Details

sample42.0ms

Algorithm

intervals

Results

26.0ms

664×

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

prune6.0ms

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 2 expressions with local error:

0.0b	(fma (* 4.0 b) b (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
0.4b	(pow (+ (* a a) (* b b)) 2.0)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
3×	`pow1` `add-exp-log` `unpow-prod-down` `pow-unpow`
2×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`pow-to-exp` `pow-pow` `pow-exp` `fma-udef` `sqr-pow`

Counts

2 → 29

Calls

2 calls:

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

series175.0ms

Counts

2 → 6

Calls

2 calls:

74.0ms	(fma (* 4.0 b) b (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
101.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify62.0ms

Algorithm

egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 3 (58.0ms)

Iter	Nodes	Cost
0	137	245
1	492	221
2	1863	214
3	5001	213

prune102.0ms

Filtered

35 candidates to 31 candidates (88.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	30	5	35
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	31	5	36

Merged error: 0.0b

Counts

36 → 5

localize17.0ms

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))
0.6b	(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))
5.0ms	(* 2.0 (pow a 2))
1.0ms	(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

series167.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(fma (* 4.0 b) b (- (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4)) 1.0))
23.0ms	(* 2.0 (pow a 2))
73.0ms	(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

simplify125.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (119.0ms)

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

prune150.0ms

Filtered

58 candidates to 42 candidates (72.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	58	0	58
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	58	5	63

Merged error: 0.0b

Counts

63 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* 4.0 b) b (- (cbrt (pow (pow (fma a a (* b b)) 2.0) 3)) 1.0))
0.2b	(pow (pow (fma a a (* b b)) 2.0) 3)
0.4b	(pow (fma a a (* b b)) 2.0)
24.4b	(cbrt (pow (pow (fma a a (* b b)) 2.0) 3))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

29×	`unpow-prod-down`
20×	`cbrt-prod`
16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
14×	`cube-prod`
7×	`add-exp-log` `sqr-pow`
6×	`pow-unpow`
5×	`pow1` `pow-exp` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp`
2×	`cube-mult` `pow-pow` `unpow3`
1×	`pow1/3` `rem-cbrt-cube` `fma-udef` `rem-cube-cbrt`

Counts

4 → 95

Calls

4 calls:

1.0ms	(fma (* 4.0 b) b (- (cbrt (pow (pow (fma a a (* b b)) 2.0) 3)) 1.0))
4.0ms	(pow (pow (fma a a (* b b)) 2.0) 3)
2.0ms	(pow (fma a a (* b b)) 2.0)
4.0ms	(cbrt (pow (pow (fma a a (* b b)) 2.0) 3))

series457.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(fma (* 4.0 b) b (- (cbrt (pow (pow (fma a a (* b b)) 2.0) 3)) 1.0))
134.0ms	(pow (pow (fma a a (* b b)) 2.0) 3)
108.0ms	(pow (fma a a (* b b)) 2.0)
153.0ms	(cbrt (pow (pow (fma a a (* b b)) 2.0) 3))

simplify49.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	317	687
1	1203	663
2	5001	637

prune225.0ms

Filtered

107 candidates to 67 candidates (62.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	107	5	112

Merged error: 0.0b

Counts

112 → 5

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (* 4.0 b) b (- (cbrt (pow (fma a a (* b b)) (* 2.0 3))) 1.0))
0.4b	(pow (fma a a (* b b)) (* 2.0 3))
24.4b	(cbrt (pow (fma a a (* b b)) (* 2.0 3)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

7×	`cbrt-prod`
6×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity`
4×	`pow1` `add-exp-log`
3×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`sqr-pow`
1×	`pow-to-exp` `pow-unpow` `pow-pow` `pow1/3` `pow-exp` `fma-udef`

Counts

3 → 44

Calls

3 calls:

1.0ms	(fma (* 4.0 b) b (- (cbrt (pow (fma a a (* b b)) (* 2.0 3))) 1.0))
2.0ms	(pow (fma a a (* b b)) (* 2.0 3))
2.0ms	(cbrt (pow (fma a a (* b b)) (* 2.0 3)))

series321.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(fma (* 4.0 b) b (- (cbrt (pow (fma a a (* b b)) (* 2.0 3))) 1.0))
105.0ms	(pow (fma a a (* b b)) (* 2.0 3))
151.0ms	(cbrt (pow (fma a a (* b b)) (* 2.0 3)))

simplify70.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 3 (64.0ms)

Iter	Nodes	Cost
0	185	412
1	622	376
2	2318	370
3	5001	368

prune126.0ms

Filtered

53 candidates to 42 candidates (79.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	53	0	53
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	53	5	58

Merged error: 0.0b

Counts

58 → 5

regimes69.0ms

Accuracy

96.1% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 11.9b

bsearch91.0ms

Steps

Iters	Range		Point
8	0.011261476250181132	4.265898263168925	0.9972258673594039
8	-2.9259323032055495	-0.0003639830197756827	-1.0188075050240837

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	15
1	32	15

end0.0ms

sample1.2s

Algorithm

intervals

Results

799.0ms

20463×

body

valid