Details

sample46.0ms

Algorithm

intervals

Results

11.0ms	200×	body	80	valid
8.0ms	24×	body	2560	valid
5.0ms	256×	pre	80	true
4.0ms	15×	body	1280	valid
2.0ms	10×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	17
1	38	17

prune6.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 12.1b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.2b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.3b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
20×	`add-cube-cbrt`
18×	`times-frac`
16×	`sqrt-prod`
8×	`pow1`
6×	`add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
4×	`flip3-+` `flip-+`
3×	`sqrt-pow1` `associate-/l*`
2×	`pow1/2` `associate-*r/` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `div-exp` `pow-prod-down` `clear-num` `sum-log` `div-inv` `distribute-lft-out`

Counts

4 → 81

Calls

4 calls:

14.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
8.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
13.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
6.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series71.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
10.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
14.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
9.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify55.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4913	1479
1	4913	1479

prune227.0ms

Filtered

74 candidates to 93 candidates (-25.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	83	10	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	10	94

Merged error: 11.8b

Counts

94 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x))))
0.2b	(* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))
2.7b	(+ 1.0 (* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x))))))
14.7b	(sqrt (+ (* 4.0 (* p p)) (* x x)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
40×	`times-frac`
36×	`*-un-lft-identity`
34×	`add-cube-cbrt`
26×	`sqrt-prod`
24×	`associate-r`
17×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`pow1`
6×	`sqrt-div` `associate-/r*` `add-log-exp`
5×	`unswap-sqr`
4×	`flip3-+` `div-exp` `prod-exp` `associate-/r/` `flip-+`
3×	`pow-flip` `associate-l` `associate-/l*`
2×	`cbrt-undiv` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 122

Calls

4 calls:

10.0ms	(/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x))))
16.0ms	(* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))
3.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x))))))
6.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

series45.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x))))
10.0ms	(* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))
16.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x))))))
8.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

simplify44.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5044	1899

prune241.0ms

Filtered

81 candidates to 134 candidates (-65.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	132	2	134
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	135	9	144

Merged error: 11.8b

Counts

144 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(log (exp (sqrt (* (+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x))))) 0.5))))
0.2b	(/ x (sqrt (+ (* 4.0 (* p p)) (* x x))))
0.3b	(+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x)))))
14.7b	(sqrt (+ (* 4.0 (* p p)) (* x x)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
22×	`add-cube-cbrt`
18×	`times-frac`
16×	`sqrt-prod`
6×	`pow1` `add-exp-log` `associate-/r*` `add-cbrt-cube` `add-log-exp`
5×	`log-pow`
4×	`exp-prod` `sqrt-div`
3×	`log-prod` `flip3-+` `flip-+` `associate-/l*`
2×	`associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `rem-log-exp` `clear-num` `sum-log` `div-inv` `distribute-lft-out`

Counts

4 → 84

Calls

4 calls:

2.0ms	(log (exp (sqrt (* (+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x))))) 0.5))))
9.0ms	(/ x (sqrt (+ (* 4.0 (* p p)) (* x x))))
14.0ms	(+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x)))))
6.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

series71.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(log (exp (sqrt (* (+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x))))) 0.5))))
13.0ms	(/ x (sqrt (+ (* 4.0 (* p p)) (* x x))))
13.0ms	(+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x)))))
9.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

simplify79.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4949	1562
1	4949	1562

prune257.0ms

Filtered

74 candidates to 96 candidates (-29.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	88	8	96
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	95	10	105

Merged error: 11.8b

Counts

105 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))
2.6b	(log (exp (sqrt (* (+ 1.0 (* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))) 0.5))))
2.7b	(+ 1.0 (* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x))))))
14.7b	(sqrt (+ (* 4.0 (* p p)) (* x x)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
24×	`associate-r`
23×	`*-un-lft-identity`
22×	`times-frac`
21×	`add-cube-cbrt`
15×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
6×	`add-log-exp`
5×	`log-pow` `unswap-sqr`
4×	`exp-prod` `sqrt-div` `prod-exp`
3×	`log-prod` `flip3-+` `associate-l` `flip-+`
2×	`div-exp` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `rem-log-exp` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 91

Calls

4 calls:

16.0ms	(* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))
2.0ms	(log (exp (sqrt (* (+ 1.0 (* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))) 0.5))))
3.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x))))))
9.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

series70.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))
35.0ms	(log (exp (sqrt (* (+ 1.0 (* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))) 0.5))))
13.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x))))))
9.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

simplify41.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5090	1467

prune205.0ms

Filtered

75 candidates to 103 candidates (-37.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	103	10	113

Merged error: 11.8b

Counts

113 → 10

regimes157.0ms

Accuracy

0% (0.5b remaining)

Error of 13.1b against oracle of 12.6b and baseline of 13.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	21
1	24	21

end0.0ms

sample1.3s

Algorithm

intervals

Results

352.0ms	6092×	body	80	valid
268.0ms	783×	body	2560	valid
165.0ms	582×	body	1280	valid
147.0ms	8000×	pre	80	true
73.0ms	320×	body	640	valid
28.0ms	154×	body	320	valid
8.0ms	69×	body	160	valid

Details

sample46.0ms

simplify3.0ms

prune6.0ms

localize17.0ms

rewrite44.0ms

series71.0ms

simplify55.0ms

prune227.0ms

localize13.0ms

rewrite40.0ms

series45.0ms

simplify44.0ms

prune241.0ms

localize15.0ms

rewrite35.0ms

series71.0ms

simplify79.0ms

prune257.0ms

localize16.0ms

rewrite34.0ms

series70.0ms

simplify41.0ms

prune205.0ms

regimes157.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.3s

Profiling