Details

sample0.0hr

Algorithm

intervals

Results

0.0hr	203×	body	80	valid
0.0hr	19×	body	2560	valid
0.0hr	20×	body	1280	valid
0.0hr	256×	pre	80	true
0.0hr	9×	body	640	valid
0.0hr	4×	body	320	valid
0.0hr	1×	body	160	valid

simplify0.0hr

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0hr)

Iter	Nodes	Cost
0	27	9
1	34	9
2	38	9
3	40	9
4	41	9
5	41	9

prune0.0hr

Filtered

1 candidates to 0 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: 11.2b

Counts

2 → 1

localize0.0hr

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.2b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite0.0hr

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:

0.0hr	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.0hr	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.0hr	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.0hr	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series0.0hr

Counts

4 → 12

Calls

4 calls:

0.0hr	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.0hr	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.0hr	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.0hr	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify0.0hr

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (0.0hr)

Iter	Nodes	Cost
0	280	888
1	816	840
2	2486	828
3	5001	827

prune0.0hr

Filtered

93 candidates to 71 candidates (23.7%)

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: 11.0b

Counts

94 → 10

localize0.0hr

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.4b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
13.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite0.0hr

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

0.0hr	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
0.0hr	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.0hr	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
0.0hr	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series0.0hr

Counts

4 → 12

Calls

4 calls:

0.0hr	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
0.0hr	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.0hr	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
0.0hr	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify0.0hr

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (0.0hr)

Iter	Nodes	Cost
0	390	903
1	1699	818
2	5001	784

prune0.0hr

Filtered

100 candidates to 71 candidates (29.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	94	6	100
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	98	12	110

Merged error: 11.0b

Counts

110 → 12

localize0.0hr

Local error

Found 4 expressions with local error:

0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.3b	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
2.4b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
13.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite0.0hr

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:

0.0hr	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.0hr	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
0.0hr	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
0.0hr	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series0.0hr

Counts

4 → 12

Calls

4 calls:

0.0hr	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.0hr	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
0.0hr	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
0.0hr	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify0.0hr

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (0.0hr)

Iter	Nodes	Cost
0	399	962
1	1650	851
2	5002	816

prune0.0hr

Filtered

103 candidates to 76 candidates (26.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	93	10	103
Fresh	9	2	11
Picked	1	0	1
Done	0	0	0
Total	103	12	115

Merged error: 11.0b

Counts

115 → 12

localize0.0hr

Local error

Found 4 expressions with local error:

1.8b	(log (log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
2.3b	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
2.4b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
13.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite0.0hr

Algorithm

rewrite-expression-head

Rules

11×	`log-prod` `log-pow`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1` `exp-prod`
6×	`add-log-exp`
5×	`add-exp-log` `sqrt-prod`
4×	`add-cbrt-cube`
2×	`flip3-+` `sqrt-div` `rem-log-exp` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log`

Counts

4 → 59

Calls

4 calls:

0.0hr	(log (log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
0.0hr	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
0.0hr	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
0.0hr	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series0.0hr

Counts

4 → 12

Calls

4 calls:

0.0hr	(log (log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
0.0hr	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
0.0hr	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
0.0hr	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify0.0hr

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (0.0hr)

Iter	Nodes	Cost
0	267	855
1	729	738
2	2550	736
3	5002	735

prune0.0hr

Filtered

71 candidates to 59 candidates (16.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	6	5	11
Picked	0	1	1
Done	0	0	0
Total	75	8	83

Merged error: 5.5b

Counts

83 → 8

regimes0.0hr

Accuracy

-10.9% (6.6b remaining)

Error of 13.9b against oracle of 7.4b and baseline of 13.3b

bsearch0.0hr

Steps

Iters	Range		Point
7	-2.450180232760445e-303	-3.4104780537685076e-305	-3.5755809718925854e-305
7	-2.414893472892736e-252	-8.944980550579625e-254	-6.219040641904291e-253

simplify0.0hr

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0hr)

Iter	Nodes	Cost
0	61	46
1	61	46

end0.0hr

sample0.0hr

Algorithm

intervals

Results

0.0hr	6055×	body	80	valid
0.0hr	796×	body	2560	valid
0.0hr	622×	body	1280	valid
0.0hr	8000×	pre	80	true
0.0hr	324×	body	640	valid
0.0hr	137×	body	320	valid
0.0hr	66×	body	160	valid

Details

sample0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

regimes0.0hr

bsearch0.0hr

simplify0.0hr

end0.0hr

sample0.0hr

Profiling