Details

sample18.0ms

Algorithm

intervals

Results

5.0ms	198×	body	80	valid
2.0ms	25×	body	640	valid
1.0ms	11×	body	1280	valid
1.0ms	13×	body	320	valid
0.0ms	9×	body	160	valid

simplify100.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (16.0ms)

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

prune7.0ms

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: 13.7b

Counts

2 → 2

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (+ y 1.0))
3.0b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

rewrite8.0ms

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:

36.0ms	(/ y (+ y 1.0))
61.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify125.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (119.0ms)

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

prune142.0ms

Filtered

51 candidates to 40 candidates (78.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	41	10	51
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	43	10	53

Merged error: 6.2b

Counts

53 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (+ y 1.0))
0.2b	(cbrt (+ y 1.0))
0.3b	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
10.2b	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

rewrite26.0ms

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))
15.0ms	(* (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)

series378.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(cbrt (+ y 1.0))
99.0ms	(cbrt (+ y 1.0))
120.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
58.0ms	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

simplify64.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (52.0ms)

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

prune327.0ms

Filtered

109 candidates to 79 candidates (72.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	103	6	109
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	106	13	119

Merged error: 6.2b

Counts

119 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
0.3b	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
0.3b	(* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))))
10.2b	(fma (* (/ 1 (* (* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))) (* (cbrt (cbrt (+ y 1.0))) (cbrt (cbrt (+ y 1.0)))))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

384×	`cbrt-div`
144×	`frac-times`
120×	`flip3-+` `flip-+`
56×	`cbrt-prod`
52×	`*-un-lft-identity`
48×	`associate-r/` `associate-l/`
44×	`add-sqr-sqrt`
25×	`pow1`
24×	`add-cube-cbrt`
22×	`swap-sqr`
18×	`pow1/3` `associate-r` `associate-l`
12×	`distribute-lft-out` `unswap-sqr`
10×	`add-exp-log`
6×	`pow-prod-down` `pow-sqr` `pow-prod-up`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`
1×	`fma-udef`

Counts

4 → 236

Calls

4 calls:

11.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
12.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
17.0ms	(* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))))
1.0ms	(fma (* (/ 1 (* (* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))) (* (cbrt (cbrt (+ y 1.0))) (cbrt (cbrt (+ y 1.0)))))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

series435.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
116.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
127.0ms	(* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))))
68.0ms	(fma (* (/ 1 (* (* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))) (* (cbrt (cbrt (+ y 1.0))) (cbrt (cbrt (+ y 1.0)))))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

simplify102.0ms

Algorithm

egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	556	4260
1	1783	4086
2	5001	3923

prune729.0ms

Filtered

248 candidates to 129 candidates (52.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	246	2	248
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	248	13	261

Merged error: 6.2b

Counts

261 → 13

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)) (cbrt (fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)))
10.2b	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)
10.2b	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)
10.2b	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

rewrite11.0ms

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:

6.0ms	(* (cbrt (fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)) (cbrt (fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)))
1.0ms	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)
1.0ms	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)
1.0ms	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

series319.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(* (cbrt (fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)) (cbrt (fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)))
57.0ms	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)
65.0ms	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)
63.0ms	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

simplify147.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (130.0ms)

Iter	Nodes	Cost
0	214	1838
1	777	1637
2	3939	1420
3	5002	1391

prune272.0ms

Filtered

84 candidates to 66 candidates (78.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	81	3	84
Fresh	4	8	12
Picked	0	1	1
Done	0	0	0
Total	85	12	97

Merged error: 6.1b

Counts

97 → 12

regimes147.0ms

Accuracy

94.7% (0.4b remaining)

Error of 7.3b against oracle of 6.9b and baseline of 15.1b

bsearch96.0ms

Steps

Iters	Range		Point
7	1.715848015119154e+77	1.1146202952519258e+79	1.743087357113103e+77
9	-937727910791.0848	-216561.7802280358	-925888037866.017

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	12
1	25	12

end0.0ms

sample443.0ms

Algorithm

intervals

Results

153.0ms	6077×	body	80	valid
74.0ms	748×	body	640	valid
39.0ms	355×	body	1280	valid
33.0ms	492×	body	320	valid
15.0ms	328×	body	160	valid