Details

sample39.0ms

Algorithm

intervals

Results

18.0ms

407×

body

valid

simplify136.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 6 (134.0ms)

Iter	Nodes	Cost
0	38	9
1	103	9
2	327	9
3	921	9
4	1996	9
5	4841	9
6	5001	8

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (- 4.0) (/ (* t a) c) (/ (fma x (* 9.0 y) b) (* z c)))
0.1b	(fma x (* 9.0 y) b)
3.7b	(/ (* t a) c)
8.7b	(/ (fma x (* 9.0 y) b) (* z c))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`times-frac`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `fma-udef` `div-inv`

Counts

4 → 66

Calls

4 calls:

0.0ms	(fma (- 4.0) (/ (* t a) c) (/ (fma x (* 9.0 y) b) (* z c)))
0.0ms	(fma x (* 9.0 y) b)
3.0ms	(/ (* t a) c)
3.0ms	(/ (fma x (* 9.0 y) b) (* z c))

series320.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(fma (- 4.0) (/ (* t a) c) (/ (fma x (* 9.0 y) b) (* z c)))
31.0ms	(fma x (* 9.0 y) b)
25.0ms	(/ (* t a) c)
52.0ms	(/ (fma x (* 9.0 y) b) (* z c))

simplify36.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	284	424
1	1137	356
2	5001	355

prune328.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma 9.0 (/ (* x y) (* z c)) (- (/ b (* z c)) (* 4.0 (/ (* a t) c))))
3.7b	(/ (* a t) c)
4.9b	(/ b (* z c))
8.2b	(/ (* x y) (* z c))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-exp-log` `add-cbrt-cube`
8×	`cbrt-undiv` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `div-exp`
7×	`times-frac`
6×	`prod-exp` `cbrt-unprod`
5×	`associate-/r` `associate-/l`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num` `div-inv`
1×	`fma-udef`

Counts

4 → 79

Calls

4 calls:

0.0ms	(fma 9.0 (/ (* x y) (* z c)) (- (/ b (* z c)) (* 4.0 (/ (* a t) c))))
3.0ms	(/ (* a t) c)
3.0ms	(/ b (* z c))
5.0ms	(/ (* x y) (* z c))

series467.0ms

Counts

4 → 12

Calls

4 calls:

398.0ms	(fma 9.0 (/ (* x y) (* z c)) (- (/ b (* z c)) (* 4.0 (/ (* a t) c))))
19.0ms	(/ (* a t) c)
20.0ms	(/ b (* z c))
30.0ms	(/ (* x y) (* z c))

simplify52.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	366	480
1	1832	391
2	5001	391

prune316.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 9.0 (/ (* x y) (* z c)))
3.7b	(/ (* a t) c)
4.9b	(/ b (* z c))
8.2b	(/ (* x y) (* z c))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-exp-log` `add-cbrt-cube`
15×	`prod-exp` `cbrt-unprod`
12×	`cbrt-undiv` `add-sqr-sqrt` `div-exp`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`times-frac`
6×	`pow1`
5×	`associate-r` `associate-/r` `associate-/l`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`frac-2neg` `associate-l` `clear-num`
1×	`associate-r/` `pow-prod-down` `-commutative` `unswap-sqr`

Counts

4 → 100

Calls

4 calls:

11.0ms	(* 9.0 (/ (* x y) (* z c)))
3.0ms	(/ (* a t) c)
3.0ms	(/ b (* z c))
4.0ms	(/ (* x y) (* z c))

series107.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* 9.0 (/ (* x y) (* z c)))
19.0ms	(/ (* a t) c)
19.0ms	(/ b (* z c))
27.0ms	(/ (* x y) (* z c))

simplify60.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	428	533
1	2373	414
2	5001	414

prune341.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (cbrt 9.0) (cbrt 9.0)) (* (cbrt 9.0) (/ (* x y) (* z c))))
3.7b	(/ (* a t) c)
4.9b	(/ b (* z c))
8.2b	(/ (* x y) (* z c))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

82×	`add-exp-log`
60×	`add-cbrt-cube`
42×	`prod-exp` `cbrt-unprod`
16×	`pow1` `cbrt-undiv` `div-exp`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `pow-prod-down`
7×	`times-frac`
5×	`associate-/r` `associate-/l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num` `div-inv`
2×	`associate-*r/`
1×	`associate-r` `associate-l` `*-commutative`

Counts

4 → 110

Calls

4 calls:

38.0ms	(* (* (cbrt 9.0) (cbrt 9.0)) (* (cbrt 9.0) (/ (* x y) (* z c))))
3.0ms	(/ (* a t) c)
3.0ms	(/ b (* z c))
4.0ms	(/ (* x y) (* z c))

series191.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(* (* (cbrt 9.0) (cbrt 9.0)) (* (cbrt 9.0) (/ (* x y) (* z c))))
22.0ms	(/ (* a t) c)
19.0ms	(/ b (* z c))
27.0ms	(/ (* x y) (* z c))

simplify72.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	547	860
1	2811	597
2	5001	547

prune330.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes520.0ms

Accuracy

23% (8.7b remaining)

Error of 9.1b against oracle of 0.4b and baseline of 11.7b

bsearch163.0ms

Steps

Iters	Range	Point
8	3.0077244934687315e+28	3.4199543026471762e+31	3.6764060547952857e+28
6	-1.641550318914516e-22	-2.4332783127346934e-23	-1.6191182781259973e-22
3	-7.993453836776187e+180	-6.902427357417022e+180	-7.788886371896345e+180

Iters

Range

Point

3.0077244934687315e+28

3.4199543026471762e+31

3.6764060547952857e+28

-1.641550318914516e-22

-2.4332783127346934e-23

-1.6191182781259973e-22

-7.993453836776187e+180

-6.902427357417022e+180

-7.788886371896345e+180

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	43
1	69	43
2	69	43

end0.0ms

sample1.1s

Algorithm

intervals

Results

580.0ms

12819×

body

valid