Details

sample20.0ms

Algorithm

intervals

Results

6.0ms	195×	body	80	valid
2.0ms	15×	body	1280	valid
2.0ms	21×	body	320	valid
2.0ms	15×	body	640	valid
1.0ms	10×	body	160	valid

simplify78.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (10.0ms)

Iter	Nodes	Cost
0	16	5
1	35	5
2	76	5
3	137	5
4	285	4
5	459	4
6	719	4
7	848	4
8	1064	4
9	1397	4
10	2101	4
11	5002	4

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: 14.2b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (+ y 1.0))
2.7b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
12×	`times-frac`
11×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `distribute-lft-out`
3×	`associate-/l*`
2×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `fma-udef` `div-inv`

Counts

2 → 45

Calls

2 calls:

5.0ms	(/ y (+ y 1.0))
1.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

series97.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(/ y (+ y 1.0))
61.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify110.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (105.0ms)

Iter	Nodes	Cost
0	203	263
1	708	238
2	3148	232
3	5002	228

prune129.0ms

Filtered

51 candidates to 40 candidates (78.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	43	8	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	8	52

Merged error: 6.8b

Counts

52 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ y 1.0))
0.3b	(cbrt (+ y 1.0))
0.3b	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
10.7b	(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

32×	`cbrt-prod` `*-un-lft-identity`
22×	`add-sqr-sqrt`
16×	`cbrt-div`
14×	`add-cube-cbrt`
11×	`pow1`
9×	`swap-sqr`
8×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 97

Calls

4 calls:

6.0ms	(cbrt (+ y 1.0))
3.0ms	(cbrt (+ y 1.0))
10.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
1.0ms	(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

series344.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(cbrt (+ y 1.0))
94.0ms	(cbrt (+ y 1.0))
106.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
55.0ms	(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

simplify51.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	365	866
1	1251	798
2	5001	736

prune291.0ms

Filtered

109 candidates to 79 candidates (72.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	106	3	109
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	107	10	117

Merged error: 6.8b

Counts

117 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ y 1.0))
0.3b	(cbrt (+ y 1.0))
0.3b	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
9.7b	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

32×	`cbrt-prod` `*-un-lft-identity`
22×	`add-sqr-sqrt`
16×	`cbrt-div`
14×	`add-cube-cbrt`
11×	`pow1`
9×	`swap-sqr`
8×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 97

Calls

4 calls:

3.0ms	(cbrt (+ y 1.0))
3.0ms	(cbrt (+ y 1.0))
10.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
1.0ms	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

series340.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(cbrt (+ y 1.0))
90.0ms	(cbrt (+ y 1.0))
104.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
56.0ms	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

simplify54.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	370	879
1	1298	813
2	5001	756

prune291.0ms

Filtered

109 candidates to 79 candidates (72.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	109	10	119

Merged error: 6.8b

Counts

119 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (fma (/ y (+ y 1.0)) (- x 1.0) 1.0)) (cbrt (fma (/ y (+ y 1.0)) (- x 1.0) 1.0)))
2.7b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
2.7b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
2.7b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`cbrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
6×	`add-exp-log` `pow1/3` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`fma-udef`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 72

Calls

4 calls:

8.0ms	(* (cbrt (fma (/ y (+ y 1.0)) (- x 1.0) 1.0)) (cbrt (fma (/ y (+ y 1.0)) (- x 1.0) 1.0)))
1.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
1.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
1.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

series284.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(* (cbrt (fma (/ y (+ y 1.0)) (- x 1.0) 1.0)) (cbrt (fma (/ y (+ y 1.0)) (- x 1.0) 1.0)))
52.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
56.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
53.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify112.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (102.0ms)

Iter	Nodes	Cost
0	203	822
1	713	736
2	3312	647
3	5001	632

prune221.0ms

Filtered

84 candidates to 66 candidates (78.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	84	10	94

Merged error: 6.8b

Counts

94 → 10

regimes111.0ms

Accuracy

96.8% (0.2b remaining)

Error of 7.7b against oracle of 7.5b and baseline of 15.2b

bsearch103.0ms

Steps

Iters	Range		Point
8	5.472625713654374e+33	5.351829534137145e+36	3.2432591410128616e+34
9	-2.9496256244778682e+47	-1.020599224133985e+40	-1.189067865360937e+40

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	12
1	25	12

end0.0ms

sample539.0ms

Algorithm

intervals

Results

183.0ms	6060×	body	80	valid
84.0ms	718×	body	640	valid
56.0ms	376×	body	1280	valid
55.0ms	531×	body	320	valid
18.0ms	315×	body	160	valid