Details

sample31.0ms

Algorithm

intervals

Results

13.0ms	87×	body	1280	valid
4.0ms	43×	body	640	valid
3.0ms	176×	body	80	valid
2.0ms	27×	body	320	valid
1.0ms	16×	body	160	valid

simplify60.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	3
1	18	3
2	27	3
3	50	3
4	115	3
5	329	3
6	1642	3
7	5001	3

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
3.8b	(- (exp (* a x)) 1.0)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
6×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `exp-prod` `flip3--` `exp-to-pow` `diff-log` `flip--` `rem-exp-log` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

1.0ms	(exp (* a x))
5.0ms	(- (exp (* a x)) 1.0)

series48.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(exp (* a x))
36.0ms	(- (exp (* a x)) 1.0)

simplify80.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (76.0ms)

Iter	Nodes	Cost
0	173	292
1	562	211
2	2710	200
3	5002	164

prune84.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 9.1b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(exp (* a x))
3.8b	(log (exp (- (exp (* a x)) 1.0)))
3.8b	(- (exp (* a x)) 1.0)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`add-cube-cbrt` `prod-diff`
14×	`log-prod`
11×	`exp-sum`
7×	`add-log-exp`
6×	`exp-prod` `log-pow`
4×	`pow1`
3×	`add-exp-log` `expm1-log1p-u` `fma-neg` `add-cbrt-cube` `log1p-expm1-u`
2×	`sub-neg` `distribute-lft-out--` `difference-of-squares`
1×	`log-div` `flip3--` `exp-to-pow` `exp-diff` `diff-log` `rem-log-exp` `flip--` `rem-exp-log`

Counts

3 → 71

Calls

3 calls:

1.0ms	(exp (* a x))
11.0ms	(log (exp (- (exp (* a x)) 1.0)))
5.0ms	(- (exp (* a x)) 1.0)

series82.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(exp (* a x))
38.0ms	(log (exp (- (exp (* a x)) 1.0)))
32.0ms	(- (exp (* a x)) 1.0)

simplify92.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 3 (86.0ms)

Iter	Nodes	Cost
0	236	562
1	667	396
2	2936	322
3	5002	304

prune141.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 9.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (sqrt (exp (* a x))) (sqrt 1.0)) (- (sqrt (exp (* a x))) (sqrt 1.0)))
0.0b	(exp (* a x))
0.0b	(exp (* a x))
3.9b	(- (sqrt (exp (* a x))) (sqrt 1.0))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

125×	`sqrt-prod`
108×	`prod-diff`
98×	`add-sqr-sqrt`
92×	`*-un-lft-identity`
80×	`add-cube-cbrt`
38×	`distribute-rgt-in` `distribute-lft-in`
10×	`add-log-exp`
9×	`associate-r`
8×	`difference-of-squares`
6×	`pow1` `add-exp-log` `fma-neg` `add-cbrt-cube`
5×	`associate-l`
4×	`expm1-log1p-u` `frac-times` `flip3--` `flip--` `log1p-expm1-u` `distribute-lft-out--`
3×	`sub-neg` `flip3-+` `flip-+`
2×	`exp-prod` `exp-to-pow` `associate-r/` `associate-l/` `rem-exp-log` `distribute-lft-out`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 198

Calls

4 calls:

55.0ms	(* (+ (sqrt (exp (* a x))) (sqrt 1.0)) (- (sqrt (exp (* a x))) (sqrt 1.0)))
1.0ms	(exp (* a x))
1.0ms	(exp (* a x))
9.0ms	(- (sqrt (exp (* a x))) (sqrt 1.0))

series203.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(* (+ (sqrt (exp (* a x))) (sqrt 1.0)) (- (sqrt (exp (* a x))) (sqrt 1.0)))
12.0ms	(exp (* a x))
12.0ms	(exp (* a x))
59.0ms	(- (sqrt (exp (* a x))) (sqrt 1.0))

simplify90.0ms

Algorithm

egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	625	4271
1	2811	3125
2	5002	2822

prune287.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 9.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
9.8b	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
17.5b	(* (pow a 2) (pow x 2))
20.7b	(* (pow a 3) (pow x 3))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
32×	`unswap-sqr`
28×	`add-exp-log` `unpow-prod-down`
20×	`associate-r` `associate-l` `sqr-pow`
18×	`prod-exp`
14×	`add-cube-cbrt` `*-un-lft-identity` `cube-prod`
12×	`pow-to-exp` `pow-exp`
10×	`unpow2`
8×	`add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cube-mult` `unpow3` `pow-prod-down` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 134

Calls

4 calls:

0.0ms	(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
0.0ms	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
9.0ms	(* (pow a 2) (pow x 2))
14.0ms	(* (pow a 3) (pow x 3))

series304.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
102.0ms	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
30.0ms	(* (pow a 2) (pow x 2))
65.0ms	(* (pow a 3) (pow x 3))

simplify80.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	369	802
1	1845	699
2	5001	656

prune339.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 5.3b

regimes182.0ms

Accuracy

96% (0.9b remaining)

Error of 5.4b against oracle of 4.5b and baseline of 26.9b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	14
1	23	14

end0.0ms

sample885.0ms

Algorithm

intervals

Results

415.0ms	2689×	body	1280	valid
122.0ms	1271×	body	640	valid
101.0ms	5525×	body	80	valid
48.0ms	760×	body	320	valid
18.0ms	433×	body	160	valid