Details

sample29.0ms

Algorithm

intervals

Results

16.0ms

256×

body

valid

simplify89.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

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

prune10.0ms

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: 17.4b

Counts

2 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (+ z 6.012459259764103) z 3.350343815022304)
0.0b	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
3.5b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
17.3b	(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

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

Counts

4 → 59

Calls

4 calls:

1.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
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)

series243.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
29.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
59.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
135.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify109.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (101.0ms)

Iter	Nodes	Cost
0	245	408
1	760	361
2	3482	358
3	5001	356

prune254.0ms

Filtered

71 candidates to 59 candidates (83.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	68	5	73

Merged error: 0.0b

Counts

73 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))))
16.1b	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
16.1b	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
17.3b	(fma (* (/ 1 (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

80×	`add-sqr-sqrt`
58×	`times-frac`
38×	`*-un-lft-identity`
35×	`sqrt-prod`
32×	`add-cube-cbrt`
26×	`add-exp-log`
22×	`associate-r` `associate-l`
16×	`add-cbrt-cube`
15×	`unswap-sqr`
8×	`pow1` `div-exp` `prod-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `div-inv`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `fma-udef`

Counts

4 → 125

Calls

4 calls:

22.0ms	(* (/ 1 (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))))
2.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
2.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
1.0ms	(fma (* (/ 1 (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series244.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (/ 1 (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))))
58.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
52.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
91.0ms	(fma (* (/ 1 (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify79.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	569	1489
1	2571	1300
2	5001	1177

prune387.0ms

Filtered

137 candidates to 91 candidates (66.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	137	5	142

Merged error: 0.0b

Counts

142 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt y)
1.1b	(/ (fma (+ z 6.012459259764103) z 3.350343815022304) (cbrt y))
2.8b	(/ (* (cbrt y) (cbrt y)) (/ (fma (+ z 6.012459259764103) z 3.350343815022304) (cbrt y)))
17.3b	(fma (/ (* (cbrt y) (cbrt y)) (/ (fma (+ z 6.012459259764103) z 3.350343815022304) (cbrt y))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
46×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
33×	`cbrt-prod`
28×	`associate-/r*`
18×	`add-exp-log`
11×	`add-cbrt-cube`
7×	`cbrt-undiv` `div-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
1×	`pow1/3` `associate-/r/` `fma-udef`

Counts

4 → 130

Calls

4 calls:

1.0ms	(cbrt y)
4.0ms	(/ (fma (+ z 6.012459259764103) z 3.350343815022304) (cbrt y))
15.0ms	(/ (* (cbrt y) (cbrt y)) (/ (fma (+ z 6.012459259764103) z 3.350343815022304) (cbrt y)))
1.0ms	(fma (/ (* (cbrt y) (cbrt y)) (/ (fma (+ z 6.012459259764103) z 3.350343815022304) (cbrt y))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series507.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(cbrt y)
89.0ms	(/ (fma (+ z 6.012459259764103) z 3.350343815022304) (cbrt y))
81.0ms	(/ (* (cbrt y) (cbrt y)) (/ (fma (+ z 6.012459259764103) z 3.350343815022304) (cbrt y)))
154.0ms	(fma (/ (* (cbrt y) (cbrt y)) (/ (fma (+ z 6.012459259764103) z 3.350343815022304) (cbrt y))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify84.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	560	1416
1	2535	1260
2	5001	1224

prune536.0ms

Filtered

142 candidates to 122 candidates (85.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	142	5	147

Merged error: 0.0b

Counts

147 → 5

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
4.3b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
20.7b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite41.0ms

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)
6.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
10.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
16.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series497.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (+ z 6.012459259764103) z)
66.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
264.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
125.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify76.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (65.0ms)

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

prune277.0ms

Filtered

108 candidates to 86 candidates (79.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	0	1	1
Picked	0	1	1
Done	2	1	3
Total	109	4	113

Merged error: 0b

Counts

113 → 4

regimes164.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 15.9b

bsearch114.0ms

Steps

Iters	Range		Point
8	62623256.830634765	266766999996.46997	132522234.411505
6	-6.565988221710644e+18	-4.809746162353075e+17	-4.8943025023709235e+17

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	13
1	40	13

end0.0ms

sample581.0ms

Algorithm

intervals

Results

408.0ms

8000×

body

valid

Details

sample29.0ms

simplify89.0ms

prune10.0ms

localize13.0ms

rewrite6.0ms

series243.0ms

simplify109.0ms

prune254.0ms

localize16.0ms

rewrite31.0ms

series244.0ms

simplify79.0ms

prune387.0ms

localize16.0ms

rewrite26.0ms

series507.0ms

simplify84.0ms

prune536.0ms

localize18.0ms

rewrite41.0ms

series497.0ms

simplify76.0ms

prune277.0ms

regimes164.0ms

bsearch114.0ms

simplify2.0ms

end0.0ms

sample581.0ms

Profiling