Details

sample90.0ms

Algorithm

intervals

Results

72.0ms

620×

body

valid

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	55	15
1	179	14
2	561	13
3	1824	13
4	5002	13

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
0.1b	(* (* a a) (+ 1.0 a))
0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.9b	(* (* b b) (- 1.0 (* 3.0 a)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

18×	`associate-*r/`
17×	`pow1` `add-exp-log`
16×	`add-sqr-sqrt` `add-cbrt-cube`
14×	`*-un-lft-identity`
12×	`add-cube-cbrt`
10×	`associate-r`
7×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`prod-diff`
5×	`associate-l`
4×	`expm1-log1p-u` `flip3-+` `frac-add` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `flip3--` `*-commutative` `flip--` `unswap-sqr`
2×	`sub-neg`
1×	`pow-to-exp` `pow-pow` `pow-exp` `distribute-lft-out` `sqr-pow`

Counts

4 → 106

Calls

4 calls:

40.0ms	(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
14.0ms	(* (* a a) (+ 1.0 a))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)
13.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

series267.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
52.0ms	(* (* a a) (+ 1.0 a))
101.0ms	(pow (+ (* a a) (* b b)) 2.0)
49.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

simplify105.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	725	894
1	4089	793
2	5001	790

prune340.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (pow a 3))
0.0b	(+ (pow (+ (* a a) (* b b)) 2.0) (fma 4.0 (fma a a (* b b)) (* 4.0 (pow a 3))))
0.0b	(fma 4.0 (fma a a (* b b)) (* 4.0 (pow a 3)))
0.3b	(pow (+ (* a a) (* b b)) 2.0)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
12×	`add-cube-cbrt` `associate-r`
10×	`add-exp-log` `unpow-prod-down`
7×	`fma-def`
6×	`add-cbrt-cube` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cube-prod` `log1p-expm1-u` `unswap-sqr` `sqr-pow`
3×	`pow-unpow` `associate-l` `prod-exp`
2×	`pow-to-exp` `pow-exp` `fma-udef`
1×	`+-commutative` `cube-mult` `associate-+r+` `pow-pow` `flip3-+` `unpow3` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out`

Counts

4 → 84

Calls

4 calls:

7.0ms	(* 4.0 (pow a 3))
28.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (fma 4.0 (fma a a (* b b)) (* 4.0 (pow a 3))))
0.0ms	(fma 4.0 (fma a a (* b b)) (* 4.0 (pow a 3)))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)

series281.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* 4.0 (pow a 3))
94.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (fma 4.0 (fma a a (* b b)) (* 4.0 (pow a 3))))
48.0ms	(fma 4.0 (fma a a (* b b)) (* 4.0 (pow a 3)))
102.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify51.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	310	566
1	1399	524
2	5002	514

prune328.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.3b	(pow (+ (* a a) (* b b)) 2.0)
14.3b	(sqrt (pow (+ (* a a) (* b b)) 2.0))
14.3b	(sqrt (pow (+ (* a a) (* b b)) 2.0))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`unpow-prod-down` `sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `add-exp-log` `rem-sqrt-square` `pow-unpow` `sqr-pow`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `pow-pow` `sqrt-pow1` `pow1/2` `pow-exp`

Counts

4 → 80

Calls

4 calls:

4.0ms	(pow (+ (* a a) (* b b)) 2.0)
4.0ms	(pow (+ (* a a) (* b b)) 2.0)
7.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))
7.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))

series499.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(pow (+ (* a a) (* b b)) 2.0)
103.0ms	(pow (+ (* a a) (* b b)) 2.0)
142.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))
145.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))

simplify59.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 3 (51.0ms)

Iter	Nodes	Cost
0	138	560
1	470	522
2	1671	512
3	5002	504

prune432.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

3.5b	(sqrt (cbrt (pow (+ (* a a) (* b b)) 2.0)))
14.3b	(sqrt (pow (+ (* a a) (* b b)) 2.0))
22.2b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
22.2b	(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-prod`
18×	`add-sqr-sqrt`
17×	`sqrt-prod`
14×	`unpow-prod-down`
13×	`add-cube-cbrt` `*-un-lft-identity`
7×	`rem-sqrt-square`
6×	`sqr-pow`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-pow1` `pow1/3`
2×	`pow1/2`

Counts

4 → 81

Calls

4 calls:

8.0ms	(sqrt (cbrt (pow (+ (* a a) (* b b)) 2.0)))
7.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))
4.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
5.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

series597.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(sqrt (cbrt (pow (+ (* a a) (* b b)) 2.0)))
148.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))
147.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
154.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify44.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (36.0ms)

Iter	Nodes	Cost
0	197	714
1	443	674
2	1374	670
3	5001	662

prune496.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes118.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	17
1	19	17

end0.0ms

sample2.8s

Algorithm

intervals

Results

2.4s

20512×

body

valid