Details

sample17.0ms

Algorithm

intervals

Results

5.0ms	205×	body	80	valid
2.0ms	22×	body	640	valid
1.0ms	9×	body	1280	valid
1.0ms	12×	body	320	valid
0.0ms	8×	body	160	valid

simplify75.0ms

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: 12.0b

localize6.0ms

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:

6.0ms	(/ y (+ y 1.0))
0.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

series94.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(/ y (+ y 1.0))
61.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify107.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (102.0ms)

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

prune145.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.0b

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

rewrite9.0ms

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:

2.0ms	(cbrt (+ y 1.0))
2.0ms	(cbrt (+ y 1.0))
2.0ms	(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)

series337.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(cbrt (+ y 1.0))
92.0ms	(cbrt (+ y 1.0))
94.0ms	(cbrt (+ y 1.0))
59.0ms	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

simplify77.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (70.0ms)

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

prune276.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.9b

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

rewrite9.0ms

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:

2.0ms	(cbrt (+ y 1.0))
2.0ms	(cbrt (+ y 1.0))
2.0ms	(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)

series340.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(cbrt (+ y 1.0))
92.0ms	(cbrt (+ y 1.0))
91.0ms	(cbrt (+ y 1.0))
59.0ms	(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

simplify68.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (61.0ms)

Iter	Nodes	Cost
0	230	552
1	657	500
2	2252	479
3	5001	448

prune284.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.9b

localize20.0ms

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

rewrite9.0ms

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:

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

series571.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(cbrt (+ y 1.0))
317.0ms	(cbrt (+ y 1.0))
100.0ms	(cbrt (+ y 1.0))
57.0ms	(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0))))) (- x 1.0) 1.0)

simplify73.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (65.0ms)

Iter	Nodes	Cost
0	235	656
1	688	593
2	2483	578
3	5001	549

prune301.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.9b

regimes113.0ms

Accuracy

97.1% (0.2b remaining)

Error of 7.0b against oracle of 6.7b and baseline of 14.9b

bsearch93.0ms

Steps

Iters	Range		Point
8	3.598893780584373e+18	4.062357698265298e+22	3.7814858199416627e+18
10	-7.255563364262488e+58	-1.2440326111864124e+49	-2.62681269552233e+49

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	12
1	25	12

end0.0ms

sample449.0ms

Algorithm

intervals

Results

157.0ms	6090×	body	80	valid
64.0ms	744×	body	640	valid
41.0ms	336×	body	1280	valid
36.0ms	548×	body	320	valid
13.0ms	282×	body	160	valid