Details

sample69.0ms

Algorithm

intervals

Results

19.0ms	256×	body	80	valid
18.0ms	252×	body	80	nan

simplify37.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	50	17
1	108	17
2	389	17
3	1761	17
4	5002	17

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* z (sqrt (+ t a)))
0.3b	(/ 2.0 (* t 3.0))
1.6b	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
3.7b	(/ (* z (sqrt (+ t a))) t)

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

75×	`*-un-lft-identity`
63×	`prod-diff`
62×	`associate--r+`
49×	`add-sqr-sqrt`
45×	`add-cube-cbrt`
36×	`times-frac`
31×	`distribute-rgt-in` `distribute-lft-in`
20×	`frac-sub`
16×	`add-exp-log` `add-cbrt-cube`
15×	`distribute-lft-out`
12×	`div-inv`
9×	`flip3--` `flip--`
8×	`frac-times` `associate-*r/`
7×	`fma-neg` `associate-r`
6×	`pow1` `add-log-exp`
5×	`flip3-+` `sqrt-prod` `flip-+`
4×	`cbrt-undiv` `expm1-log1p-u` `sqrt-div` `div-exp` `associate-/r` `log1p-expm1-u` `associate-/l`
3×	`sub-neg` `associate-l` `prod-exp` `cbrt-unprod`
2×	`frac-2neg` `associate-*l/` `associate--l+` `clear-num` `associate-/l/` `unswap-sqr`
1×	`diff-log` `pow-prod-down` `*-commutative`

Counts

4 → 179

Calls

4 calls:

7.0ms	(* z (sqrt (+ t a)))
5.0ms	(/ 2.0 (* t 3.0))
24.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
8.0ms	(/ (* z (sqrt (+ t a))) t)

series326.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* z (sqrt (+ t a)))
19.0ms	(/ 2.0 (* t 3.0))
175.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
73.0ms	(/ (* z (sqrt (+ t a))) t)

simplify58.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1377	2637
1	5001	2324

prune944.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))
0.2b	(* z (sqrt (+ t a)))
0.3b	(/ 2.0 (* t 3.0))
4.2b	(fma (* z (sqrt (+ t a))) (/ 1 t) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
56×	`prod-diff`
51×	`add-sqr-sqrt`
41×	`add-cube-cbrt`
31×	`distribute-rgt-in` `distribute-lft-in`
27×	`times-frac`
16×	`distribute-lft-out`
13×	`add-exp-log` `associate-r` `add-cbrt-cube`
9×	`div-inv`
8×	`pow1` `frac-times` `flip3--` `associate-l` `flip--`
6×	`associate-*r/` `frac-sub`
5×	`sqrt-prod`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp` `cbrt-unprod` `associate-/l*` `distribute-lft-out--` `unswap-sqr`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `pow-prod-down` `associate-l/` `associate--l+` `-commutative` `difference-of-squares`
1×	`frac-2neg` `clear-num` `associate-/r*` `fma-udef`

Counts

4 → 161

Calls

4 calls:

20.0ms	(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))
7.0ms	(* z (sqrt (+ t a)))
5.0ms	(/ 2.0 (* t 3.0))
1.0ms	(fma (* z (sqrt (+ t a))) (/ 1 t) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

series334.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))
62.0ms	(* z (sqrt (+ t a)))
16.0ms	(/ 2.0 (* t 3.0))
195.0ms	(fma (* z (sqrt (+ t a))) (/ 1 t) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

simplify106.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	900	2516
1	4225	1991
2	5001	1986

prune667.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 0.6666666666666666 (/ b t))
0.2b	(* z (sqrt (+ t a)))
1.0b	(fma 0.6666666666666666 (/ c t) (- (* 0.8333333333333334 b) (* 0.6666666666666666 (/ b t))))
3.8b	(fma (* z (sqrt (+ t a))) (/ 1 t) (- (fma 0.6666666666666666 (/ c t) (- (* 0.8333333333333334 b) (* 0.6666666666666666 (/ b t))))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
20×	`associate-r`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
11×	`add-exp-log` `add-cbrt-cube`
10×	`times-frac`
8×	`pow1`
6×	`associate-l`
5×	`sqrt-prod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-*r/` `prod-exp` `cbrt-unprod`
2×	`sqrt-div` `pow-prod-down` `*-commutative` `fma-udef`
1×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+` `div-inv` `distribute-lft-out`

Counts

4 → 81

Calls

4 calls:

7.0ms	(* 0.6666666666666666 (/ b t))
7.0ms	(* z (sqrt (+ t a)))
1.0ms	(fma 0.6666666666666666 (/ c t) (- (* 0.8333333333333334 b) (* 0.6666666666666666 (/ b t))))
1.0ms	(fma (* z (sqrt (+ t a))) (/ 1 t) (- (fma 0.6666666666666666 (/ c t) (- (* 0.8333333333333334 b) (* 0.6666666666666666 (/ b t))))))

series315.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* 0.6666666666666666 (/ b t))
59.0ms	(* z (sqrt (+ t a)))
46.0ms	(fma 0.6666666666666666 (/ c t) (- (* 0.8333333333333334 b) (* 0.6666666666666666 (/ b t))))
187.0ms	(fma (* z (sqrt (+ t a))) (/ 1 t) (- (fma 0.6666666666666666 (/ c t) (- (* 0.8333333333333334 b) (* 0.6666666666666666 (/ b t))))))

simplify51.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	437	581
1	1802	511
2	5001	502

prune448.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (exp (* 2.0 (fma c a (- (* 0.8333333333333334 c) (* a b))))))
0.0b	(/ x (+ x (* y (exp (* 2.0 (fma c a (- (* 0.8333333333333334 c) (* a b))))))))
0.0b	(- (* 0.8333333333333334 c) (* a b))
0.5b	(fma c a (- (* 0.8333333333333334 c) (* a b)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
8×	`add-cbrt-cube`
7×	`add-exp-log`
6×	`pow1` `add-log-exp`
5×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-l` `associate-/r` `fma-udef` `associate-/l`
2×	`exp-sum` `associate-/r/`
1×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `flip3--` `frac-2neg` `distribute-lft-in` `flip3-+` `fma-neg` `diff-log` `div-exp` `prod-diff` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `div-inv` `unswap-sqr`

Counts

4 → 79

Calls

4 calls:

5.0ms	(* y (exp (* 2.0 (fma c a (- (* 0.8333333333333334 c) (* a b))))))
4.0ms	(/ x (+ x (* y (exp (* 2.0 (fma c a (- (* 0.8333333333333334 c) (* a b))))))))
4.0ms	(- (* 0.8333333333333334 c) (* a b))
1.0ms	(fma c a (- (* 0.8333333333333334 c) (* a b)))

series258.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* y (exp (* 2.0 (fma c a (- (* 0.8333333333333334 c) (* a b))))))
105.0ms	(/ x (+ x (* y (exp (* 2.0 (fma c a (- (* 0.8333333333333334 c) (* a b))))))))
44.0ms	(- (* 0.8333333333333334 c) (* a b))
41.0ms	(fma c a (- (* 0.8333333333333334 c) (* a b)))

simplify102.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 3 (92.0ms)

Iter	Nodes	Cost
0	336	842
1	1192	764
2	4110	756
3	5001	753

prune319.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.2b

regimes267.0ms

Accuracy

0% (2.0b remaining)

Error of 2.8b against oracle of 0.7b and baseline of 2.8b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	18
1	46	18
2	46	18

end0.0ms

sample2.1s

Algorithm

intervals

Results

824.0ms	8000×	body	80	valid
586.0ms	8094×	body	80	nan