Details

sample48.0ms

Algorithm

intervals

Results

22.0ms	92×	body	1280	valid
7.0ms	43×	body	640	valid
6.0ms	175×	body	80	valid
3.0ms	26×	body	320	valid
1.0ms	8×	body	160	valid

simplify63.0ms

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: 29.1b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
2.2b	(- (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)

series46.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(exp (* a x))
34.0ms	(- (exp (* a x)) 1.0)

simplify83.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (79.0ms)

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

prune99.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.7b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* a x))
0.0b	(pow (- (exp (* a x)) 1.0) 3)
0.0b	(cbrt (pow (- (exp (* a x)) 1.0) 3))
2.2b	(- (exp (* a x)) 1.0)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt` `*-un-lft-identity`
17×	`add-cube-cbrt`
16×	`cbrt-prod`
10×	`unpow-prod-down` `cube-prod`
9×	`prod-diff`
8×	`add-log-exp`
5×	`pow1` `add-exp-log` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
4×	`cube-div` `expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `flip3--` `fma-neg` `flip--`
2×	`cube-mult` `cbrt-div` `unpow3` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `exp-prod` `exp-to-pow` `pow-pow` `pow1/3` `diff-log` `pow-exp` `rem-cbrt-cube` `rem-exp-log` `rem-cube-cbrt`

Counts

4 → 100

Calls

4 calls:

1.0ms	(exp (* a x))
6.0ms	(pow (- (exp (* a x)) 1.0) 3)
9.0ms	(cbrt (pow (- (exp (* a x)) 1.0) 3))
5.0ms	(- (exp (* a x)) 1.0)

series134.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(exp (* a x))
53.0ms	(pow (- (exp (* a x)) 1.0) 3)
33.0ms	(cbrt (pow (- (exp (* a x)) 1.0) 3))
35.0ms	(- (exp (* a x)) 1.0)

simplify47.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	333	721
1	1342	623
2	5001	613

prune219.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (+ (exp (* a x)) 1.0) 3)
0.0b	(cbrt (/ (pow (- (* (exp (* a x)) (exp (* a x))) (* 1.0 1.0)) 3) (pow (+ (exp (* a x)) 1.0) 3)))
0.0b	(* (exp (* a x)) (exp (* a x)))
2.1b	(- (* (exp (* a x)) (exp (* a x))) (* 1.0 1.0))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

202×	`cbrt-prod`
196×	`times-frac`
156×	`*-un-lft-identity`
116×	`unpow-prod-down` `cube-prod`
98×	`add-sqr-sqrt`
96×	`add-cube-cbrt`
30×	`distribute-lft-out`
29×	`cube-mult` `unpow3` `difference-of-squares` `sqr-pow`
18×	`add-log-exp`
12×	`pow1` `exp-prod` `exp-to-pow`
7×	`add-cbrt-cube`
5×	`add-exp-log` `pow-prod-down` `pow-sqr` `pow-prod-up`
4×	`cube-div` `expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `swap-sqr` `associate-r` `associate-l`
2×	`flip3-+` `associate-/r/` `flip-+`
1×	`pow2` `pow-to-exp` `sub-neg` `cbrt-div` `flip3--` `pow-pow` `pow-plus` `fma-neg` `pow1/3` `diff-log` `prod-diff` `pow-exp` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `div-inv` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 298

Calls

4 calls:

6.0ms	(pow (+ (exp (* a x)) 1.0) 3)
30.0ms	(cbrt (/ (pow (- (* (exp (* a x)) (exp (* a x))) (* 1.0 1.0)) 3) (pow (+ (exp (* a x)) 1.0) 3)))
7.0ms	(* (exp (* a x)) (exp (* a x)))
6.0ms	(- (* (exp (* a x)) (exp (* a x))) (* 1.0 1.0))

series170.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(pow (+ (exp (* a x)) 1.0) 3)
69.0ms	(cbrt (/ (pow (- (* (exp (* a x)) (exp (* a x))) (* 1.0 1.0)) 3) (pow (+ (exp (* a x)) 1.0) 3)))
19.0ms	(* (exp (* a x)) (exp (* a x)))
51.0ms	(- (* (exp (* a x)) (exp (* a x))) (* 1.0 1.0))

simplify171.0ms

Algorithm

egg-herbie

Counts

310 → 310

Iterations

Useful iterations: 2 (112.0ms)

Iter	Nodes	Cost
0	801	6255
1	4142	6107
2	5002	6104

prune457.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (/ (pow (- (exp (fma a x (* a x))) (* 1.0 1.0)) 3) (pow (+ (exp (* a x)) 1.0) 3)))
0.0b	(pow (- (exp (fma a x (* a x))) (* 1.0 1.0)) 3)
0.0b	(pow (+ (exp (* a x)) 1.0) 3)
2.1b	(- (exp (fma a x (* a x))) (* 1.0 1.0))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

230×	`cbrt-prod`
224×	`times-frac`
171×	`*-un-lft-identity`
143×	`unpow-prod-down` `cube-prod`
134×	`add-sqr-sqrt`
103×	`add-cube-cbrt`
62×	`difference-of-squares`
34×	`distribute-lft-out`
33×	`exp-sum` `fma-udef`
32×	`cube-mult` `unpow3` `sqr-pow`
6×	`pow1` `add-exp-log` `cube-div` `pow-unpow` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `fma-neg` `prod-diff` `log1p-expm1-u`
2×	`pow-to-exp` `flip3--` `pow-pow` `flip3-+` `pow-exp` `associate-/r/` `flip--` `flip-+` `rem-cube-cbrt`
1×	`sub-neg` `cbrt-div` `pow1/3` `diff-log` `div-inv`

Counts

4 → 325

Calls

4 calls:

27.0ms	(cbrt (/ (pow (- (exp (fma a x (* a x))) (* 1.0 1.0)) 3) (pow (+ (exp (* a x)) 1.0) 3)))
7.0ms	(pow (- (exp (fma a x (* a x))) (* 1.0 1.0)) 3)
6.0ms	(pow (+ (exp (* a x)) 1.0) 3)
6.0ms	(- (exp (fma a x (* a x))) (* 1.0 1.0))

series229.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(cbrt (/ (pow (- (exp (fma a x (* a x))) (* 1.0 1.0)) 3) (pow (+ (exp (* a x)) 1.0) 3)))
69.0ms	(pow (- (exp (fma a x (* a x))) (* 1.0 1.0)) 3)
31.0ms	(pow (+ (exp (* a x)) 1.0) 3)
56.0ms	(- (exp (fma a x (* a x))) (* 1.0 1.0))

simplify170.0ms

Algorithm

egg-herbie

Counts

337 → 337

Iterations

Useful iterations: 2 (111.0ms)

Iter	Nodes	Cost
0	895	6294
1	4633	6107
2	5001	6105

prune544.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.6b

regimes197.0ms

Accuracy

89.8% (2.2b remaining)

Error of 10.2b against oracle of 8.0b and baseline of 29.4b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	33
1	41	33

end0.0ms

sample1.3s

Algorithm

intervals

Results

612.0ms	2746×	body	1280	valid
206.0ms	1339×	body	640	valid
193.0ms	5526×	body	80	valid
80.0ms	739×	body	320	valid
28.0ms	368×	body	160	valid