Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

321×

body

valid

simplify147.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 8 (49.0ms)

Iter	Nodes	Cost
0	14	4
1	34	4
2	92	4
3	232	4
4	491	4
5	785	4
6	1115	4
7	1482	4
8	2218	3
9	3349	3
10	4819	3
11	5001	3

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: 2.8b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma (- y 1.0) z 1.0)
2.7b	(* (fma (- y 1.0) z 1.0) x)

rewrite5.0ms

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`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

2 → 30

Calls

2 calls:

1.0ms	(fma (- y 1.0) z 1.0)
3.0ms	(* (fma (- y 1.0) z 1.0) x)

series84.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(fma (- y 1.0) z 1.0)
56.0ms	(* (fma (- y 1.0) z 1.0) x)

simplify51.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	108	166
1	323	137
2	1922	133
3	5001	133

prune81.0ms

Filtered

36 candidates to 26 candidates (72.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	29	7	36
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	29	8	37

Merged error: 2.7b

Counts

37 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
2.5b	(* (fma (- y 1.0) z 1.0) (* (cbrt x) (cbrt x)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-exp-log` `cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`associate-r` `*-commutative` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
11.0ms	(* (fma (- y 1.0) z 1.0) (* (cbrt x) (cbrt x)))

series712.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(cbrt x)
192.0ms	(cbrt x)
188.0ms	(cbrt x)
144.0ms	(* (fma (- y 1.0) z 1.0) (* (cbrt x) (cbrt x)))

simplify109.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (103.0ms)

Iter	Nodes	Cost
0	181	351
1	665	301
2	3282	274
3	5002	271

prune202.0ms

Filtered

72 candidates to 60 candidates (83.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	71	9	80

Merged error: 2.7b

Counts

80 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
2.9b	(cbrt (fma (- y 1.0) z 1.0))
2.9b	(cbrt (fma (- y 1.0) z 1.0))
2.9b	(cbrt (fma (- y 1.0) z 1.0))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt (fma (- y 1.0) z 1.0))
1.0ms	(cbrt (fma (- y 1.0) z 1.0))
1.0ms	(cbrt (fma (- y 1.0) z 1.0))

series511.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(cbrt x)
106.0ms	(cbrt (fma (- y 1.0) z 1.0))
105.0ms	(cbrt (fma (- y 1.0) z 1.0))
105.0ms	(cbrt (fma (- y 1.0) z 1.0))

simplify52.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 3 (46.0ms)

Iter	Nodes	Cost
0	179	457
1	433	430
2	1563	395
3	5001	374

prune234.0ms

Filtered

64 candidates to 59 candidates (92.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	64	9	73

Merged error: 2.7b

Counts

73 → 9

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt (fma (- y 1.0) z 1.0)) (sqrt (fma (- y 1.0) z 1.0)))
1.2b	(sqrt (fma (- y 1.0) z 1.0))
1.2b	(sqrt (fma (- y 1.0) z 1.0))
1.2b	(* (* (sqrt (fma (- y 1.0) z 1.0)) (sqrt (fma (- y 1.0) z 1.0))) x)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
26×	`pow1`
24×	`sqrt-prod`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
10×	`sqrt-pow1` `pow1/2`
9×	`associate-r`
8×	`swap-sqr`
7×	`associate-l`
6×	`pow-prod-down`
5×	`pow-prod-up` `unswap-sqr`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow-sqr`
2×	`rem-sqrt-square` `*-commutative`
1×	`pow2` `pow-plus` `sqrt-unprod` `rem-square-sqrt`

Counts

4 → 102

Calls

4 calls:

10.0ms	(* (sqrt (fma (- y 1.0) z 1.0)) (sqrt (fma (- y 1.0) z 1.0)))
1.0ms	(sqrt (fma (- y 1.0) z 1.0))
1.0ms	(sqrt (fma (- y 1.0) z 1.0))
8.0ms	(* (* (sqrt (fma (- y 1.0) z 1.0)) (sqrt (fma (- y 1.0) z 1.0))) x)

series293.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (sqrt (fma (- y 1.0) z 1.0)) (sqrt (fma (- y 1.0) z 1.0)))
109.0ms	(sqrt (fma (- y 1.0) z 1.0))
105.0ms	(sqrt (fma (- y 1.0) z 1.0))
51.0ms	(* (* (sqrt (fma (- y 1.0) z 1.0)) (sqrt (fma (- y 1.0) z 1.0))) x)

simplify49.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	258	632
1	1045	531
2	5001	506

prune187.0ms

Filtered

114 candidates to 65 candidates (57.0%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	114	9	123

Merged error: 2.7b

Counts

123 → 9

regimes103.0ms

Accuracy

0% (0.1b remaining)

Error of 3.4b against oracle of 3.3b and baseline of 3.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	3
1	8	3

end0.0ms

sample488.0ms

Algorithm

intervals

Results

287.0ms

10182×

body

valid