Details

sample25.0ms

Algorithm

intervals

Results

12.0ms

256×

body

valid

simplify86.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	38	7
1	72	7
2	167	6
3	354	6
4	646	6
5	921	6
6	1060	6
7	1331	6
8	1792	6
9	1860	6
10	1861	6
11	1861	6

prune9.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 16.4b

Counts

2 → 2

localize17.0ms

Local error

Found 3 expressions with local error:

0.1b

(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)

3.8b

(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))

16.5b

(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`fma-udef`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 49

Calls

3 calls:

1.0ms

(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)

3.0ms

(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))

1.0ms

(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series225.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms

(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)

63.0ms

(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))

136.0ms

(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify103.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (96.0ms)

Iter	Nodes	Cost
0	232	361
1	733	322
2	3221	319
3	5002	317

prune204.0ms

Filtered

58 candidates to 48 candidates (82.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	52	6	58
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	53	7	60

Merged error: 0.0b

Counts

60 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (fma z 0.0692910599291889 0.4917317610505968) z) 0.279195317918525)
0.1b	(* (fma z 0.0692910599291889 0.4917317610505968) z)
3.8b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
16.5b	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (+ (* (fma z 0.0692910599291889 0.4917317610505968) z) 0.279195317918525) x)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r` `associate-l` `associate-/r` `associate-/l`
1×	`cbrt-undiv` `+-commutative` `fma-def` `frac-2neg` `flip3-+` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `fma-udef` `div-inv` `unswap-sqr`

Counts

4 → 73

Calls

4 calls:

4.0ms	(+ (* (fma z 0.0692910599291889 0.4917317610505968) z) 0.279195317918525)
4.0ms	(* (fma z 0.0692910599291889 0.4917317610505968) z)
3.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
1.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (+ (* (fma z 0.0692910599291889 0.4917317610505968) z) 0.279195317918525) x)

series288.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* (fma z 0.0692910599291889 0.4917317610505968) z) 0.279195317918525)
64.0ms	(* (fma z 0.0692910599291889 0.4917317610505968) z)
63.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
136.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (+ (* (fma z 0.0692910599291889 0.4917317610505968) z) 0.279195317918525) x)

simplify45.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	346	487
1	1161	435
2	5002	430

prune237.0ms

Filtered

85 candidates to 65 candidates (76.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	86	6	92

Merged error: 0.0b

Counts

92 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
5.9b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
19.0b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-exp-log` `add-cbrt-cube`
14×	`*-un-lft-identity`
12×	`add-cube-cbrt`
10×	`pow1` `associate-l`
9×	`associate-r`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `associate-r/` `associate-l/` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `pow-prod-down` `associate-/r` `-commutative` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-/r/` `associate-/l/`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `div-inv` `distribute-lft-out` `associate-/l*`

Counts

4 → 96

Calls

4 calls:

6.0ms	(* (+ z 6.012459259764103) z)
7.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
10.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
15.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series286.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (+ z 6.012459259764103) z)
67.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
52.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
121.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify79.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	549	703
1	2591	599
2	5001	580

prune287.0ms

Filtered

108 candidates to 86 candidates (79.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	109	5	114

Merged error: 0b

Counts

114 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (* y (/ (* (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) 1) (fma (+ z 6.012459259764103) z 3.350343815022304))))
0.1b	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
0.1b	(* y (/ (* (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) 1) (fma (+ z 6.012459259764103) z 3.350343815022304)))
15.9b	(/ (* (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) 1) (fma (+ z 6.012459259764103) z 3.350343815022304))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
18×	`add-cbrt-cube`
12×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`prod-exp`
7×	`associate-r`
6×	`pow1` `times-frac` `div-exp` `add-log-exp`
5×	`cbrt-unprod`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `associate-l` `associate-/r*`
2×	`1-exp` `div-inv`
1×	`+-commutative` `frac-2neg` `flip3-+` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+` `fma-udef` `associate-/l*` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

3.0ms	(+ x (* y (/ (* (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) 1) (fma (+ z 6.012459259764103) z 3.350343815022304))))
1.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
7.0ms	(* y (/ (* (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) 1) (fma (+ z 6.012459259764103) z 3.350343815022304)))
5.0ms	(/ (* (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) 1) (fma (+ z 6.012459259764103) z 3.350343815022304))

series357.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(+ x (* y (/ (* (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) 1) (fma (+ z 6.012459259764103) z 3.350343815022304))))
27.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
112.0ms	(* y (/ (* (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) 1) (fma (+ z 6.012459259764103) z 3.350343815022304)))
75.0ms	(/ (* (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) 1) (fma (+ z 6.012459259764103) z 3.350343815022304))

simplify56.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	410	742
1	1568	631
2	5001	623

prune226.0ms

Filtered

92 candidates to 69 candidates (75.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	92	5	97

Merged error: 0b

Counts

97 → 5

regimes198.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 16.7b

bsearch156.0ms

Steps

Iters	Range		Point
9	25340457.240933813	24331955248945.938	368397930.6992925
10	-5.630651790137533e+148	-3.2958475431658706e+136	-2.5941619095089283e+142

simplify11.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	11
1	38	11
2	38	11

end0.0ms

sample572.0ms

Algorithm

intervals

Results

402.0ms

8000×

body

valid