Details

sample80.0ms

Algorithm

intervals

Results

20.0ms	108×	body	2560	nan
16.0ms	489×	body	80	nan
10.0ms	65×	body	1280	nan
10.0ms	256×	body	80	valid
4.0ms	31×	body	640	nan
2.0ms	23×	body	320	nan
1.0ms	13×	body	160	nan

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	9
1	11	9

prune2.0ms

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: 30.6b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (sqrt (- (* x x) 1.0)))
0.2b	(log (+ x (sqrt (- (* x x) 1.0))))
28.5b	(sqrt (- (* x x) 1.0))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
7×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `add-log-exp`
4×	`add-exp-log` `log-prod` `sqrt-prod`
3×	`add-cbrt-cube`
2×	`log-div` `flip3-+` `sqrt-div` `flip-+` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log` `log-pow` `flip--` `difference-of-squares`

Counts

3 → 43

Calls

3 calls:

6.0ms	(+ x (sqrt (- (* x x) 1.0)))
6.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
4.0ms	(sqrt (- (* x x) 1.0))

series18.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ x (sqrt (- (* x x) 1.0)))
10.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
4.0ms	(sqrt (- (* x x) 1.0))

simplify63.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4948	610
1	4948	610

prune92.0ms

Filtered

43 candidates to 52 candidates (-20.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	50	3	53

Merged error: 0b

Counts

53 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (log x) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x))))
0.2b	(+ (log 2) (- (log x) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))))
0.3b	(/ 0.09375 (pow x 4))
0.6b	(/ 0.25 (* x x))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
25×	`add-cube-cbrt`
24×	`times-frac`
16×	`distribute-lft-out`
15×	`pow1`
14×	`add-exp-log`
12×	`unpow-prod-down` `distribute-lft-out--`
11×	`log-pow` `add-cbrt-cube` `add-log-exp`
9×	`log-prod`
8×	`associate-/r*`
6×	`associate--l+` `associate-/l*`
5×	`associate-+r+` `div-exp` `sum-log`
4×	`diff-log` `sqr-pow`
3×	`cbrt-undiv` `associate-+l+`
2×	`sub-neg` `frac-2neg` `clear-num` `div-inv`
1×	`+-commutative` `pow-to-exp` `associate-+r-` `flip3--` `flip3-+` `pow-exp` `prod-exp` `flip--` `cbrt-unprod` `flip-+` `associate--r+` `difference-of-squares`

Counts

4 → 120

Calls

4 calls:

17.0ms	(- (log x) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x))))
20.0ms	(+ (log 2) (- (log x) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))))
4.0ms	(/ 0.09375 (pow x 4))
5.0ms	(/ 0.25 (* x x))

series25.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (log x) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x))))
12.0ms	(+ (log 2) (- (log x) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))))
3.0ms	(/ 0.09375 (pow x 4))
3.0ms	(/ 0.25 (* x x))

simplify58.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4968	1655
1	4968	1655

prune192.0ms

Filtered

84 candidates to 132 candidates (-57.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	132	3	135

Merged error: 0b

Counts

135 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.0b	(sqrt (+ x (sqrt 1.0)))
0.2b	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
0.5b	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`sqrt-prod`
16×	`*-un-lft-identity`
14×	`sqrt-div`
10×	`pow1` `add-cube-cbrt`
9×	`associate-r`
7×	`add-exp-log` `associate-l`
6×	`flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
4×	`frac-times` `unswap-sqr`
3×	`log-prod` `flip3--` `sqrt-pow1` `pow1/2` `pow-prod-down` `flip--`
2×	`log-div` `associate-r/` `associate-l/` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `rem-sqrt-square` `sqrt-unprod` `rem-log-exp` `prod-exp` `sum-log` `log-pow` `*-commutative` `cbrt-unprod` `distribute-lft-out--`

Counts

4 → 83

Calls

4 calls:

2.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
4.0ms	(sqrt (+ x (sqrt 1.0)))
2.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
12.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series38.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
4.0ms	(sqrt (+ x (sqrt 1.0)))
13.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
13.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify45.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5198	1470

prune196.0ms

Filtered

72 candidates to 95 candidates (-31.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	95	3	98

Merged error: 0b

Counts

98 → 3

regimes90.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	17
1	16	17

end0.0ms

sample2.5s

Algorithm

intervals

Results

552.0ms	2942×	body	2560	nan
533.0ms	16308×	body	80	nan
397.0ms	2530×	body	1280	nan
312.0ms	8000×	body	80	valid
153.0ms	1241×	body	640	nan
62.0ms	648×	body	320	nan
21.0ms	305×	body	160	nan

Details

sample80.0ms

simplify3.0ms

prune2.0ms

localize9.0ms

rewrite16.0ms

series18.0ms

simplify63.0ms

prune92.0ms

localize13.0ms

rewrite50.0ms

series25.0ms

simplify58.0ms

prune192.0ms

localize10.0ms

rewrite23.0ms

series38.0ms

simplify45.0ms

prune196.0ms

regimes90.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.5s

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