Details

sample36.0ms

Algorithm

intervals

Results

25.0ms

275×

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: 26.9b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.2b	(+ (* a c) (* b d))
26.5b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite18.0ms

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:

3.0ms	(+ (* c c) (* d d))
3.0ms	(+ (* a c) (* b d))
12.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series144.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (* c c) (* d d))
34.0ms	(+ (* a c) (* b d))
82.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify131.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (29.0ms)

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

prune211.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 17.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (* (hypot c d) 1))
0.0b	(fma a c (* b d))
0.2b	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
17.5b	(/ (fma a c (* b d)) (* (hypot c d) 1))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

170×	`add-exp-log`
92×	`prod-exp`
63×	`div-exp`
50×	`add-cbrt-cube`
41×	`1-exp`
17×	`cbrt-unprod`
16×	`cbrt-undiv`
15×	`rec-exp`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
9×	`pow1`
7×	`associate-r` `associate-l`
6×	`associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`pow-flip` `frac-2neg` `pow-prod-down` `clear-num` `associate-/r*`
1×	`frac-times` `associate-r/` `associate-l/` `*-commutative` `fma-udef` `inv-pow` `unswap-sqr`

Counts

4 → 145

Calls

4 calls:

5.0ms	(/ 1 (* (hypot c d) 1))
1.0ms	(fma a c (* b d))
22.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
3.0ms	(/ (fma a c (* b d)) (* (hypot c d) 1))

series398.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ 1 (* (hypot c d) 1))
37.0ms	(fma a c (* b d))
188.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
117.0ms	(/ (fma a c (* b d)) (* (hypot c d) 1))

simplify46.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	486	1191
1	1654	892
2	5002	884

prune290.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.7b

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))
17.5b	(/ (fma a c (* b d)) (hypot c d))

rewrite13.0ms

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))
7.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
2.0ms	(/ (fma a c (* b d)) (hypot c d))

series320.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(hypot c d)
38.0ms	(fma a c (* b d))
121.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
113.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify81.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 3 (71.0ms)

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

prune326.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.6b

localize15.0ms

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))))
17.5b	(/ (hypot c d) (fma a c (* b d)))

rewrite36.0ms

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))
16.0ms	(/ (/ 1 (/ (hypot c d) (fma a c (* b d)))) (* (hypot c d) 1))
5.0ms	(/ 1 (/ (hypot c d) (fma a c (* b d))))
2.0ms	(/ (hypot c d) (fma a c (* b d)))

series433.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(fma a c (* b d))
181.0ms	(/ (/ 1 (/ (hypot c d) (fma a c (* b d)))) (* (hypot c d) 1))
116.0ms	(/ 1 (/ (hypot c d) (fma a c (* b d))))
95.0ms	(/ (hypot c d) (fma a c (* b d)))

simplify82.0ms

Algorithm

egg-herbie

Counts

258 → 258

Iterations

Useful iterations: 2 (58.0ms)

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

prune503.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.6b

regimes172.0ms

Accuracy

38.5% (6.8b remaining)

Error of 12.2b against oracle of 5.5b and baseline of 16.5b

bsearch70.0ms

Steps

Iters	Range		Point
8	3.938121820157591e+142	6.559931041703192e+145	9.012016494007182e+142
5	-2.0487505030059975e+136	-9.39907926608248e+135	-1.3620016266644103e+136

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	15
1	31	15
2	31	15

end0.0ms

sample895.0ms

Algorithm

intervals

Results

668.0ms

8450×

body

valid