Details

sample34.0ms

Algorithm

intervals

Results

24.0ms

272×

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: 25.7b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.8b	(+ (* a c) (* b d))
25.2b	(/ (+ (* 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))
2.0ms	(+ (* a c) (* b d))
11.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series140.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* c c) (* d d))
32.0ms	(+ (* a c) (* b d))
82.0ms	(/ (+ (* 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

prune193.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.4b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (* (hypot c d) 1))
0.3b	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
16.0b	(/ (fma a c (* b d)) (* (hypot c d) 1))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 135

Calls

3 calls:

4.0ms	(/ 1 (* (hypot c d) 1))
21.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
5.0ms	(/ (fma a c (* b d)) (* (hypot c d) 1))

series344.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(/ 1 (* (hypot c d) 1))
180.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
109.0ms	(/ (fma a c (* b d)) (* (hypot c d) 1))

simplify48.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	479	1150
1	1617	856
2	5001	848

prune241.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.1b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
16.0b	(/ (fma a c (* b d)) (hypot c d))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

40×	`times-frac`
24×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
21×	`add-exp-log`
16×	`add-cbrt-cube` `associate-/l*`
10×	`div-exp`
7×	`cbrt-undiv`
4×	`prod-exp` `associate-/r*` `div-inv`
2×	`pow1` `expm1-log1p-u` `frac-2neg` `1-exp` `clear-num` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
1×	`associate-/l/`

Counts

2 → 79

Calls

2 calls:

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

series224.0ms

Counts

2 → 6

Calls

2 calls:

114.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
110.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify80.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (72.0ms)

Iter	Nodes	Cost
0	290	726
1	1060	641
2	3129	641
3	5001	634

prune228.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (/ (fma a c (* b d)) (sqrt (hypot c d))) (sqrt (hypot c d))) (* (hypot c d) 1))
7.6b	(/ (/ (fma a c (* b d)) (sqrt (hypot c d))) (sqrt (hypot c d)))
8.5b	(/ (fma a c (* b d)) (sqrt (hypot c d)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

892×	`times-frac`
401×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
384×	`sqrt-prod`
161×	`associate-/l*`
40×	`add-exp-log`
31×	`add-cbrt-cube`
24×	`div-inv`
22×	`div-exp`
16×	`cbrt-undiv`
13×	`associate-/r*`
6×	`prod-exp`
3×	`pow1` `expm1-log1p-u` `frac-2neg` `1-exp` `clear-num` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`associate-/l/`

Counts

3 → 519

Calls

3 calls:

38.0ms	(/ (/ (/ (fma a c (* b d)) (sqrt (hypot c d))) (sqrt (hypot c d))) (* (hypot c d) 1))
11.0ms	(/ (/ (fma a c (* b d)) (sqrt (hypot c d))) (sqrt (hypot c d)))
3.0ms	(/ (fma a c (* b d)) (sqrt (hypot c d)))

series429.0ms

Counts

3 → 9

Calls

3 calls:

114.0ms	(/ (/ (/ (fma a c (* b d)) (sqrt (hypot c d))) (sqrt (hypot c d))) (* (hypot c d) 1))
114.0ms	(/ (/ (fma a c (* b d)) (sqrt (hypot c d))) (sqrt (hypot c d)))
200.0ms	(/ (fma a c (* b d)) (sqrt (hypot c d)))

simplify96.0ms

Algorithm

egg-herbie

Counts

528 → 528

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1230	8430
1	5001	7455

prune1.0s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.1b

regimes187.0ms

Accuracy

25.8% (8.8b remaining)

Error of 14.3b against oracle of 5.6b and baseline of 17.4b

bsearch72.0ms

Steps

Iters	Range		Point
7	1.1491683383299206e+265	4.6716414844908043e+266	1.1661264907998782e+265
6	-4.297055379359757e+148	-3.3081908876611885e+147	-3.9328947580125936e+148

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

sample966.0ms

Algorithm

intervals

Results

749.0ms

8457×

body

valid