Details

sample30.0ms

Algorithm

intervals

Results

20.0ms

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: 27.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.9b	(+ (* a c) (* b d))
26.6b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite17.0ms

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))
10.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series139.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* c c) (* d d))
34.0ms	(+ (* a c) (* b d))
79.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify134.0ms

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

prune209.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 16.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot c d)
0.3b	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
0.8b	(fma a c (* b d))
15.9b	(/ (fma a c (* b d)) (* (hypot c d) 1))

rewrite30.0ms

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)
20.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
0.0ms	(fma a c (* b d))
3.0ms	(/ (fma a c (* b d)) (* (hypot c d) 1))

series370.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(hypot c d)
176.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
35.0ms	(fma a c (* b d))
112.0ms	(/ (fma a c (* b d)) (* (hypot c d) 1))

simplify48.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (37.0ms)

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

prune272.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot c d)
0.1b	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
0.8b	(fma a c (* b d))
15.9b	(/ (fma a c (* b d)) (hypot c d))

rewrite12.0ms

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)
6.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
0.0ms	(fma a c (* b d))
2.0ms	(/ (fma a c (* b d)) (hypot c d))

series309.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(hypot c d)
113.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
39.0ms	(fma a c (* b d))
113.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify86.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 3 (73.0ms)

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

prune302.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (hypot c d) (/ (fma a c (* b d)) (hypot c d)))
0.8b	(fma a c (* b d))
0.8b	(/ 1 (/ (hypot c d) (/ (fma a c (* b d)) (hypot c d))))
15.9b	(/ (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:

5.0ms	(/ (hypot c d) (/ (fma a c (* b d)) (hypot c d)))
0.0ms	(fma a c (* b d))
15.0ms	(/ 1 (/ (hypot c d) (/ (fma a c (* b d)) (hypot c d))))
2.0ms	(/ (fma a c (* b d)) (hypot c d))

series409.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ (hypot c d) (/ (fma a c (* b d)) (hypot c d)))
38.0ms	(fma a c (* b d))
175.0ms	(/ 1 (/ (hypot c d) (/ (fma a c (* b d)) (hypot c d))))
110.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify123.0ms

Algorithm

egg-herbie

Counts

329 → 329

Iterations

Useful iterations: 1 (25.0ms)

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

prune701.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.8b

regimes181.0ms

Accuracy

34.2% (7.3b remaining)

Error of 13.3b against oracle of 5.9b and baseline of 17.1b

bsearch92.0ms

Steps

Iters	Range		Point
9	6.881289457293598e+137	1.4895865368921783e+145	6.226031540458845e+142
8	-9.641701532767943e+179	-1.1625254677380091e+176	-2.741292395726274e+176

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

sample852.0ms

Algorithm

intervals

Results

637.0ms

8444×

body

valid