Details

sample19.0ms

Algorithm

intervals

Results

5.0ms	193×	body	80	valid
3.0ms	26×	body	640	valid
2.0ms	14×	body	1280	valid
1.0ms	15×	body	320	valid
0.0ms	8×	body	160	valid

simplify93.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (15.0ms)

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

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (+ y 1.0))
2.3b	(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:

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

series101.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(/ y (+ y 1.0))
64.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify118.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (113.0ms)

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

prune159.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.9b

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))
11.0b	(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)

series365.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(cbrt (+ y 1.0))
100.0ms	(cbrt (+ y 1.0))
101.0ms	(cbrt (+ y 1.0))
65.0ms	(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

simplify95.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (85.0ms)

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

prune286.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ y 1.0))
0.3b	(cbrt (cbrt (+ y 1.0)))
0.3b	(cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))
10.8b	(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)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

26×	`cbrt-div`
16×	`cbrt-prod`
11×	`*-un-lft-identity`
8×	`flip3-+` `flip-+`
7×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`associate-r/` `associate-l/` `distribute-lft-out`
1×	`fma-udef`

Counts

4 → 64

Calls

4 calls:

2.0ms	(cbrt (+ y 1.0))
3.0ms	(cbrt (cbrt (+ y 1.0)))
12.0ms	(cbrt (* (cbrt (+ y 1.0)) (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)

series391.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(cbrt (+ y 1.0))
101.0ms	(cbrt (cbrt (+ y 1.0)))
128.0ms	(cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))
61.0ms	(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)

simplify143.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (134.0ms)

Iter	Nodes	Cost
0	459	840
1	1326	768
2	4857	745
3	5001	743

prune364.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt y)
0.5b	(cbrt y)
0.5b	(cbrt y)
11.7b	(fma (/ (* (cbrt y) (cbrt y)) (/ (+ y 1.0) (cbrt y))) (- 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:

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

series688.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(cbrt y)
197.0ms	(cbrt y)
208.0ms	(cbrt y)
79.0ms	(fma (/ (* (cbrt y) (cbrt y)) (/ (+ y 1.0) (cbrt y))) (- x 1.0) 1.0)

simplify48.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	104	277
1	278	244
2	1012	231
3	5002	227

prune200.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.9b

regimes138.0ms

Accuracy

97.5% (0.2b remaining)

Error of 7.1b against oracle of 6.9b and baseline of 14.7b

bsearch110.0ms

Steps

Iters	Range		Point
8	29561296481055.625	1.4777983484669568e+17	1.3726044535258429e+17
10	-3.341477536928727e+31	-7.482341115906907e+20	-7.584316785868146e+20

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	16
1	33	16

end0.0ms

sample456.0ms

Algorithm

intervals

Results

156.0ms	6147×	body	80	valid
73.0ms	723×	body	640	valid
42.0ms	367×	body	1280	valid
34.0ms	498×	body	320	valid
12.0ms	265×	body	160	valid