Details

sample42.0ms

Algorithm

intervals

Results

26.0ms

676×

body

valid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (4.0ms)

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: 0.1b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

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

4.0ms	(+ (* a a) (* b b))
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)

series213.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(+ (* a a) (* b b))
77.0ms	(fma (* 4.0 b) b (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
102.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify110.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (105.0ms)

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

prune138.0ms

Filtered

52 candidates to 43 candidates (82.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	47	5	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	5	53

Merged error: 0.0b

Counts

53 → 5

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 39

Calls

3 calls:

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

series215.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(fma a a (* b b))
69.0ms	(fma (* 4.0 b) b (- (pow (fma a a (* b b)) 2.0) 1.0))
112.0ms	(pow (fma a a (* b b)) 2.0)

simplify73.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	143	254
1	533	227
2	2126	221
3	5001	221

prune121.0ms

Filtered

48 candidates to 37 candidates (77.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	47	1	48
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	48	5	53

Merged error: 0.0b

Counts

53 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* 4.0 b) b (- (pow (cbrt (pow (fma a a (* b b)) 3)) 2.0) 1.0))
0.3b	(pow (cbrt (pow (fma a a (* b b)) 3)) 2.0)
0.3b	(pow (fma a a (* b b)) 3)
23.7b	(cbrt (pow (fma a a (* b b)) 3))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

1.0ms	(fma (* 4.0 b) b (- (pow (cbrt (pow (fma a a (* b b)) 3)) 2.0) 1.0))
4.0ms	(pow (cbrt (pow (fma a a (* b b)) 3)) 2.0)
2.0ms	(pow (fma a a (* b b)) 3)
3.0ms	(cbrt (pow (fma a a (* b b)) 3))

series299.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(fma (* 4.0 b) b (- (pow (cbrt (pow (fma a a (* b b)) 3)) 2.0) 1.0))
111.0ms	(pow (cbrt (pow (fma a a (* b b)) 3)) 2.0)
81.0ms	(pow (fma a a (* b b)) 3)
39.0ms	(cbrt (pow (fma a a (* b b)) 3))

simplify46.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	277	642
1	1094	561
2	5001	515

prune220.0ms

Filtered

102 candidates to 62 candidates (60.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	102	5	107

Merged error: 0.0b

Counts

107 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (cbrt (* (fma a a (* b b)) (fma a a (* b b)))) 2.0)
0.5b	(pow (cbrt (fma a a (* b b))) 2.0)
9.4b	(cbrt (fma a a (* b b)))
20.0b	(cbrt (* (fma a a (* b b)) (fma a a (* b b))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

3.0ms	(pow (cbrt (* (fma a a (* b b)) (fma a a (* b b)))) 2.0)
3.0ms	(pow (cbrt (fma a a (* b b))) 2.0)
1.0ms	(cbrt (fma a a (* b b)))
3.0ms	(cbrt (* (fma a a (* b b)) (fma a a (* b b))))

series534.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(pow (cbrt (* (fma a a (* b b)) (fma a a (* b b)))) 2.0)
152.0ms	(pow (cbrt (fma a a (* b b))) 2.0)
106.0ms	(cbrt (fma a a (* b b)))
110.0ms	(cbrt (* (fma a a (* b b)) (fma a a (* b b))))

simplify118.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 3 (110.0ms)

Iter	Nodes	Cost
0	271	564
1	954	530
2	3717	526
3	5001	523

prune245.0ms

Filtered

80 candidates to 62 candidates (77.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	80	5	85

Merged error: 0.0b

Counts

85 → 5

regimes50.0ms

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	12	6
1	12	6

end0.0ms

sample1.1s

Algorithm

intervals

Results

776.0ms

20103×

body

valid