Details

sample34.0ms

Algorithm

intervals

Results

6.0ms	186×	body	80	valid
6.0ms	29×	body	2560	valid
4.0ms	256×	pre	80	true
3.0ms	20×	body	1280	valid
1.0ms	9×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	4×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 14.6b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
1.3b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite38.0ms

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:

12.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
7.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series457.0ms

Counts

4 → 12

Calls

4 calls:

272.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
50.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
75.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
60.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify71.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (61.0ms)

Iter	Nodes	Cost
0	280	888
1	816	840
2	2500	828
3	5001	827

prune243.0ms

Filtered

93 candidates to 71 candidates (76.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	80	13	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	13	94

Merged error: 14.3b

Counts

94 → 13

localize12.0ms

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)))))
2.8b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
15.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite27.0ms

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:

4.0ms	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
13.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series459.0ms

Counts

4 → 12

Calls

4 calls:

270.0ms	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
57.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
75.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
56.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify47.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	390	900
1	1684	818
2	5001	784

prune240.0ms

Filtered

100 candidates to 71 candidates (71.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	96	4	100
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	100	13	113

Merged error: 14.3b

Counts

113 → 13

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.5b	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
2.8b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
15.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite26.0ms

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:

14.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
3.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series480.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
276.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
90.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify45.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (35.0ms)

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

prune311.0ms

Filtered

103 candidates to 76 candidates (73.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	93	10	103
Fresh	8	4	12
Picked	1	0	1
Done	0	0	0
Total	102	14	116

Merged error: 14.3b

Counts

116 → 14

localize18.0ms

Local error

Found 4 expressions with local error:

0.7b	(log (log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
2.5b	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
2.8b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
15.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite13.0ms

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:

2.0ms	(log (log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
2.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
3.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series771.0ms

Counts

4 → 12

Calls

4 calls:

363.0ms	(log (log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
272.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
77.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify71.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (62.0ms)

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

prune224.0ms

Filtered

71 candidates to 59 candidates (83.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	67	4	71
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	73	12	85

Merged error: 8.9b

Counts

85 → 12

regimes202.0ms

Accuracy

0.7% (6.9b remaining)

Error of 14.1b against oracle of 7.3b and baseline of 14.2b

bsearch333.0ms

Steps

Iters	Range		Point
9	-458620530.10775155	-5878.690365136192	-454354590.67968696
8	-4.483429892166135e+24	-1.207936976621e+20	-1.4053102055050533e+20
8	-7.83177520472042e+125	-2.1084671656053772e+122	-4.708638998895936e+125
6	-7.855319431460923e+138	-9.824461211299318e+137	-1.1394059361264092e+138

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	77	84
1	81	84
2	84	84
3	84	84

end0.0ms

sample898.0ms

Algorithm

intervals

Results

222.0ms	6033×	body	80	valid
193.0ms	819×	body	2560	valid
123.0ms	8000×	pre	80	true
113.0ms	596×	body	1280	valid
49.0ms	304×	body	640	valid
19.0ms	168×	body	320	valid
6.0ms	80×	body	160	valid