Details

sample38.0ms

Algorithm

intervals

Results

23.0ms

640×

body

valid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	26	8
1	51	8
2	88	7
3	153	7
4	357	7
5	1572	7
6	5002	7

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-exp-log` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
7×	`fma-def`
6×	`unpow-prod-down`
5×	`add-log-exp`
3×	`expm1-log1p-u` `pow-unpow` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
2×	`sqr-pow`
1×	`+-commutative` `pow-to-exp` `pow-pow` `flip3-+` `associate-r` `pow-exp` `sum-log` `*-commutative` `flip-+` `unswap-sqr`

Counts

3 → 60

Calls

3 calls:

6.0ms	(* 4.0 (* b b))
31.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)

series197.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(* 4.0 (* b b))
69.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
104.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify116.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (110.0ms)

Iter	Nodes	Cost
0	261	370
1	1003	336
2	3910	326
3	5001	322

prune180.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma b (* b (fma b b (* 2 (pow a 2)))) (pow a 4))
0.2b	(* b (fma b b (* 2 (pow a 2))))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`associate-r` `associate-l` `fma-udef`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

2 → 32

Calls

2 calls:

0.0ms	(fma b (* b (fma b b (* 2 (pow a 2)))) (pow a 4))
3.0ms	(* b (fma b b (* 2 (pow a 2))))

series136.0ms

Counts

2 → 6

Calls

2 calls:

74.0ms	(fma b (* b (fma b b (* 2 (pow a 2)))) (pow a 4))
62.0ms	(* b (fma b b (* 2 (pow a 2))))

simplify103.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	131	256
1	578	220
2	2835	220
3	5001	220

prune120.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 4.0 (* b b))
0.0b	(+ (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4)) (* 4.0 (* b b)))
0.7b	(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
3×	`expm1-log1p-u` `fma-def` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
2×	`fma-udef`
1×	`+-commutative` `associate-+l+` `flip3-+` `associate-r` `sum-log` `*-commutative` `flip-+` `unswap-sqr`

Counts

3 → 48

Calls

3 calls:

6.0ms	(* 4.0 (* b b))
3.0ms	(+ (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4)) (* 4.0 (* b b)))
0.0ms	(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

series166.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(* 4.0 (* b b))
66.0ms	(+ (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4)) (* 4.0 (* b b)))
75.0ms	(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

simplify117.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 3 (112.0ms)

Iter	Nodes	Cost
0	192	359
1	807	325
2	3679	308
3	5001	301

prune167.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (- (* 4.0 4.0)) (pow b 4) (pow (fma a a (* b b)) (* 2 2.0)))
0.3b	(pow (fma a a (* b b)) (* 2 2.0))
0.3b	(pow (fma a a (* b b)) 2.0)
35.5b	(/ (fma (- (* 4.0 4.0)) (pow b 4) (pow (fma a a (* b b)) (* 2 2.0))) (fma (- b) (* 4.0 b) (pow (fma a a (* b b)) 2.0)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
8×	`add-exp-log`
6×	`pow1` `unpow-prod-down` `add-cbrt-cube`
4×	`expm1-log1p-u` `pow-unpow` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow-to-exp` `pow-pow` `pow-exp` `sqr-pow`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

4 → 75

Calls

4 calls:

0.0ms	(fma (- (* 4.0 4.0)) (pow b 4) (pow (fma a a (* b b)) (* 2 2.0)))
1.0ms	(pow (fma a a (* b b)) (* 2 2.0))
1.0ms	(pow (fma a a (* b b)) 2.0)
2.0ms	(/ (fma (- (* 4.0 4.0)) (pow b 4) (pow (fma a a (* b b)) (* 2 2.0))) (fma (- b) (* 4.0 b) (pow (fma a a (* b b)) 2.0)))

series479.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(fma (- (* 4.0 4.0)) (pow b 4) (pow (fma a a (* b b)) (* 2 2.0)))
119.0ms	(pow (fma a a (* b b)) (* 2 2.0))
115.0ms	(pow (fma a a (* b b)) 2.0)
168.0ms	(/ (fma (- (* 4.0 4.0)) (pow b 4) (pow (fma a a (* b b)) (* 2 2.0))) (fma (- b) (* 4.0 b) (pow (fma a a (* b b)) 2.0)))

simplify50.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	304	1052
1	1244	957
2	5001	947

prune352.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes52.0ms

Accuracy

82.3% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 1.1b

bsearch108.0ms

Steps

Iters	Range		Point
7	1.1338573995210022e-07	2.2112458842293344e-05	4.1950544641832567e-07
10	-48697182374164.98	-30.29444851407267	-30.610781749505392

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	16
1	36	16

end0.0ms

sample1.1s

Algorithm

intervals

Results

742.0ms

20316×

body

valid