Details

sample18.0ms

Algorithm

intervals

Results

5.0ms	196×	body	80	valid
2.0ms	19×	body	640	valid
1.0ms	13×	body	1280	valid
1.0ms	18×	body	320	valid
0.0ms	10×	body	160	valid

simplify86.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (12.0ms)

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: 14.1b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (+ y 1.0))
3.3b	(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)

series99.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(/ y (+ y 1.0))
62.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify116.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (111.0ms)

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

prune145.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.7b

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))
10.8b	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
1×	`fma-udef`

Counts

4 → 58

Calls

4 calls:

3.0ms	(cbrt (+ y 1.0))
3.0ms	(cbrt (+ y 1.0))
3.0ms	(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)

series355.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(cbrt (+ y 1.0))
98.0ms	(cbrt (+ y 1.0))
99.0ms	(cbrt (+ y 1.0))
62.0ms	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

simplify84.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (76.0ms)

Iter	Nodes	Cost
0	235	565
1	699	515
2	2697	493
3	5001	461

prune280.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.6b

localize17.0ms

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))
10.8b	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0)))))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
1×	`fma-udef`

Counts

4 → 58

Calls

4 calls:

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

series355.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(cbrt (+ y 1.0))
99.0ms	(cbrt (+ y 1.0))
96.0ms	(cbrt (+ y 1.0))
61.0ms	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0)))))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

simplify94.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (85.0ms)

Iter	Nodes	Cost
0	241	669
1	728	603
2	3039	588
3	5002	559

prune335.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt y)
0.7b	(cbrt y)
0.7b	(cbrt y)
11.5b	(fma (* (* (cbrt y) (cbrt y)) (/ (cbrt y) (+ y 1.0))) (- x 1.0) 1.0)

rewrite5.0ms

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:

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

series660.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(cbrt y)
192.0ms	(cbrt y)
197.0ms	(cbrt y)
77.0ms	(fma (* (* (cbrt y) (cbrt y)) (/ (cbrt y) (+ y 1.0))) (- x 1.0) 1.0)

simplify54.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (49.0ms)

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

prune187.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.6b

regimes107.0ms

Accuracy

95.5% (0.3b remaining)

Error of 8.0b against oracle of 7.6b and baseline of 15.1b

bsearch115.0ms

Steps

Iters	Range		Point
9	1.9953183704216438e+61	3.9737512383462755e+67	1.2215535105105902e+62
9	-4.804704296627161e+20	-742734949029190.9	-3.186285420639384e+16

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	21
1	37	21

end0.0ms

sample448.0ms

Algorithm

intervals

Results

153.0ms	6075×	body	80	valid
74.0ms	731×	body	640	valid
42.0ms	370×	body	1280	valid
35.0ms	531×	body	320	valid
13.0ms	293×	body	160	valid