Details

sample20.0ms

Algorithm

intervals

Results

8.0ms

266×

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.0b	(+ (* a c) (* b d))
22.6b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite48.0ms

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

Counts

3 → 61

Calls

3 calls:

8.0ms	(+ (* c c) (* d d))
8.0ms	(+ (* a c) (* b d))
31.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series129.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(+ (* c c) (* d d))
32.0ms	(+ (* a c) (* b d))
74.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify133.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	290	532
1	1199	475
2	4872	462
3	5001	462

prune199.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot c d)
0.0b	(fma a c (* b d))
0.2b	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
12.3b	(/ (fma a c (* b d)) (* (hypot c d) 1))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 122

Calls

4 calls:

0.0ms	(hypot c d)
0.0ms	(fma a c (* b d))
49.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
8.0ms	(/ (fma a c (* b d)) (* (hypot c d) 1))

series344.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(hypot c d)
33.0ms	(fma a c (* b d))
163.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
104.0ms	(/ (fma a c (* b d)) (* (hypot c d) 1))

simplify46.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	486	1106
1	1625	820
2	5001	818

prune265.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot c d)
0.0b	(fma a c (* b d))
0.1b	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
12.3b	(/ (fma a c (* b d)) (hypot c d))

rewrite22.0ms

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`
4×	`pow1` `expm1-log1p-u` `prod-exp` `associate-/r*` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`frac-2neg` `1-exp` `clear-num` `cbrt-unprod`
1×	`hypot-udef` `fma-udef` `associate-/l/`

Counts

4 → 99

Calls

4 calls:

0.0ms	(hypot c d)
0.0ms	(fma a c (* b d))
13.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
5.0ms	(/ (fma a c (* b d)) (hypot c d))

series284.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(hypot c d)
38.0ms	(fma a c (* b d))
105.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
101.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify78.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	308	794
1	1149	701
2	3275	701
3	5001	693

prune309.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 4.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma a c (* b d))
0.1b	(/ (/ 1 (/ (hypot c d) (fma a c (* b d)))) (* (hypot c d) 1))
0.2b	(/ 1 (/ (hypot c d) (fma a c (* b d))))
12.5b	(/ (hypot c d) (fma a c (* b d)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

260×	`times-frac`
124×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
81×	`add-exp-log`
50×	`div-exp` `associate-/l*`
32×	`add-cbrt-cube`
17×	`associate-/r*`
16×	`cbrt-undiv`
15×	`1-exp` `div-inv`
14×	`prod-exp`
8×	`rec-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num` `associate-/r/` `cbrt-unprod`
1×	`pow-flip` `fma-udef` `associate-/l/` `inv-pow`

Counts

4 → 246

Calls

4 calls:

0.0ms	(fma a c (* b d))
27.0ms	(/ (/ 1 (/ (hypot c d) (fma a c (* b d)))) (* (hypot c d) 1))
10.0ms	(/ 1 (/ (hypot c d) (fma a c (* b d))))
5.0ms	(/ (hypot c d) (fma a c (* b d)))

series385.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(fma a c (* b d))
165.0ms	(/ (/ 1 (/ (hypot c d) (fma a c (* b d)))) (* (hypot c d) 1))
102.0ms	(/ 1 (/ (hypot c d) (fma a c (* b d))))
83.0ms	(/ (hypot c d) (fma a c (* b d)))

simplify87.0ms

Algorithm

egg-herbie

Counts

258 → 258

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	795	2590
1	3687	2260
2	5001	2098

prune464.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 4.5b

regimes196.0ms

Accuracy

33.5% (7.5b remaining)

Error of 13.0b against oracle of 5.4b and baseline of 16.7b

bsearch67.0ms

Steps

Iters	Range		Point
9	5.298754271440407e+215	1.7144382061264391e+223	5.258979463944342e+219
7	-1.6689308349593681e+136	-7.115247008094498e+134	-2.760768008240295e+135

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	14
1	30	14
2	30	14

end0.0ms

sample551.0ms

Algorithm

intervals

Results

269.0ms

8491×

body

valid