* eps a) 3) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0)))
3.4b	(- (exp (* b eps)) 1.0)
6.0b	(- (exp (* (+ a b) eps)) 1.0)
15.9b	(* (pow a 2) (pow eps 2))

rewrite37.0ms

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:

15.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma 1/6 (pow (* eps a) 3) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0)))
5.0ms	(- (exp (* b eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)
7.0ms	(* (pow a 2) (pow eps 2))

series862.0ms

Counts

4 → 12

Calls

4 calls:

748.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma 1/6 (pow (* eps a) 3) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0)))
36.0ms	(- (exp (* b eps)) 1.0)
45.0ms	(- (exp (* (+ a b) eps)) 1.0)
32.0ms	(* (pow a 2) (pow eps 2))

simplify99.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	732	1665
1	3649	1263
2	5002	1252

prune603.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite17.0ms

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:

15.0ms

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

series11.0ms

Counts

1 → 3

Calls

1 calls:

11.0ms

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

simplify70.0ms

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

prune69.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

regimes78.0ms

Accuracy

0% (3.2b remaining)

Error of 3.3b against oracle of 0.1b and baseline of 3.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	3
1	9	3

end0.0ms

sample6.7s

Algorithm

intervals

Results

2.5s	2549×	body	2560	valid
1.7s	1938×	body	10240	exit
1.7s	3451×	body	1280	valid
283.0ms	1070×	body	640	valid
159.0ms	9938×	pre	80	true
64.0ms	350×	body	320	valid
23.0ms	441×	body	80	valid
16.0ms	139×	body	160	valid