Details

sample20.0ms

Algorithm

intervals

Results

9.0ms

271×

body

valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	7
1	40	7
2	56	7
3	76	7
4	90	7
5	94	7
6	94	7

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.3b

localize10.0ms

Local error

Found 2 expressions with local error:

0.5b	(- (* b c) (* a d))
27.8b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite14.0ms

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×	`associate-/r` `associate-/l`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `clear-num` `flip-+` `div-inv`

Counts

2 → 50

Calls

2 calls:

3.0ms	(- (* b c) (* a d))
10.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series125.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(- (* b c) (* a d))
86.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify106.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 3 (100.0ms)

Iter	Nodes	Cost
0	268	481
1	1010	432
2	3840	422
3	5001	421

prune156.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 14.4b

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
0.5b	(- (* b c) (* a d))
17.3b	(/ (- (* b c) (* a d)) (hypot c d))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
32×	`prod-exp`
26×	`add-cbrt-cube`
25×	`add-sqr-sqrt`
23×	`div-exp`
22×	`times-frac`
20×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r`
12×	`1-exp`
8×	`cbrt-undiv` `cbrt-unprod`
7×	`associate-l`
6×	`rec-exp`
5×	`pow1` `add-log-exp`
3×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `div-inv` `associate-/l`
2×	`flip3--` `flip--` `associate-/l/` `unswap-sqr`
1×	`frac-times` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `associate-r/` `prod-diff` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

3 → 110

Calls

3 calls:

27.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
3.0ms	(- (* b c) (* a d))
7.0ms	(/ (- (* b c) (* a d)) (hypot c d))

series336.0ms

Counts

3 → 9

Calls

3 calls:

180.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
39.0ms	(- (* b c) (* a d))
117.0ms	(/ (- (* b c) (* a d)) (hypot c d))

simplify59.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	535	1095
1	2234	907
2	5003	905

prune274.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
0.5b	(- (* b c) (* a d))
17.3b	(/ (- (* b c) (* a d)) (hypot c d))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
53×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`associate-/l*`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `div-sub` `log1p-expm1-u` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

3 → 121

Calls

3 calls:

9.0ms	(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
3.0ms	(- (* b c) (* a d))
7.0ms	(/ (- (* b c) (* a d)) (hypot c d))

series273.0ms

Counts

3 → 9

Calls

3 calls:

116.0ms	(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
41.0ms	(- (* b c) (* a d))
116.0ms	(/ (- (* b c) (* a d)) (hypot c d))

simplify54.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	449	1408
1	1657	1307
2	5001	1298

prune354.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.6b

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ 1 (* (hypot c d) 1)) (/ (fma b c (- (* a d))) (hypot c d)))
0.3b	(fma b c (- (* a d)))
17.3b	(/ (fma b c (- (* a d))) (hypot c d))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
32×	`prod-exp`
26×	`add-cbrt-cube`
25×	`add-sqr-sqrt`
23×	`div-exp`
22×	`times-frac`
20×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r`
12×	`1-exp`
8×	`cbrt-undiv` `cbrt-unprod`
7×	`associate-l`
6×	`rec-exp`
5×	`pow1`
3×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `div-inv` `associate-/l` `add-log-exp`
2×	`unswap-sqr`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `fma-udef`

Counts

3 → 101

Calls

3 calls:

19.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (fma b c (- (* a d))) (hypot c d)))
0.0ms	(fma b c (- (* a d)))
2.0ms	(/ (fma b c (- (* a d))) (hypot c d))

series350.0ms

Counts

3 → 9

Calls

3 calls:

183.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (fma b c (- (* a d))) (hypot c d)))
45.0ms	(fma b c (- (* a d)))
122.0ms	(/ (fma b c (- (* a d))) (hypot c d))

simplify47.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	427	1041
1	1749	853
2	5002	851

prune240.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.6b

regimes173.0ms

Accuracy

28.1% (8.8b remaining)

Error of 13.3b against oracle of 4.5b and baseline of 16.7b

bsearch82.0ms

Steps

Iters	Range		Point
9	6.479814166339293e+202	2.7363046317489248e+212	6.602179941996442e+202
9	-2.886273399460008e+138	-2.6889041873995e+131	-2.8763806766248217e+136

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	16
1	48	16
2	55	16
3	55	16

end0.0ms

sample506.0ms

Algorithm

intervals

Results

286.0ms

8457×

body

valid