Details

sample25.0ms

Algorithm

intervals

Results

9.0ms

273×

body

valid

simplify120.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	24	8
1	43	8
2	75	8
3	120	8
4	156	8
5	189	8
6	265	8
7	451	8
8	1023	8
9	3632	8
10	5001	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.0b	(* z (- b y))
0.6b	(+ (* x y) (* z (- t a)))
23.9b	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
54×	`prod-diff`
52×	`add-cube-cbrt`
33×	`distribute-rgt-in` `distribute-lft-in`
22×	`associate-+r+`
10×	`add-exp-log` `associate-r` `add-cbrt-cube`
9×	`times-frac`
8×	`pow1`
6×	`sub-neg` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`flip3--` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `flip--` `cbrt-unprod` `associate-/l/` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `fma-def` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 161

Calls

4 calls:

23.0ms	(* z (- t a))
21.0ms	(* z (- b y))
12.0ms	(+ (* x y) (* z (- t a)))
33.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

series370.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* z (- t a))
30.0ms	(* z (- b y))
38.0ms	(+ (* x y) (* z (- t a)))
272.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify76.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	623	1398
1	2536	1029
2	5002	1026

prune399.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 24.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- b y))
0.6b	(+ (* x y) (+ (* z t) (* z (- a))))
1.2b	(+ (* z t) (* z (- a)))
23.9b	(/ (+ (* x y) (+ (* z t) (* z (- a)))) (+ y (* z (- b y))))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`add-cube-cbrt`
18×	`prod-diff`
11×	`distribute-rgt-in` `distribute-lft-in` `add-log-exp`
9×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `distribute-rgt-neg-out`
5×	`associate-r`
4×	`expm1-log1p-u` `associate-+r-` `flip3-+` `sum-log` `flip-+` `log1p-expm1-u`
3×	`associate-l` `unsub-neg` `associate-/r` `associate-/l`
2×	`+-commutative` `sub-neg` `fma-def` `div-sub` `associate-*r/` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `associate-+r+` `flip3--` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 116

Calls

4 calls:

22.0ms	(* z (- b y))
18.0ms	(+ (* x y) (+ (* z t) (* z (- a))))
8.0ms	(+ (* z t) (* z (- a)))
69.0ms	(/ (+ (* x y) (+ (* z t) (* z (- a)))) (+ y (* z (- b y))))

series377.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* z (- b y))
36.0ms	(+ (* x y) (+ (* z t) (* z (- a))))
30.0ms	(+ (* z t) (* z (- a)))
278.0ms	(/ (+ (* x y) (+ (* z t) (* z (- a)))) (+ y (* z (- b y))))

simplify80.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	515	1134
1	2439	903
2	5001	889

prune322.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 22.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma t z (* x y))
2.6b	(/ a (/ (fma z (- b y) y) z))
12.7b	(/ (fma z (- b y) y) z)
22.1b	(/ (fma t z (* x y)) (fma z (- b y) y))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 140

Calls

4 calls:

0.0ms	(fma t z (* x y))
8.0ms	(/ a (/ (fma z (- b y) y) z))
5.0ms	(/ (fma z (- b y) y) z)
5.0ms	(/ (fma t z (* x y)) (fma z (- b y) y))

series231.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(fma t z (* x y))
51.0ms	(/ a (/ (fma z (- b y) y) z))
29.0ms	(/ (fma z (- b y) y) z)
117.0ms	(/ (fma t z (* x y)) (fma z (- b y) y))

simplify49.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	430	1181
1	1684	1108
2	5001	1107

prune515.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (fma t z (* x y)) (fma z (- b y) y)) (/ a (- (+ (/ y z) b) y)))
0.3b	(fma t z (* x y))
2.6b	(/ a (- (+ (/ y z) b) y))
22.1b	(/ (fma t z (* x y)) (fma z (- b y) y))

rewrite327.0ms

Algorithm

rewrite-expression-head

Rules

560×	`*-un-lft-identity`
496×	`times-frac`
426×	`add-sqr-sqrt`
328×	`add-cube-cbrt`
312×	`prod-diff`
92×	`distribute-lft-out--`
47×	`difference-of-squares`
44×	`distribute-lft-out`
40×	`div-inv`
28×	`associate-/r/`
15×	`flip3--` `flip--`
13×	`fma-neg`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`sub-neg` `diff-log` `frac-sub` `fma-udef`

Counts

4 → 430

Calls

4 calls:

199.0ms	(- (/ (fma t z (* x y)) (fma z (- b y) y)) (/ a (- (+ (/ y z) b) y)))
0.0ms	(fma t z (* x y))
85.0ms	(/ a (- (+ (/ y z) b) y))
5.0ms	(/ (fma t z (* x y)) (fma z (- b y) y))

series516.0ms

Counts

4 → 12

Calls

4 calls:

317.0ms	(- (/ (fma t z (* x y)) (fma z (- b y) y)) (/ a (- (+ (/ y z) b) y)))
35.0ms	(fma t z (* x y))
41.0ms	(/ a (- (+ (/ y z) b) y))
123.0ms	(/ (fma t z (* x y)) (fma z (- b y) y))

simplify173.0ms

Algorithm

egg-herbie

Counts

442 → 442

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	1051	16472
1	3018	12590
2	5001	11531

prune767.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.8b

regimes491.0ms

Accuracy

-6.4% (7.0b remaining)

Error of 17.9b against oracle of 10.9b and baseline of 17.5b

bsearch119.0ms

Steps

Iters	Range		Point
10	2.997466419422173e-271	7.200386832681243e-261	1.3630801030974825e-270
10	-5.073065905379409e-216	-3.318013815777787e-229	-5.783355807704604e-229

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	17
1	33	17

end0.0ms

sample730.0ms

Algorithm

intervals

Results

333.0ms

8443×

body

valid