Details

sample21.0ms

Algorithm

intervals

Results

8.0ms

279×

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: 30.0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.6b	(+ (* a c) (* b d))
29.4b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite39.0ms

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:

8.0ms	(+ (* a c) (* b d))
30.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series104.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(+ (* a c) (* b d))
74.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify85.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 2 (24.0ms)

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

prune147.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 19.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (* (hypot c d) 1))
0.2b	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
0.8b	(fma a c (* b d))
18.5b	(/ (fma a c (* b d)) (* (hypot c d) 1))

rewrite75.0ms

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:

13.0ms	(/ 1 (* (hypot c d) 1))
46.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
0.0ms	(fma a c (* b d))
10.0ms	(/ (fma a c (* b d)) (* (hypot c d) 1))

series352.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ 1 (* (hypot c d) 1))
166.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
34.0ms	(fma a c (* b d))
103.0ms	(/ (fma a c (* b d)) (* (hypot c d) 1))

simplify47.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (35.0ms)

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

prune265.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.7b

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
0.8b	(fma a c (* b d))
18.5b	(/ (fma a c (* b d)) (hypot c d))

rewrite22.0ms

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:

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

series252.0ms

Counts

3 → 9

Calls

3 calls:

107.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
37.0ms	(fma a c (* b d))
107.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify81.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 3 (72.0ms)

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

prune264.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.6b

localize11.0ms

Local error

Found 4 expressions with local error:

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))))
0.8b	(fma a c (* b d))
18.5b	(/ (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:

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

series398.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(/ (/ 1 (/ (hypot c d) (fma a c (* b d)))) (* (hypot c d) 1))
103.0ms	(/ 1 (/ (hypot c d) (fma a c (* b d))))
35.0ms	(fma a c (* b d))
88.0ms	(/ (hypot c d) (fma a c (* b d)))

simplify83.0ms

Algorithm

egg-herbie

Counts

258 → 258

Iterations

Useful iterations: 2 (59.0ms)

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

prune492.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 7.6b

regimes232.0ms

Accuracy

26.8% (7.9b remaining)

Error of 13.9b against oracle of 6.0b and baseline of 16.8b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	18
1	31	18
2	31	18

end0.0ms

sample560.0ms

Algorithm

intervals

Results

275.0ms

8493×

body

valid