Details

sample20.0ms

Algorithm

intervals

Results

9.0ms

271×

body

valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	7
1	21	7
2	21	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: 27.8b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* a c) (* b d))
27.3b	(/ (+ (* a c) (* b 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×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `fma-def` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 47

Calls

2 calls:

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

series117.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(+ (* a c) (* b d))
84.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify87.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	244	458
1	872	411
2	3164	403
3	5001	403

prune151.0ms

Filtered

53 candidates to 44 candidates (83.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	44	9	53
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	9	54

Merged error: 17.5b

Counts

54 → 9

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma a c (* b d))
0.2b	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
17.1b	(/ (fma a c (* b d)) (* (hypot c d) 1))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

154×	`add-exp-log`
86×	`prod-exp`
57×	`div-exp`
44×	`add-cbrt-cube`
35×	`1-exp`
16×	`cbrt-unprod`
14×	`cbrt-undiv`
12×	`rec-exp`
11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
7×	`associate-r` `associate-l`
5×	`pow1`
3×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `associate-/r` `-commutative` `fma-udef` `unswap-sqr`

Counts

3 → 112

Calls

3 calls:

1.0ms	(fma a c (* b d))
11.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
4.0ms	(/ (fma a c (* b d)) (* (hypot c d) 1))

series339.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(fma a c (* b d))
186.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
115.0ms	(/ (fma a c (* b d)) (* (hypot c d) 1))

simplify46.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	472	1079
1	1607	796
2	5001	794

prune203.0ms

Filtered

121 candidates to 59 candidates (48.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	115	6	121
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	119	11	130

Merged error: 5.7b

Counts

130 → 11

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma a c (* b d))
0.1b	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
17.1b	(/ (fma a c (* b d)) (hypot c d))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

40×	`times-frac`
25×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
22×	`add-exp-log`
17×	`add-cbrt-cube`
16×	`associate-/l*`
10×	`div-exp`
7×	`cbrt-undiv`
4×	`prod-exp` `associate-/r*` `div-inv`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `1-exp` `clear-num` `cbrt-unprod`
1×	`fma-udef` `associate-/l/`

Counts

3 → 89

Calls

3 calls:

1.0ms	(fma a c (* b d))
7.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
3.0ms	(/ (fma a c (* b d)) (hypot c d))

series268.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(fma a c (* b d))
115.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
113.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify80.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	297	767
1	1133	677
2	3251	677
3	5001	670

prune242.0ms

Filtered

98 candidates to 75 candidates (76.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	94	4	98
Fresh	3	6	9
Picked	0	1	1
Done	0	1	1
Total	97	12	109

Merged error: 5.6b

Counts

109 → 12

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma a c (* b d))
0.1b	(/ (hypot c d) (/ (fma a c (* b d)) (hypot c d)))
0.6b	(/ 1 (/ (hypot c d) (/ (fma a c (* b d)) (hypot c d))))
17.1b	(/ (fma a c (* b d)) (hypot c d))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

480×	`times-frac`
239×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
60×	`associate-/r*`
32×	`add-exp-log`
23×	`div-inv`
20×	`add-cbrt-cube`
19×	`div-exp`
10×	`cbrt-undiv`
9×	`associate-/l*`
6×	`associate-/r/`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`pow-flip` `fma-udef` `inv-pow`

Counts

4 → 317

Calls

4 calls:

1.0ms	(fma a c (* b d))
6.0ms	(/ (hypot c d) (/ (fma a c (* b d)) (hypot c d)))
12.0ms	(/ 1 (/ (hypot c d) (/ (fma a c (* b d)) (hypot c d))))
3.0ms	(/ (fma a c (* b d)) (hypot c d))

series428.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(fma a c (* b d))
89.0ms	(/ (hypot c d) (/ (fma a c (* b d)) (hypot c d)))
182.0ms	(/ 1 (/ (hypot c d) (/ (fma a c (* b d)) (hypot c d))))
119.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify136.0ms

Algorithm

egg-herbie

Counts

329 → 329

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	975	4412
1	4990	3959
2	5001	3959

prune624.0ms

Filtered

329 candidates to 208 candidates (63.2%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	326	3	329
Fresh	0	9	9
Picked	0	1	1
Done	1	1	2
Total	327	14	341

Merged error: 5.6b

Counts

341 → 14

regimes271.0ms

Accuracy

35.1% (7.1b remaining)

Error of 12.7b against oracle of 5.6b and baseline of 16.6b

bsearch81.0ms

Steps

Iters	Range		Point
8	2.6639915875115466e+105	1.2401134344781783e+109	4.1722391275213826e+108
10	-7.322685498206333e+190	-5.591969180972269e+180	-3.2727313730029946e+183

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	16
1	32	16
2	32	16

end0.0ms

sample507.0ms

Algorithm

intervals

Results

300.0ms

8443×

body

valid