Details

sample23.0ms

Algorithm

intervals

Results

12.0ms

269×

body

valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	7
1	40	7
2	56	7
3	76	7
4	90	7
5	94	7
6	94	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: 25.3b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

0.3b	(- (* b c) (* a d))
24.8b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `clear-num` `flip-+` `div-inv`

Counts

2 → 50

Calls

2 calls:

4.0ms	(- (* b c) (* a d))
11.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series124.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(- (* b c) (* a d))
83.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify103.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 3 (97.0ms)

Iter	Nodes	Cost
0	268	481
1	1010	432
2	3840	422
3	5001	421

prune148.0ms

Filtered

56 candidates to 46 candidates (82.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	50	6	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	51	6	57

Merged error: 13.1b

Counts

57 → 6

localize14.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
0.3b	(- (* b c) (* a d))
16.7b	(/ (- (* b c) (* a d)) (hypot c d))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
32×	`prod-exp`
26×	`add-cbrt-cube`
25×	`add-sqr-sqrt`
23×	`div-exp`
22×	`times-frac`
20×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r`
12×	`1-exp`
8×	`cbrt-undiv` `cbrt-unprod`
7×	`associate-l`
6×	`rec-exp`
5×	`pow1` `add-log-exp`
3×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `div-inv` `associate-/l`
2×	`flip3--` `flip--` `associate-/l/` `unswap-sqr`
1×	`frac-times` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `associate-r/` `prod-diff` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

3 → 110

Calls

3 calls:

12.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
4.0ms	(- (* b c) (* a d))
6.0ms	(/ (- (* b c) (* a d)) (hypot c d))

series340.0ms

Counts

3 → 9

Calls

3 calls:

182.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
41.0ms	(- (* b c) (* a d))
117.0ms	(/ (- (* b c) (* a d)) (hypot c d))

simplify64.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	535	1095
1	2234	907
2	5003	905

prune252.0ms

Filtered

119 candidates to 78 candidates (65.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	113	6	119
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	114	11	125

Merged error: 2.9b

Counts

125 → 11

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
0.3b	(- (* b c) (* a d))
16.7b	(/ (- (* b c) (* a d)) (hypot c d))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
53×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`associate-/l*`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `div-sub` `log1p-expm1-u` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

3 → 121

Calls

3 calls:

7.0ms	(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
3.0ms	(- (* b c) (* a d))
6.0ms	(/ (- (* b c) (* a d)) (hypot c d))

series267.0ms

Counts

3 → 9

Calls

3 calls:

113.0ms	(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
38.0ms	(- (* b c) (* a d))
116.0ms	(/ (- (* b c) (* a d)) (hypot c d))

simplify53.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	449	1408
1	1657	1307
2	5001	1298

prune273.0ms

Filtered

130 candidates to 98 candidates (75.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	124	6	130
Fresh	6	3	9
Picked	1	0	1
Done	1	0	1
Total	132	9	141

Merged error: 2.9b

Counts

141 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (* b c) (hypot c d)) (/ (* a d) (hypot c d)))
0.1b	(/ (- (/ (* b c) (hypot c d)) (/ (* a d) (hypot c d))) (hypot c d))
9.6b	(/ (* a d) (hypot c d))
10.4b	(/ (* b c) (hypot c d))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

69×	`times-frac`
59×	`add-sqr-sqrt` `*-un-lft-identity`
49×	`add-cube-cbrt` `prod-diff`
28×	`div-inv`
16×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/r*`
8×	`associate-/l*`
7×	`fma-neg`
6×	`add-log-exp`
5×	`cbrt-undiv` `distribute-rgt-out--` `div-exp` `distribute-lft-out--` `difference-of-squares`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/`
3×	`frac-2neg` `clear-num`
2×	`flip3--` `prod-exp` `frac-sub` `flip--` `cbrt-unprod` `sub-div`
1×	`sub-neg` `diff-log` `div-sub`

Counts

4 → 167

Calls

4 calls:

13.0ms	(- (/ (* b c) (hypot c d)) (/ (* a d) (hypot c d)))
13.0ms	(/ (- (/ (* b c) (hypot c d)) (/ (* a d) (hypot c d))) (hypot c d))
4.0ms	(/ (* a d) (hypot c d))
5.0ms	(/ (* b c) (hypot c d))

series556.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(- (/ (* b c) (hypot c d)) (/ (* a d) (hypot c d)))
235.0ms	(/ (- (/ (* b c) (hypot c d)) (/ (* a d) (hypot c d))) (hypot c d))
72.0ms	(/ (* a d) (hypot c d))
66.0ms	(/ (* b c) (hypot c d))

simplify86.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	607	2530
1	2576	1870
2	5001	1867

prune321.0ms

Filtered

179 candidates to 113 candidates (63.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	175	4	179
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	180	8	188

Merged error: 0b

Counts

188 → 8

regimes140.0ms

Accuracy

0% (0.8b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 0.9b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	30
1	31	30
2	31	30

end0.0ms

sample604.0ms

Algorithm

intervals

Results

375.0ms

8478×

body

valid