Details

sample32.0ms

Algorithm

intervals

Results

21.0ms

268×

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: 26.3b

localize9.0ms

Local error

Found 2 expressions with local error:

0.3b	(+ (* a c) (* b d))
25.8b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite16.0ms

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:

3.0ms	(+ (* a c) (* b d))
11.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series121.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(+ (* a c) (* b d))
84.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify89.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 2 (26.0ms)

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

prune165.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 16.7b

localize11.0ms

Local error

Found 3 expressions with local error:

0.3b	(fma a c (* b d))
0.3b	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
16.4b	(/ (fma a c (* b d)) (* (hypot c d) 1))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

154×	`add-exp-log`
86×	`prod-exp`
57×	`div-exp`
44×	`add-cbrt-cube`
35×	`1-exp`
16×	`cbrt-unprod`
14×	`cbrt-undiv`
12×	`rec-exp`
11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
7×	`associate-r` `associate-l`
5×	`pow1`
3×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `associate-/r` `-commutative` `fma-udef` `unswap-sqr`

Counts

3 → 112

Calls

3 calls:

0.0ms	(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))

series336.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(fma a c (* b d))
185.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
113.0ms	(/ (fma a c (* b d)) (* (hypot c d) 1))

simplify45.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	472	1079
1	1607	796
2	5001	794

prune226.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
0.3b	(fma a c (* b d))
16.4b	(/ (fma a c (* b d)) (hypot c d))

rewrite13.0ms

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:

7.0ms	(/ (/ (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))

series279.0ms

Counts

3 → 9

Calls

3 calls:

121.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
38.0ms	(fma a c (* b d))
120.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify78.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 3 (69.0ms)

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

prune272.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma a c (* b d))
0.3b	(* (sqrt (/ 1 (* (hypot c d) 1))) (/ (* (sqrt (/ 1 (* (hypot c d) 1))) (fma a c (* b d))) (hypot c d)))
7.4b	(/ (* (sqrt (/ 1 (* (hypot c d) 1))) (fma a c (* b d))) (hypot c d))
9.2b	(* (sqrt (/ 1 (* (hypot c d) 1))) (fma a c (* b d)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
20×	`add-exp-log` `associate-l` `add-cbrt-cube`
16×	`sqrt-prod`
15×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
10×	`associate-r`
8×	`pow1`
6×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `expm1-log1p-u` `sqrt-div` `div-exp` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`
3×	`associate-l/` `associate-/r` `fma-udef`
2×	`pow-prod-down` `*-commutative`
1×	`distribute-rgt-in` `frac-times` `frac-2neg` `distribute-lft-in` `associate-r/` `clear-num` `associate-/l/` `associate-/l`

Counts

4 → 104

Calls

4 calls:

0.0ms	(fma a c (* b d))
55.0ms	(* (sqrt (/ 1 (* (hypot c d) 1))) (/ (* (sqrt (/ 1 (* (hypot c d) 1))) (fma a c (* b d))) (hypot c d)))
15.0ms	(/ (* (sqrt (/ 1 (* (hypot c d) 1))) (fma a c (* b d))) (hypot c d))
20.0ms	(* (sqrt (/ 1 (* (hypot c d) 1))) (fma a c (* b d)))

series651.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(fma a c (* b d))
186.0ms	(* (sqrt (/ 1 (* (hypot c d) 1))) (/ (* (sqrt (/ 1 (* (hypot c d) 1))) (fma a c (* b d))) (hypot c d)))
256.0ms	(/ (* (sqrt (/ 1 (* (hypot c d) 1))) (fma a c (* b d))) (hypot c d))
169.0ms	(* (sqrt (/ 1 (* (hypot c d) 1))) (fma a c (* b d)))

simplify64.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	403	1276
1	2075	1059
2	5001	1017

prune317.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.7b

regimes173.0ms

Accuracy

36.3% (7.0b remaining)

Error of 13.0b against oracle of 6.0b and baseline of 17.0b

bsearch71.0ms

Steps

Iters	Range		Point
6	1.6842624621209925e+118	8.576113840527978e+118	7.643933836198129e+118
7	-2.0391789022290126e+127	-3.2664701214032027e+125	-4.15437883947267e+126

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

sample898.0ms

Algorithm

intervals

Results

680.0ms

8488×

body

valid