Details

sample69.0ms

Algorithm

intervals

Results

47.0ms

351×

body

valid

simplify61.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (13.0ms)

Iter	Nodes	Cost
0	25	8
1	50	8
2	106	8
3	208	8
4	322	6
5	520	6
6	1439	6
7	5002	6

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.1b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma (/ (fma z (- 1.0 t) 1) z) (/ 2.0 t) (/ x y))
10.3b	(/ (fma z (- 1.0 t) 1) z)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 39

Calls

2 calls:

0.0ms	(fma (/ (fma z (- 1.0 t) 1) z) (/ 2.0 t) (/ x y))
2.0ms	(/ (fma z (- 1.0 t) 1) z)

series118.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(fma (/ (fma z (- 1.0 t) 1) z) (/ 2.0 t) (/ x y))
31.0ms	(/ (fma z (- 1.0 t) 1) z)

simplify40.0ms

Algorithm

egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 3 (35.0ms)

Iter	Nodes	Cost
0	142	296
1	371	268
2	1311	266
3	5001	265

prune146.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 1 expressions with local error:

0.1b	(fma (- (+ (/ 1 z) 1.0) t) (/ 2.0 t) (/ x y))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma (- (+ (/ 1 z) 1.0) t) (/ 2.0 t) (/ x y))

series74.0ms

Counts

1 → 3

Calls

1 calls:

74.0ms

(fma (- (+ (/ 1 z) 1.0) t) (/ 2.0 t) (/ x y))

simplify100.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 3 (28.0ms)

Iter	Nodes	Cost
0	59	106
1	137	92
2	598	90
3	3188	89
4	5002	89

prune49.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma 2.0 (/ 1 t) (- (/ x y) 2.0))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma 2.0 (/ 1 t) (- (/ x y) 2.0))

series29.0ms

Counts

1 → 3

Calls

1 calls:

29.0ms

(fma 2.0 (/ 1 t) (- (/ x y) 2.0))

simplify50.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	34	77
1	66	65
2	301	64
3	1777	64
4	5001	64

prune41.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* z 2.0) (- 1.0 t))
0.0b	(+ 2.0 (* (* z 2.0) (- 1.0 t)))
0.0b	(+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z)))
11.4b	(/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
41×	`add-sqr-sqrt`
39×	`add-cube-cbrt`
36×	`prod-diff`
22×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in`
16×	`fma-def`
14×	`add-exp-log` `add-cbrt-cube`
12×	`times-frac`
9×	`pow1`
8×	`add-log-exp`
5×	`associate-r`
4×	`expm1-log1p-u` `sub-neg` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`flip3-+` `pow-prod-down` `flip-+` `associate-/l*`
2×	`cbrt-undiv` `+-commutative` `associate-*r/` `div-exp` `sum-log` `div-inv` `associate-/l/`
1×	`flip3--` `frac-2neg` `associate-l` `frac-add` `clear-num` `associate-/r` `-commutative` `flip--` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 137

Calls

4 calls:

13.0ms	(* (* z 2.0) (- 1.0 t))
6.0ms	(+ 2.0 (* (* z 2.0) (- 1.0 t)))
19.0ms	(+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z)))
10.0ms	(/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))

series193.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (* z 2.0) (- 1.0 t))
35.0ms	(+ 2.0 (* (* z 2.0) (- 1.0 t)))
47.0ms	(+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z)))
65.0ms	(/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))

simplify76.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	622	1150
1	2605	863
2	5001	850

prune344.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes172.0ms

Accuracy

98.4% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 14.8b

bsearch107.0ms

Steps

Iters	Range		Point
9	0.08936077200344487	181026.7805503304	178345.00744601226
6	-6.228819855298706e+22	-6.162994032929348e+21	-1.4970573561140433e+22

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	11
1	30	11

end0.0ms

sample1.1s

Algorithm

intervals

Results

811.0ms

10346×

body

valid