Details

sample21.0ms

Algorithm

intervals

Results

9.0ms

270×

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: 27.6b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
1.2b	(- (* b c) (* a d))
27.2b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite19.0ms

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))
4.0ms	(- (* b c) (* a d))
9.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series152.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* c c) (* d d))
41.0ms	(- (* b c) (* a d))
86.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify41.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (33.0ms)

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

prune182.0ms

Filtered

73 candidates to 59 candidates (80.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	66	7	73
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	66	8	74

Merged error: 13.8b

Counts

74 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (* (hypot c d) 1))
0.3b	(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
1.2b	(- (* b c) (* a d))
17.4b	(/ (- (* b c) (* a d)) (hypot c d))

rewrite37.0ms

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:

5.0ms	(/ 1 (* (hypot c d) 1))
14.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
6.0ms	(- (* b c) (* a d))
6.0ms	(/ (- (* b c) (* a d)) (hypot c d))

series420.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ 1 (* (hypot c d) 1))
178.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
65.0ms	(- (* b c) (* a d))
127.0ms	(/ (- (* b c) (* a d)) (hypot c d))

simplify64.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (50.0ms)

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

prune278.0ms

Filtered

155 candidates to 94 candidates (60.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	149	6	155
Fresh	3	3	6
Picked	1	0	1
Done	1	0	1
Total	154	9	163

Merged error: 6.0b

Counts

163 → 9

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
1.2b	(- (* b c) (* a d))
17.4b	(/ (- (* b c) (* a d)) (hypot c d))

rewrite23.0ms

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:

8.0ms	(/ (/ (- (* 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))

series264.0ms

Counts

3 → 9

Calls

3 calls:

113.0ms	(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
37.0ms	(- (* b c) (* a d))
114.0ms	(/ (- (* b c) (* a d)) (hypot c d))

simplify54.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (37.0ms)

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

prune266.0ms

Filtered

130 candidates to 99 candidates (76.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	125	5	130
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	129	10	139

Merged error: 6.0b

Counts

139 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (hypot c d))
0.1b	(/ (* (- (* b c) (* a d)) (/ 1 (hypot c d))) (hypot c d))
1.2b	(- (* b c) (* a d))
17.5b	(* (- (* b c) (* a d)) (/ 1 (hypot c d)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 124

Calls

4 calls:

3.0ms	(/ 1 (hypot c d))
13.0ms	(/ (* (- (* b c) (* a d)) (/ 1 (hypot c d))) (hypot c d))
4.0ms	(- (* b c) (* a d))
10.0ms	(* (- (* b c) (* a d)) (/ 1 (hypot c d)))

series324.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ 1 (hypot c d))
120.0ms	(/ (* (- (* b c) (* a d)) (/ 1 (hypot c d))) (hypot c d))
38.0ms	(- (* b c) (* a d))
116.0ms	(* (- (* b c) (* a d)) (/ 1 (hypot c d)))

simplify57.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	417	955
1	1964	794
2	5002	763

prune231.0ms

Filtered

136 candidates to 87 candidates (64.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	136	10	146

Merged error: 6.0b

Counts

146 → 10

regimes170.0ms

Accuracy

30.9% (8.3b remaining)

Error of 13.2b against oracle of 4.9b and baseline of 16.9b

bsearch64.0ms

Steps

Iters	Range		Point
7	6.541359801632276e+170	1.3077683363582606e+173	1.5341000055018517e+171
8	-1.3837984933343309e+138	-7.385943653936415e+134	-1.1492385806048738e+136

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	12
1	25	12
2	25	12

end0.0ms

sample532.0ms

Algorithm

intervals

Results

309.0ms

8483×

body

valid