Details

sample22.0ms

Algorithm

intervals

Results

11.0ms

273×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	7
1	15	7

prune2.0ms

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: 29.3b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
1.2b	(+ (* a c) (* b d))
28.7b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
4×	`flip3-+` `flip-+`
3×	`pow1` `associate-/r` `associate-/l`
2×	`+-commutative` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 53

Calls

3 calls:

4.0ms	(+ (* c c) (* d d))
8.0ms	(+ (* a c) (* b d))
8.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series146.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* c c) (* d d))
37.0ms	(+ (* a c) (* b d))
82.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify132.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	272	527
1	1164	479
2	4451	477
3	5003	477

prune177.0ms

Filtered

62 candidates to 49 candidates (79.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	53	9	62
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	9	63

Merged error: 28.5b

Counts

63 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ (* a c) (* b d))
16.5b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
30.6b	(sqrt (+ (* c c) (* d d)))
30.6b	(sqrt (+ (* c c) (* d d)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

4.0ms	(+ (* a c) (* b d))
10.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
4.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series221.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (* a c) (* b d))
115.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
35.0ms	(sqrt (+ (* c c) (* d d)))
37.0ms	(sqrt (+ (* c c) (* d d)))

simplify84.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	273	893
1	868	840
2	2693	828
3	5001	828

prune260.0ms

Filtered

96 candidates to 74 candidates (77.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	90	6	96
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	94	11	105

Merged error: 25.4b

Counts

105 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ (* a c) (* b d))
16.6b	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
30.6b	(sqrt (+ (* c c) (* d d)))
30.6b	(sqrt (+ (* c c) (* d d)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

7.0ms	(+ (* a c) (* b d))
15.0ms	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
4.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series224.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (* a c) (* b d))
118.0ms	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
36.0ms	(sqrt (+ (* c c) (* d d)))
37.0ms	(sqrt (+ (* c c) (* d d)))

simplify49.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	385	911
1	1913	826
2	5002	802

prune445.0ms

Filtered

106 candidates to 74 candidates (69.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	106	11	117

Merged error: 25.4b

Counts

117 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* c c) (* d d))
1.2b	(+ (* a c) (* b d))
1.2b	(/ 1 (+ (* c c) (* d d)))
28.1b	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`add-cube-cbrt` `times-frac`
17×	`add-exp-log`
15×	`associate-r`
11×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`flip3-+` `flip-+`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`associate-l` `associate-/r` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `+-commutative` `frac-times` `rec-exp` `1-exp` `associate-*l/` `sum-log` `cbrt-unprod` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 97

Calls

4 calls:

4.0ms	(+ (* c c) (* d d))
4.0ms	(+ (* a c) (* b d))
6.0ms	(/ 1 (+ (* c c) (* d d)))
13.0ms	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))

series183.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* c c) (* d d))
34.0ms	(+ (* a c) (* b d))
40.0ms	(/ 1 (+ (* c c) (* d d)))
82.0ms	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))

simplify58.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	393	853
1	2037	749
2	5003	720

prune177.0ms

Filtered

109 candidates to 69 candidates (63.3%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	109	11	120

Merged error: 25.4b

Counts

120 → 11

regimes175.0ms

Accuracy

-6.2% (3.2b remaining)

Error of 26.7b against oracle of 23.5b and baseline of 26.5b

bsearch49.0ms

Steps

Iters	Range		Point
10	-2.457675435220466e+63	-1.0994978804728814e+53	-1.637041891041799e+58

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	19
1	27	19
2	27	19

end0.0ms

sample583.0ms

Algorithm

intervals

Results

364.0ms

8488×

body

valid