Details

sample25.0ms

Algorithm

intervals

Results

11.0ms

272×

body

valid

simplify125.0ms

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: 19.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.0b	(+ y (* z (- b y)))
0.9b	(+ (* x y) (* z (- t a)))
18.9b	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 153

Calls

4 calls:

7.0ms	(* z (- t a))
6.0ms	(+ y (* z (- b y)))
6.0ms	(+ (* x y) (* z (- t a)))
8.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

series430.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* z (- t a))
29.0ms	(+ y (* z (- b y)))
41.0ms	(+ (* x y) (* z (- t a)))
322.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify77.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	608	1288
1	2360	956
2	5001	942

prune497.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 18.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- t a) z)
0.0b	(+ y (* z (- b y)))
0.9b	(+ (* x y) (* (- t a) z))
18.9b	(/ (+ (* x y) (* (- t a) z)) (+ y (* z (- b y))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

6.0ms	(* (- t a) z)
6.0ms	(+ y (* z (- b y)))
4.0ms	(+ (* x y) (* (- t a) z))
9.0ms	(/ (+ (* x y) (* (- t a) z)) (+ y (* z (- b y))))

series364.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (- t a) z)
28.0ms	(+ y (* z (- b y)))
43.0ms	(+ (* x y) (* (- t a) z))
265.0ms	(/ (+ (* x y) (* (- t a) z)) (+ y (* z (- b y))))

simplify63.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	471	866
1	1831	720
2	5001	706

prune411.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 18.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- t a) z)
0.3b	(/ 1 (fma (- b y) z y))
0.9b	(+ (* x y) (* (- t a) z))
18.6b	(* (+ (* x y) (* (- t a) z)) (/ 1 (fma (- b y) z y)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
22×	`add-cube-cbrt`
20×	`times-frac`
19×	`add-exp-log`
16×	`associate-r`
13×	`add-cbrt-cube`
9×	`pow1`
8×	`associate-l`
6×	`add-log-exp`
5×	`prod-exp`
4×	`expm1-log1p-u` `div-exp` `associate-*l/` `log1p-expm1-u` `unswap-sqr`
3×	`flip3-+` `associate-/r` `cbrt-unprod` `flip-+` `associate-/l`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`+-commutative` `flip3--` `pow-flip` `fma-def` `frac-2neg` `associate-*r/` `clear-num` `sum-log` `un-div-inv` `flip--` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 113

Calls

4 calls:

6.0ms	(* (- t a) z)
3.0ms	(/ 1 (fma (- b y) z y))
4.0ms	(+ (* x y) (* (- t a) z))
9.0ms	(* (+ (* x y) (* (- t a) z)) (/ 1 (fma (- b y) z y)))

series421.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (- t a) z)
92.0ms	(/ 1 (fma (- b y) z y))
38.0ms	(+ (* x y) (* (- t a) z))
262.0ms	(* (+ (* x y) (* (- t a) z)) (/ 1 (fma (- b y) z y)))

simplify63.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	395	826
1	1733	725
2	5001	694

prune384.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 18.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- t a) z)
0.3b	(fma x y (* (- t a) z))
0.3b	(/ 1 (/ (fma (- b y) z y) (fma x y (* (- t a) z))))
18.9b	(/ (fma (- b y) z y) (fma x y (* (- t a) z)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
60×	`add-sqr-sqrt`
58×	`*-un-lft-identity`
56×	`add-cube-cbrt`
19×	`add-exp-log`
16×	`associate-/r*`
13×	`add-cbrt-cube`
8×	`div-exp`
7×	`pow1`
6×	`div-inv` `associate-/l*`
5×	`associate-l`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r`
2×	`rec-exp` `frac-2neg` `1-exp` `associate-*l/` `clear-num`
1×	`flip3--` `pow-flip` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `distribute-lft-out--` `inv-pow` `difference-of-squares` `unswap-sqr`

Counts

4 → 141

Calls

4 calls:

6.0ms	(* (- t a) z)
1.0ms	(fma x y (* (- t a) z))
6.0ms	(/ 1 (/ (fma (- b y) z y) (fma x y (* (- t a) z))))
3.0ms	(/ (fma (- b y) z y) (fma x y (* (- t a) z)))

series1.4s

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (- t a) z)
49.0ms	(fma x y (* (- t a) z))
1.2s	(/ 1 (/ (fma (- b y) z y) (fma x y (* (- t a) z))))
147.0ms	(/ (fma (- b y) z y) (fma x y (* (- t a) z)))

simplify57.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	440	1512
1	1791	1365
2	5001	1288

prune397.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 9.5b

regimes478.0ms

Accuracy

26.5% (8.9b remaining)

Error of 19.5b against oracle of 10.6b and baseline of 22.8b

bsearch114.0ms

Steps

Iters	Range		Point
11	4.519164425443069e+160	5.962840217746747e+181	4.663714500791799e+160
8	-1.6406409362584404e+46	-6.23051408650639e+43	-4.028259719465096e+45

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	11
1	31	11

end0.0ms

sample660.0ms

Algorithm

intervals

Results

357.0ms

8436×

body

valid