Details

sample22.0ms

Algorithm

intervals

Results

11.0ms

268×

body

valid

simplify13.0ms

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: 23.6b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.5b	(- (* b c) (* a d))
23.3b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite16.0ms

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`
3×	`pow1` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `fma-def` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `clear-num` `sum-log` `div-inv`

Counts

3 → 64

Calls

3 calls:

4.0ms	(+ (* c c) (* d d))
3.0ms	(- (* b c) (* a d))
8.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series148.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ (* c c) (* d d))
37.0ms	(- (* b c) (* a d))
83.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify38.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	314	555
1	1341	496
2	5001	481

prune168.0ms

Filtered

73 candidates to 59 candidates (80.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	67	6	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	6	74

Merged error: 12.1b

Counts

74 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (* (hypot c d) 1))
0.2b	(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
0.5b	(- (* b c) (* a d))
14.4b	(/ (- (* b c) (* a d)) (hypot c d))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

83×	`add-exp-log`
38×	`prod-exp`
32×	`add-cbrt-cube`
29×	`div-exp`
28×	`add-sqr-sqrt`
25×	`times-frac`
23×	`add-cube-cbrt` `*-un-lft-identity`
18×	`1-exp`
13×	`associate-r`
10×	`cbrt-undiv`
9×	`pow1` `rec-exp` `cbrt-unprod`
7×	`associate-l`
6×	`associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `div-inv`
2×	`flip3--` `pow-flip` `frac-2neg` `pow-prod-down` `clear-num` `flip--` `associate-/l/` `unswap-sqr`
1×	`frac-times` `sub-neg` `fma-neg` `diff-log` `div-sub` `associate-r/` `prod-diff` `associate-l/` `*-commutative` `inv-pow`

Counts

4 → 143

Calls

4 calls:

4.0ms	(/ 1 (* (hypot c d) 1))
12.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
3.0ms	(- (* b c) (* a d))
6.0ms	(/ (- (* b c) (* a d)) (hypot c d))

series393.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ 1 (* (hypot c d) 1))
179.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
39.0ms	(- (* b c) (* a d))
120.0ms	(/ (- (* b c) (* a d)) (hypot c d))

simplify63.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	553	1207
1	2304	1003
2	5001	995

prune288.0ms

Filtered

155 candidates to 94 candidates (60.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	146	9	155
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	150	11	161

Merged error: 5.7b

Counts

161 → 11

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
0.5b	(- (* b c) (* a d))
14.4b	(/ (- (* 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))
4.0ms	(- (* b c) (* a d))
6.0ms	(/ (- (* b c) (* a d)) (hypot c d))

series266.0ms

Counts

3 → 9

Calls

3 calls:

113.0ms	(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
41.0ms	(- (* b c) (* a d))
111.0ms	(/ (- (* b c) (* a d)) (hypot c d))

simplify51.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (37.0ms)

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

prune320.0ms

Filtered

130 candidates to 99 candidates (76.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	124	6	130
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	131	10	141

Merged error: 5.7b

Counts

141 → 10

localize12.0ms

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))
9.4b	(/ (* a d) (hypot c d))
10.0b	(/ (* b c) (hypot c d))

rewrite38.0ms

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:

10.0ms	(- (/ (* b c) (hypot c d)) (/ (* a d) (hypot c d)))
14.0ms	(/ (- (/ (* 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))

series539.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(- (/ (* b c) (hypot c d)) (/ (* a d) (hypot c d)))
222.0ms	(/ (- (/ (* b c) (hypot c d)) (/ (* a d) (hypot c d))) (hypot c d))
68.0ms	(/ (* a d) (hypot c d))
70.0ms	(/ (* b c) (hypot c d))

simplify84.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (59.0ms)

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

prune340.0ms

Filtered

179 candidates to 113 candidates (63.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	176	3	179
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	181	8	189

Merged error: 0.0b

Counts

189 → 8

regimes138.0ms

Accuracy

0% (0.9b 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	31	30
1	35	30
2	35	30

end0.0ms

sample529.0ms

Algorithm

intervals

Results

304.0ms

8493×

body

valid