Details

sample54.0ms

Algorithm

intervals

Results

36.0ms

675×

body

valid

simplify80.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	53	14
1	173	13
2	532	12
3	1681	12
4	4278	12
5	5001	12

prune7.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

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) (+ 3.0 a)))))
0.1b	(* (* a a) (- 1.0 a))
0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.4b	(* (* b b) (+ 3.0 a))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt` `*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`prod-diff`
15×	`pow1` `add-exp-log`
14×	`add-cbrt-cube`
13×	`distribute-rgt-in` `distribute-lft-in`
9×	`associate-r`
7×	`fma-def`
6×	`unpow-prod-down` `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` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 114

Calls

4 calls:

28.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
17.0ms	(* (* a a) (- 1.0 a))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)
15.0ms	(* (* b b) (+ 3.0 a))

series306.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
57.0ms	(* (* a a) (- 1.0 a))
103.0ms	(pow (+ (* a a) (* b b)) 2.0)
37.0ms	(* (* b b) (+ 3.0 a))

simplify86.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	646	990
1	3454	779
2	5001	776

prune332.0ms

Filtered

126 candidates to 80 candidates (63.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.4b	(* (* b b) (+ 3.0 a))
9.9b	(sqrt (pow (+ (* a a) (* b b)) 2.0))
9.9b	(sqrt (pow (+ (* a a) (* b b)) 2.0))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`sqrt-prod`
13×	`*-un-lft-identity`
11×	`add-cube-cbrt` `unpow-prod-down`
10×	`pow1` `add-exp-log`
9×	`add-cbrt-cube`
6×	`rem-sqrt-square`
5×	`sqr-pow`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`sqrt-pow1` `pow1/2` `associate-*r/`
1×	`distribute-rgt-in` `pow-to-exp` `pow-pow` `distribute-lft-in` `flip3-+` `associate-l` `pow-exp` `*-commutative` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

4 → 87

Calls

4 calls:

4.0ms	(pow (+ (* a a) (* b b)) 2.0)
14.0ms	(* (* b b) (+ 3.0 a))
7.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))
7.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))

series433.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(pow (+ (* a a) (* b b)) 2.0)
32.0ms	(* (* b b) (+ 3.0 a))
142.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))
149.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))

simplify44.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	299	564
1	1364	514
2	5002	509

prune400.0ms

Filtered

99 candidates to 79 candidates (79.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

8.0b	(cbrt (+ (* a a) (* b b)))
8.0b	(cbrt (+ (* a a) (* b b)))
9.9b	(sqrt (pow (+ (* a a) (* b b)) 2.0))
9.9b	(sqrt (* (pow (* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b)))) 2.0) (pow (cbrt (+ (* a a) (* b b))) 2.0)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
6×	`cbrt-prod`
5×	`pow1` `unpow-prod-down`
4×	`add-exp-log` `expm1-log1p-u` `cbrt-div` `sqrt-pow1` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square`
2×	`flip3-+` `pow1/2` `pow1/3` `flip-+` `sqr-pow`
1×	`pow3` `pow-prod-down`

Counts

4 → 65

Calls

4 calls:

2.0ms	(cbrt (+ (* a a) (* b b)))
2.0ms	(cbrt (+ (* a a) (* b b)))
7.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))
13.0ms	(sqrt (* (pow (* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b)))) 2.0) (pow (cbrt (+ (* a a) (* b b))) 2.0)))

series482.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(cbrt (+ (* a a) (* b b)))
95.0ms	(cbrt (+ (* a a) (* b b)))
147.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))
146.0ms	(sqrt (* (pow (* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b)))) 2.0) (pow (cbrt (+ (* a a) (* b b))) 2.0)))

simplify71.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (64.0ms)

Iter	Nodes	Cost
0	213	638
1	733	594
2	2350	588
3	5001	586

prune446.0ms

Filtered

77 candidates to 70 candidates (90.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

8.0b	(cbrt (+ (* a a) (* b b)))
8.0b	(cbrt (+ (* a a) (* b b)))
9.9b	(sqrt (pow (+ (* a a) (* b b)) 2.0))
9.9b	(sqrt (* (pow (* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b)))) 2.0) (pow (* (cbrt (* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b))))) (cbrt (cbrt (+ (* a a) (* b b))))) 2.0)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
6×	`cbrt-prod`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `unpow-prod-down` `cbrt-div` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1`
2×	`flip3-+` `pow1/2` `pow1/3` `flip-+` `sqr-pow`
1×	`pow-prod-down`

Counts

4 → 64

Calls

4 calls:

2.0ms	(cbrt (+ (* a a) (* b b)))
2.0ms	(cbrt (+ (* a a) (* b b)))
7.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))
29.0ms	(sqrt (* (pow (* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b)))) 2.0) (pow (* (cbrt (* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b))))) (cbrt (cbrt (+ (* a a) (* b b))))) 2.0)))

series480.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(cbrt (+ (* a a) (* b b)))
93.0ms	(cbrt (+ (* a a) (* b b)))
139.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))
148.0ms	(sqrt (* (pow (* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b)))) 2.0) (pow (* (cbrt (* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b))))) (cbrt (cbrt (+ (* a a) (* b b))))) 2.0)))

simplify80.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (66.0ms)

Iter	Nodes	Cost
0	219	782
1	745	726
2	2373	720
3	5001	718

prune495.0ms

Filtered

76 candidates to 69 candidates (90.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes127.0ms

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	25	20
1	25	20

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.1s

20504×

body

valid