Details

sample64.0ms

Algorithm

intervals

Results

40.0ms	215×	body	10240	exit
6.0ms	201×	body	80	valid
2.0ms	17×	body	640	valid
2.0ms	22×	body	320	valid
1.0ms	18×	body	160	valid

simplify50.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (8.0ms)

Iter	Nodes	Cost
0	21	9
1	52	9
2	113	9
3	240	8
4	1625	8
5	5001	8

prune6.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 13.5b

Counts

2 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ wj 1))
0.0b	(/ wj (+ wj 1))
0.0b	(/ (/ x (+ wj 1)) (exp wj))
5.7b	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

243×	`*-un-lft-identity`
175×	`times-frac`
135×	`add-sqr-sqrt`
130×	`add-cube-cbrt`
72×	`prod-diff`
55×	`distribute-lft-out`
33×	`associate-/l*`
23×	`associate-/r*`
20×	`flip3-+` `associate-/r/` `frac-sub` `flip-+`
16×	`add-exp-log`
13×	`add-cbrt-cube`
11×	`div-inv`
10×	`associate-/l/`
9×	`add-log-exp`
8×	`div-exp`
6×	`frac-2neg` `clear-num`
5×	`cbrt-undiv`
4×	`pow1` `expm1-log1p-u` `fma-neg` `log1p-expm1-u`
2×	`diff-log` `associate--l+` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `sub-neg` `flip3--` `sum-log` `flip--`

Counts

4 → 290

Calls

4 calls:

5.0ms	(/ x (+ wj 1))
5.0ms	(/ wj (+ wj 1))
11.0ms	(/ (/ x (+ wj 1)) (exp wj))
40.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

series158.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ x (+ wj 1))
28.0ms	(/ wj (+ wj 1))
42.0ms	(/ (/ x (+ wj 1)) (exp wj))
64.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

simplify78.0ms

Algorithm

egg-herbie

Counts

302 → 302

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1184	4862
1	5001	4114

prune476.0ms

Filtered

302 candidates to 184 candidates (60.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	297	5	302
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	299	5	304

Merged error: 0.2b

Counts

304 → 5

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (pow wj 2))
0.0b	(- (+ x (pow wj 2)) (* 2 (* wj x)))
0.0b	(* 2 (* wj x))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

109×	`*-un-lft-identity`
95×	`add-sqr-sqrt`
88×	`prod-diff`
75×	`associate-r`
51×	`add-cube-cbrt`
32×	`associate-l`
26×	`distribute-lft-out`
23×	`unswap-sqr`
10×	`*-commutative` `add-log-exp`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`fma-neg` `distribute-lft-out--`
3×	`expm1-log1p-u` `fma-def` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `difference-of-squares`
2×	`+-commutative` `diff-log` `associate--l+` `sum-log`
1×	`sub-neg` `flip3--` `flip3-+` `flip--` `flip-+`

Counts

3 → 166

Calls

3 calls:

8.0ms	(+ x (pow wj 2))
18.0ms	(- (+ x (pow wj 2)) (* 2 (* wj x)))
8.0ms	(* 2 (* wj x))

series90.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(+ x (pow wj 2))
32.0ms	(- (+ x (pow wj 2)) (* 2 (* wj x)))
21.0ms	(* 2 (* wj x))

simplify97.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	633	2426
1	2483	1671
2	5002	1458

prune176.0ms

Filtered

175 candidates to 74 candidates (42.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	173	2	175
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	174	6	180

Merged error: 0.1b

Counts

180 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2)
1.0b	(cbrt 2)
1.0b	(cbrt 2)
1.0b	(cbrt 2)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

1.0ms	(cbrt 2)
1.0ms	(cbrt 2)
1.0ms	(cbrt 2)
2.0ms	(cbrt 2)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(cbrt 2)
0.0ms	(cbrt 2)
0.0ms	(cbrt 2)
0.0ms	(cbrt 2)

simplify184.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 4 (180.0ms)

Iter	Nodes	Cost
0	57	232
1	179	200
2	763	156
3	3612	140
4	5001	136

prune163.0ms

Filtered

56 candidates to 49 candidates (87.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	56	0	56
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	56	6	62

Merged error: 0.1b

Counts

62 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ wj (+ wj 1))
0.0b	(* (/ x (+ (pow wj 3) 1)) (/ (+ (* wj wj) (- 1 (* wj 1))) (exp wj)))
0.0b	(/ (+ (* wj wj) (- 1 (* wj 1))) (exp wj))
5.7b	(- (+ (* (/ x (+ (pow wj 3) 1)) (/ (+ (* wj wj) (- 1 (* wj 1))) (exp wj))) wj) (/ wj (+ wj 1)))

rewrite243.0ms

Algorithm

rewrite-expression-head

Rules

944×	`*-un-lft-identity`
316×	`distribute-lft-out`
274×	`associate-/l*`
230×	`frac-times`
210×	`add-sqr-sqrt`
193×	`add-cube-cbrt`
190×	`associate-l`
179×	`times-frac`
144×	`associate-/r*`
117×	`distribute-lft-out--`
90×	`prod-diff`
87×	`associate-r`
76×	`distribute-rgt-out--`
40×	`clear-num`
39×	`frac-2neg` `*-commutative`
29×	`flip3-+` `flip-+`
26×	`add-exp-log`
24×	`associate-/l/`
23×	`associate-*r/`
20×	`frac-sub` `add-cbrt-cube`
14×	`associate-/r/` `un-div-inv`
10×	`div-exp` `associate-*l/`
9×	`div-inv` `add-log-exp`
6×	`pow1` `cbrt-undiv` `prod-exp`
5×	`fma-neg`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `unswap-sqr`
2×	`diff-log` `associate--l+` `difference-of-squares`
1×	`+-commutative` `associate-+r-` `sub-neg` `flip3--` `div-sub` `pow-prod-down` `sum-log` `flip--`

Counts

4 → 622

Calls

4 calls:

5.0ms	(/ wj (+ wj 1))
60.0ms	(* (/ x (+ (pow wj 3) 1)) (/ (+ (* wj wj) (- 1 (* wj 1))) (exp wj)))
34.0ms	(/ (+ (* wj wj) (- 1 (* wj 1))) (exp wj))
97.0ms	(- (+ (* (/ x (+ (pow wj 3) 1)) (/ (+ (* wj wj) (- 1 (* wj 1))) (exp wj))) wj) (/ wj (+ wj 1)))

series516.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ wj (+ wj 1))
94.0ms	(* (/ x (+ (pow wj 3) 1)) (/ (+ (* wj wj) (- 1 (* wj 1))) (exp wj)))
24.0ms	(/ (+ (* wj wj) (- 1 (* wj 1))) (exp wj))
376.0ms	(- (+ (* (/ x (+ (pow wj 3) 1)) (/ (+ (* wj wj) (- 1 (* wj 1))) (exp wj))) wj) (/ wj (+ wj 1)))

simplify157.0ms

Algorithm

egg-herbie

Counts

634 → 634

Iterations

Useful iterations: 1 (47.0ms)

Iter	Nodes	Cost
0	1924	10767
1	5002	9756

prune847.0ms

Filtered

634 candidates to 240 candidates (37.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	633	1	634
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	635	5	640

Merged error: 0.1b

Counts

640 → 5

regimes55.0ms

Accuracy

64.9% (0.6b remaining)

Error of 0.9b against oracle of 0.3b and baseline of 2.0b

bsearch47.0ms

Steps

Iters	Range		Point
8	4.134031166731471e-11	1.0482644148039984e-06	6.662618440192689e-09

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	55	50
1	59	50
2	59	50

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.4s	7625×	body	10240	exit
187.0ms	6235×	body	80	valid
75.0ms	503×	body	640	valid
71.0ms	787×	body	320	valid
34.0ms	575×	body	160	valid