Details

sample37.0ms

Algorithm

intervals

Results

15.0ms	204×	body	80	valid
6.0ms	26×	body	640	valid
4.0ms	12×	body	160	valid
2.0ms	8×	body	1280	valid
1.0ms	6×	body	320	valid

simplify98.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (+ y 1.0))
2.4b	(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)

series97.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(/ y (+ y 1.0))
62.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify120.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (114.0ms)

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

prune145.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (+ y 1.0))
0.2b	(cbrt (+ y 1.0))
0.2b	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
8.4b	(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

rewrite27.0ms

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))
19.0ms	(* (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)

series377.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(cbrt (+ y 1.0))
99.0ms	(cbrt (+ y 1.0))
116.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
62.0ms	(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

simplify58.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (47.0ms)

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

prune363.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
0.6b	(cbrt y)
8.2b	(fma (* (* (cbrt y) (cbrt y)) (/ (cbrt y) (+ y 1.0))) (- x 1.0) 1.0)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

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

series683.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(cbrt y)
199.0ms	(cbrt y)
197.0ms	(cbrt y)
80.0ms	(fma (* (* (cbrt y) (cbrt y)) (/ (cbrt y) (+ y 1.0))) (- x 1.0) 1.0)

simplify58.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (53.0ms)

Iter	Nodes	Cost
0	104	277
1	282	243
2	1092	232
3	5002	228

prune228.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
8.2b	(fma (* (* (cbrt y) (cbrt y)) (/ (cbrt y) (+ y 1.0))) (- x 1.0) 1.0)
8.2b	(fma (* (* (cbrt y) (cbrt y)) (/ (cbrt y) (+ y 1.0))) (- x 1.0) 1.0)
8.2b	(fma (* (* (cbrt y) (cbrt y)) (/ (cbrt y) (+ y 1.0))) (- x 1.0) 1.0)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `fma-udef`
1×	`pow1/3`

Counts

4 → 43

Calls

4 calls:

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

series427.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(cbrt y)
78.0ms	(fma (* (* (cbrt y) (cbrt y)) (/ (cbrt y) (+ y 1.0))) (- x 1.0) 1.0)
78.0ms	(fma (* (* (cbrt y) (cbrt y)) (/ (cbrt y) (+ y 1.0))) (- x 1.0) 1.0)
77.0ms	(fma (* (* (cbrt y) (cbrt y)) (/ (cbrt y) (+ y 1.0))) (- x 1.0) 1.0)

simplify58.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 3 (51.0ms)

Iter	Nodes	Cost
0	104	487
1	282	409
2	1092	392
3	5002	380

prune256.0ms

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 5.8b

regimes164.0ms

Accuracy

91.5% (0.6b remaining)

Error of 7.9b against oracle of 7.4b and baseline of 14.1b

bsearch115.0ms

Steps

Iters	Range		Point
8	1.6181465099452298e+83	1.07853335669406e+87	1.6483859772857023e+83
9	-9.778561198240692e+82	-4.6118413363907316e+76	-4.6712571438578067e+76

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	8
1	21	8

end0.0ms

sample983.0ms

Algorithm

intervals

Results

447.0ms	6129×	body	80	valid
164.0ms	723×	body	640	valid
104.0ms	367×	body	1280	valid
85.0ms	502×	body	320	valid
34.0ms	279×	body	160	valid