Details

sample62.0ms

Algorithm

intervals

Results

42.0ms

723×

body

valid

simplify57.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

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

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (+ (* a a) (* b b)) 2.0) (* 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)
0.6b	(* (* b b) (- 1.0 (* 3.0 a)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

27.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
16.0ms	(* (* a a) (+ 1.0 a))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)
12.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

series330.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
51.0ms	(* (* a a) (+ 1.0 a))
113.0ms	(pow (+ (* a a) (* b b)) 2.0)
52.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

simplify81.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	564	828
1	2826	724
2	5001	715

prune354.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

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))
0.2b	(fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.6b	(* (* b b) (- 1.0 (* 3.0 a)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

18×	`associate-*r/`
16×	`pow1` `add-exp-log` `add-cbrt-cube`
14×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt` `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×	`flip3--` `*-commutative` `flip--` `unswap-sqr`
2×	`sub-neg`
1×	`fma-udef` `distribute-lft-out`

Counts

4 → 97

Calls

4 calls:

36.0ms	(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
14.0ms	(* (* a a) (+ 1.0 a))
0.0ms	(fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
15.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

series296.0ms

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))
125.0ms	(fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
54.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

simplify109.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	666	1047
1	3763	904
2	5001	897

prune382.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (* b b) (- 1.0 (* 3.0 a)))
16.1b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
16.1b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
16.1b	(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

21×	`cbrt-prod`
14×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1` `add-exp-log` `unpow-prod-down` `add-cbrt-cube`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `sqr-pow`
2×	`sub-neg` `associate-*r/`
1×	`flip3--` `associate-l` `*-commutative` `flip--` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

12.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
4.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
4.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
4.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

series555.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
177.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
164.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
158.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify48.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	315	769
1	1231	692
2	5002	681

prune421.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

9.0b	(sqrt (pow (+ (* a a) (* b b)) 2.0))
9.0b	(sqrt (pow (+ (* a a) (* b b)) 2.0))
16.1b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
16.1b	(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`cbrt-prod` `unpow-prod-down` `sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
6×	`rem-sqrt-square` `sqr-pow`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 76

Calls

4 calls:

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

series686.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))
171.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))
176.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
174.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify130.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 3 (32.0ms)

Iter	Nodes	Cost
0	147	644
1	323	600
2	1002	596
3	3983	592
4	5002	592

prune498.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes134.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	21
1	28	21

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.2s

20670×

body

valid