Details

sample110.0ms

Algorithm

intervals

Results

34.0ms	62×	body	1280	valid
31.0ms	360×	body	80	valid
13.0ms	38×	body	640	valid
5.0ms	70×	body	80	overflowed
5.0ms	22×	body	320	valid
1.0ms	8×	body	160	valid

simplify36.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (34.0ms)

Iter	Nodes	Cost
0	46	16
1	122	16
2	347	16
3	1295	16
4	5001	15

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 30.7b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
0.0b	(exp (* (- 1.0 eps) x))
0.0b	(exp (* (+ 1.0 eps) x))
2.4b	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

99×	`*-un-lft-identity`
84×	`times-frac`
59×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
22×	`distribute-lft-out--`
14×	`add-log-exp`
10×	`distribute-lft-out`
9×	`difference-of-squares`
6×	`add-cbrt-cube`
5×	`add-exp-log`
4×	`pow1` `exp-to-pow` `associate-/l*`
3×	`associate-/r*` `div-inv`
2×	`exp-prod` `diff-log` `div-sub` `rem-exp-log` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `flip3--` `distribute-rgt-out--` `frac-2neg` `flip3-+` `div-exp` `clear-num` `sum-log` `frac-sub` `flip--` `flip-+` `sub-div` `associate--r-`

Counts

4 → 96

Calls

4 calls:

10.0ms	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
3.0ms	(exp (* (- 1.0 eps) x))
3.0ms	(exp (* (+ 1.0 eps) x))
138.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series75.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
4.0ms	(exp (* (- 1.0 eps) x))
4.0ms	(exp (* (+ 1.0 eps) x))
55.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

simplify44.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	458	1482
1	1346	1407
2	5001	1383

prune247.0ms

Filtered

77 candidates to 108 candidates (-40.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	104	4	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	4	109

Merged error: 0.3b

Counts

109 → 4

localize7.0ms

Local error

Found 1 expressions with local error:

0.1b	(* (pow x 2) (- (* x 0.33333333333333337) 0.5))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`associate-l`
6×	`add-exp-log`
4×	`add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity` `unswap-sqr`
3×	`associate-r` `prod-exp` `add-cbrt-cube`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*r/` `unpow2` `sqr-pow`
1×	`pow1` `pow-to-exp` `flip3--` `pow-exp` `*-commutative` `flip--` `cbrt-unprod` `add-log-exp`

Counts

1 → 33

Calls

1 calls:

7.0ms

(* (pow x 2) (- (* x 0.33333333333333337) 0.5))

series7.0ms

Counts

1 → 3

Calls

1 calls:

7.0ms

(* (pow x 2) (- (* x 0.33333333333333337) 0.5))

simplify159.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	158	214
1	638	189
2	4553	189
3	5001	189

prune55.0ms

Filtered

22 candidates to 36 candidates (-63.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	35	1	36
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	36	4	40

Merged error: 0.3b

Counts

40 → 4

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (pow x 2) (- (* x 0.33333333333333337) 0.5))
2.4b	(log (exp (* (pow x 2) (- (* x 0.33333333333333337) 0.5))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`associate-l`
7×	`add-exp-log` `log-prod`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`distribute-rgt-in` `sub-neg` `unpow-prod-down` `distribute-lft-in` `exp-sum` `add-cbrt-cube` `unswap-sqr`
3×	`pow1` `associate-r` `prod-exp` `log-pow` `add-log-exp`
2×	`associate-*r/` `unpow2` `sqr-pow`
1×	`pow-to-exp` `exp-prod` `flip3--` `exp-to-pow` `rem-log-exp` `pow-exp` `*-commutative` `flip--` `cbrt-unprod`

Counts

2 → 51

Calls

2 calls:

7.0ms	(* (pow x 2) (- (* x 0.33333333333333337) 0.5))
2.0ms	(log (exp (* (pow x 2) (- (* x 0.33333333333333337) 0.5))))

series14.0ms

Counts

2 → 6

Calls

2 calls:

7.0ms	(* (pow x 2) (- (* x 0.33333333333333337) 0.5))
7.0ms	(log (exp (* (pow x 2) (- (* x 0.33333333333333337) 0.5))))

simplify169.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	191	345
1	701	301
2	4708	301
3	5001	301

prune87.0ms

Filtered

35 candidates to 57 candidates (-62.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	56	1	57
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	56	5	61

Merged error: 0.3b

Counts

61 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (exp (* (pow x 2) (- (* x 0.33333333333333337) 0.5))))
0.1b	(cbrt (exp (* (pow x 2) (- (* x 0.33333333333333337) 0.5))))
2.2b	(log (cbrt (exp (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))))
2.2b	(log (cbrt (exp (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
20×	`log-prod`
16×	`exp-sum`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
6×	`pow1` `add-exp-log`
4×	`pow1/3` `log-pow` `add-cbrt-cube` `add-log-exp`
2×	`rem-log-exp`

Counts

4 → 70

Calls

4 calls:

2.0ms	(cbrt (exp (* (pow x 2) (- (* x 0.33333333333333337) 0.5))))
2.0ms	(cbrt (exp (* (pow x 2) (- (* x 0.33333333333333337) 0.5))))
3.0ms	(log (cbrt (exp (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))))
3.0ms	(log (cbrt (exp (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))))

series127.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt (exp (* (pow x 2) (- (* x 0.33333333333333337) 0.5))))
24.0ms	(cbrt (exp (* (pow x 2) (- (* x 0.33333333333333337) 0.5))))
37.0ms	(log (cbrt (exp (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))))
41.0ms	(log (cbrt (exp (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))))

simplify49.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (40.0ms)

Iter	Nodes	Cost
0	138	838
1	376	760
2	1185	750
3	5001	734

prune215.0ms

Filtered

60 candidates to 82 candidates (-36.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	80	2	82
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	81	6	87

Merged error: 0.3b

Counts

87 → 6

regimes132.0ms

Accuracy

96.3% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.7b

bsearch102.0ms

Steps

Iters	Range		Point
10	2.4879688186424768e-05	51082621280221.5	13.335055754899628

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	33
1	42	33

end0.0ms

sample3.0s

Algorithm

intervals

Results

953.0ms	1729×	body	1280	valid
783.0ms	10127×	body	80	valid
436.0ms	1259×	body	640	valid
155.0ms	654×	body	320	valid
145.0ms	1911×	body	80	overflowed
47.0ms	314×	body	160	valid

Details

sample110.0ms

simplify36.0ms

prune8.0ms

localize16.0ms

rewrite158.0ms

series75.0ms

simplify44.0ms

prune247.0ms

localize7.0ms

rewrite8.0ms

series7.0ms

simplify159.0ms

prune55.0ms

localize9.0ms

rewrite11.0ms

series14.0ms

simplify169.0ms

prune87.0ms

localize12.0ms

rewrite12.0ms

series127.0ms

simplify49.0ms

prune215.0ms

regimes132.0ms

bsearch102.0ms

simplify1.0ms

end0.0ms

sample3.0s

Profiling