Details

sample18.0ms

Algorithm

intervals

Results

5.0ms	200×	body	80	valid
2.0ms	26×	body	640	valid
1.0ms	8×	body	1280	valid
1.0ms	11×	body	320	valid
1.0ms	11×	body	160	valid

simplify77.0ms

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

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.3b

localize6.0ms

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)

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))
0.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

series98.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(/ y (+ y 1.0))
58.0ms	(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

prune291.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.2b

localize11.0ms

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)))
9.0b	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

rewrite30.0ms

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:

2.0ms	(cbrt (+ y 1.0))
2.0ms	(cbrt (+ y 1.0))
22.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
0.0ms	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

series341.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(cbrt (+ y 1.0))
89.0ms	(cbrt (+ y 1.0))
108.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
53.0ms	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

simplify53.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (43.0ms)

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

prune337.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.2b

localize13.0ms

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)))
10.3b	(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

rewrite28.0ms

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:

2.0ms	(cbrt (+ y 1.0))
2.0ms	(cbrt (+ y 1.0))
20.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
0.0ms	(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

series341.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(cbrt (+ y 1.0))
89.0ms	(cbrt (+ y 1.0))
104.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
58.0ms	(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 (41.0ms)

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

prune329.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cbrt (+ y 1.0)))
0.3b	(cbrt (cbrt (+ y 1.0)))
0.3b	(* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))))
9.5b	(fma (/ (/ y (* (* (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)))))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 164

Calls

4 calls:

2.0ms	(cbrt (cbrt (+ y 1.0)))
3.0ms	(cbrt (cbrt (+ y 1.0)))
20.0ms	(* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))))
0.0ms	(fma (/ (/ y (* (* (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)))))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

series368.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(cbrt (cbrt (+ y 1.0)))
93.0ms	(cbrt (cbrt (+ y 1.0)))
122.0ms	(* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))))
61.0ms	(fma (/ (/ y (* (* (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)))))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

simplify74.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	526	3715
1	1442	3572
2	5001	3489

prune516.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.2b

regimes271.0ms

Accuracy

96.4% (0.3b remaining)

Error of 7.4b against oracle of 7.1b and baseline of 14.8b

bsearch76.0ms

Steps

Iters	Range		Point
7	3412093047689.5835	105140736935169.5	103782153027757.69
8	-3.6618581120833803e+31	-4.314447465097623e+28	-4.389623817229428e+28

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	10
1	25	10

end0.0ms

sample445.0ms

Algorithm

intervals

Results

157.0ms	6103×	body	80	valid
65.0ms	742×	body	640	valid
42.0ms	343×	body	1280	valid
33.0ms	497×	body	320	valid
14.0ms	315×	body	160	valid