Details

sample20.0ms

Algorithm

intervals

Results

10.0ms

272×

body

valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 26.0b

Counts

2 → 1

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (* b c) (* a d))
25.5b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite13.0ms

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

series125.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(- (* b c) (* a d))
87.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify104.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 3 (98.0ms)

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

prune156.0ms

Filtered

56 candidates to 46 candidates (82.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	48	8	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	49	8	57

Merged error: 12.1b

Counts

57 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (* (hypot c d) 1))
0.0b	(- (* b c) (* a d))
0.3b	(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
15.9b	(/ (- (* b c) (* a d)) (hypot c d))

rewrite34.0ms

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

series393.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ 1 (* (hypot c d) 1))
39.0ms	(- (* b c) (* a d))
181.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
116.0ms	(/ (- (* b c) (* a d)) (hypot c d))

simplify63.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (49.0ms)

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

prune325.0ms

Filtered

155 candidates to 94 candidates (60.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	147	8	155
Fresh	6	1	7
Picked	0	1	1
Done	0	0	0
Total	153	10	163

Merged error: 4.5b

Counts

163 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot c d)
0.0b	(- (* b c) (* a d))
0.1b	(/ (/ (- (* b c) (* a d)) (hypot c d)) (* (hypot c d) 1))
15.9b	(/ (- (* b c) (* a d)) (hypot c d))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

40×	`times-frac`
26×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
23×	`add-exp-log`
18×	`add-cbrt-cube`
16×	`associate-/l*`
10×	`div-exp`
7×	`cbrt-undiv`
6×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `prod-exp` `associate-/r*` `log1p-expm1-u` `div-inv`
3×	`div-sub` `associate-/l/`
2×	`flip3--` `frac-2neg` `1-exp` `clear-num` `flip--` `cbrt-unprod`
1×	`sub-neg` `hypot-udef` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 109

Calls

4 calls:

1.0ms	(hypot c d)
4.0ms	(- (* b c) (* a d))
8.0ms	(/ (/ (- (* b c) (* a d)) (hypot c d)) (* (hypot c d) 1))
6.0ms	(/ (- (* b c) (* a d)) (hypot c d))

series322.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(hypot c d)
38.0ms	(- (* b c) (* a d))
116.0ms	(/ (/ (- (* b c) (* a d)) (hypot c d)) (* (hypot c d) 1))
120.0ms	(/ (- (* b c) (* a d)) (hypot c d))

simplify49.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	430	989
1	1703	876
2	5001	875

prune324.0ms

Filtered

121 candidates to 96 candidates (79.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	116	5	121
Fresh	5	3	8
Picked	0	1	1
Done	0	1	1
Total	121	10	131

Merged error: 4.5b

Counts

131 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (hypot c d))
0.0b	(- (* b c) (* a d))
0.1b	(/ (* (- (* b c) (* a d)) (/ 1 (hypot c d))) (* (hypot c d) 1))
16.0b	(* (- (* b c) (* a d)) (/ 1 (hypot c d)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
32×	`add-cbrt-cube`
27×	`add-sqr-sqrt`
26×	`prod-exp`
25×	`div-exp`
21×	`*-un-lft-identity` `times-frac`
20×	`add-cube-cbrt`
13×	`associate-r`
10×	`cbrt-undiv` `1-exp`
9×	`cbrt-unprod`
7×	`pow1`
6×	`associate-/l/` `add-log-exp`
5×	`rec-exp` `flip3--` `flip--`
4×	`expm1-log1p-u` `frac-times` `associate-l/` `associate-/r` `log1p-expm1-u` `associate-/l*`
3×	`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 → 133

Calls

4 calls:

3.0ms	(/ 1 (hypot c d))
4.0ms	(- (* b c) (* a d))
11.0ms	(/ (* (- (* b c) (* a d)) (/ 1 (hypot c d))) (* (hypot c d) 1))
9.0ms	(* (- (* b c) (* a d)) (/ 1 (hypot c d)))

series327.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ 1 (hypot c d))
42.0ms	(- (* b c) (* a d))
117.0ms	(/ (* (- (* b c) (* a d)) (/ 1 (hypot c d))) (* (hypot c d) 1))
116.0ms	(* (- (* b c) (* a d)) (/ 1 (hypot c d)))

simplify61.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	522	1094
1	2270	875
2	5002	842

prune286.0ms

Filtered

145 candidates to 84 candidates (57.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	144	1	145
Fresh	2	5	7
Picked	0	1	1
Done	0	2	2
Total	146	9	155

Merged error: 4.5b

Counts

155 → 9

regimes221.0ms

Accuracy

36.6% (8.0b remaining)

Error of 12.4b against oracle of 4.5b and baseline of 17.0b

bsearch141.0ms

Steps

Iters	Range		Point
9	6.8936041022612285e+124	2.2139006002200146e+132	3.708838431511528e+128
8	4.239010840471068e+114	1.6648652189877165e+118	5.729735287031129e+117
4	13523.20185778739	24418.2543350018	15887.488683001407
9	-1.7937751735940947e+171	-3.504983770057452e+165	-3.801771634560153e+166

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	32
1	45	32
2	45	32

end0.0ms

sample528.0ms

Algorithm

intervals

Results

317.0ms

8486×

body

valid