Details

sample43.0ms

Algorithm

intervals

Results

27.0ms

699×

body

valid

simplify52.0ms

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

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.2b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (* 4.0 b) b (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
0.0b	(+ (* a a) (* b b))
0.3b	(pow (+ (* a a) (* b b)) 2.0)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
4×	`pow1` `add-exp-log`
3×	`expm1-log1p-u` `unpow-prod-down` `pow-unpow` `add-cbrt-cube` `log1p-expm1-u`
1×	`+-commutative` `pow-to-exp` `pow-pow` `fma-def` `flip3-+` `pow-exp` `sum-log` `flip-+` `fma-udef` `sqr-pow`

Counts

3 → 43

Calls

3 calls:

1.0ms	(fma (* 4.0 b) b (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
4.0ms	(+ (* a a) (* b b))
5.0ms	(pow (+ (* a a) (* b b)) 2.0)

series200.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(fma (* 4.0 b) b (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
26.0ms	(+ (* a a) (* b b))
99.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify114.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (109.0ms)

Iter	Nodes	Cost
0	226	319
1	972	282
2	3693	275
3	5001	274

prune150.0ms

Filtered

52 candidates to 43 candidates (82.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	48	4	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	49	4	53

Merged error: 0b

Counts

53 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (cbrt (pow (+ (* a a) (* b b)) 2.0)))
20.4b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
20.4b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
20.4b	(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

73×	`cbrt-prod`
46×	`add-sqr-sqrt`
29×	`unpow-prod-down`
22×	`add-cube-cbrt` `*-un-lft-identity`
16×	`unswap-sqr`
15×	`sqr-pow`
11×	`pow1`
10×	`swap-sqr` `associate-r` `associate-l`
9×	`pow1/3`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 117

Calls

4 calls:

13.0ms	(* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (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))
4.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

series574.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (cbrt (pow (+ (* a a) (* b b)) 2.0)))
141.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
146.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
142.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify104.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 3 (88.0ms)

Iter	Nodes	Cost
0	217	1556
1	702	1473
2	3308	1390
3	5001	1383

prune409.0ms

Filtered

129 candidates to 96 candidates (74.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	129	4	133

Merged error: 0b

Counts

133 → 4

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (* 4.0 b) b (- (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4)) 1.0))
0.0b	(* 2.0 (pow a 2))
0.7b	(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`add-exp-log` `associate-r`
6×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-cbrt-cube`
4×	`unpow-prod-down` `unswap-sqr`
3×	`pow1` `expm1-log1p-u` `associate-l` `prod-exp` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef` `unpow2` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`

Counts

3 → 49

Calls

3 calls:

1.0ms	(fma (* 4.0 b) b (- (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4)) 1.0))
6.0ms	(* 2.0 (pow a 2))
1.0ms	(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

series170.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(fma (* 4.0 b) b (- (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4)) 1.0))
24.0ms	(* 2.0 (pow a 2))
72.0ms	(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

simplify128.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (122.0ms)

Iter	Nodes	Cost
0	172	328
1	661	285
2	3351	281
3	5001	279

prune174.0ms

Filtered

58 candidates to 42 candidates (72.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	58	0	58
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	58	4	62

Merged error: 0b

Counts

62 → 4

localize8.0ms

Local error

Found 1 expressions with local error:

0.4b	(pow (/ 1 a) -4.0)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

13×	`unpow-prod-down`
9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
6×	`add-exp-log`
4×	`pow-exp`
3×	`pow1` `pow-unpow` `pow-pow`
2×	`div-exp`
1×	`expm1-log1p-u` `pow-to-exp` `rec-exp` `pow-flip` `1-exp` `add-cbrt-cube` `log1p-expm1-u` `div-inv` `inv-pow` `add-log-exp` `sqr-pow`

Counts

1 → 34

Calls

1 calls:

5.0ms

(pow (/ 1 a) -4.0)

series177.0ms

Counts

1 → 3

Calls

1 calls:

177.0ms

(pow (/ 1 a) -4.0)

simplify52.0ms

Algorithm

egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	183	164
1	582	153
2	1915	151
3	5001	135

prune56.0ms

Filtered

37 candidates to 18 candidates (48.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	37	0	37
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	37	4	41

Merged error: 0b

Counts

41 → 4

regimes59.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	20
1	18	20

end0.0ms

sample1.2s

Algorithm

intervals

Results

796.0ms

20696×

body

valid