Details

sample27.0ms

Algorithm

intervals

Results

12.0ms

269×

body

valid

simplify141.0ms

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: 23.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- b y))
0.0b	(+ y (* z (- b y)))
1.4b	(+ (* x y) (* z (- t a)))
22.2b	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

rewrite45.0ms

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:

12.0ms	(* z (- b y))
6.0ms	(+ y (* z (- b y)))
6.0ms	(+ (* x y) (* z (- t a)))
12.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

series527.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* z (- b y))
36.0ms	(+ y (* z (- b y)))
55.0ms	(+ (* x y) (* z (- t a)))
392.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify90.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	602	1288
1	2282	956
2	5001	937

prune543.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 22.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ y (* z (- b y)))
0.4b	(/ 1 (+ y (* z (- b y))))
1.4b	(+ (* x y) (* z (- t a)))
22.0b	(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
45×	`add-cube-cbrt`
44×	`associate-+r+`
36×	`prod-diff`
22×	`distribute-rgt-in` `distribute-lft-in`
20×	`times-frac`
17×	`add-exp-log`
15×	`associate-r`
11×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `sub-neg` `fma-def` `div-exp` `prod-exp` `associate-/r/` `log1p-expm1-u`
3×	`associate-l` `associate-/r` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `+-commutative` `frac-times` `rec-exp` `1-exp` `associate-*l/` `sum-log` `cbrt-unprod` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 153

Calls

4 calls:

6.0ms	(+ y (* z (- b y)))
4.0ms	(/ 1 (+ y (* z (- b y))))
6.0ms	(+ (* x y) (* z (- t a)))
19.0ms	(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

series535.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(+ y (* z (- b y)))
102.0ms	(/ 1 (+ y (* z (- b y))))
47.0ms	(+ (* x y) (* z (- t a)))
344.0ms	(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

simplify85.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	636	1265
1	2433	974
2	5002	935

prune561.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 22.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (- b y) z y)
0.0b	(* z (- t a))
0.8b	(fma x y (* z (- t a)))
22.2b	(/ (fma x y (* z (- t a))) (fma (- b y) z y))

rewrite17.0ms

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`
9×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
5×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `associate-/r` `associate-/l`
2×	`sub-neg` `associate-*r/` `fma-udef`
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 → 95

Calls

4 calls:

0.0ms	(fma (- b y) z y)
12.0ms	(* z (- t a))
0.0ms	(fma x y (* z (- t a)))
2.0ms	(/ (fma x y (* z (- t a))) (fma (- b y) z y))

series546.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(fma (- b y) z y)
44.0ms	(* z (- t a))
59.0ms	(fma x y (* z (- t a)))
400.0ms	(/ (fma x y (* z (- t a))) (fma (- b y) z y))

simplify47.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	307	774
1	1107	590
2	5001	584

prune335.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 22.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.3b	(/ 1 (/ (fma (- b y) z y) (fma x y (* z (- t a)))))
0.8b	(fma x y (* z (- t a)))
22.2b	(/ (fma (- b y) z y) (fma x y (* z (- t a))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
72×	`add-sqr-sqrt`
70×	`*-un-lft-identity`
68×	`add-cube-cbrt`
19×	`add-exp-log`
18×	`prod-diff`
16×	`associate-/r*`
13×	`add-cbrt-cube`
11×	`distribute-rgt-in` `distribute-lft-in`
8×	`div-exp`
7×	`pow1`
6×	`div-inv` `associate-/l*`
5×	`associate-r`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l`
2×	`sub-neg` `rec-exp` `frac-2neg` `1-exp` `associate-*r/` `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 → 163

Calls

4 calls:

12.0ms	(* z (- t a))
9.0ms	(/ 1 (/ (fma (- b y) z y) (fma x y (* z (- t a)))))
0.0ms	(fma x y (* z (- t a)))
2.0ms	(/ (fma (- b y) z y) (fma x y (* z (- t a))))

series1.5s

Counts

4 → 12

Calls

4 calls:

47.0ms	(* z (- t a))
1.2s	(/ 1 (/ (fma (- b y) z y) (fma x y (* z (- t a)))))
56.0ms	(fma x y (* z (- t a)))
159.0ms	(/ (fma (- b y) z y) (fma x y (* z (- t a))))

simplify74.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	520	1776
1	2146	1503
2	5001	1426

prune454.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 9.7b

regimes599.0ms

Accuracy

25.7% (9.1b remaining)

Error of 20.0b against oracle of 10.9b and baseline of 23.1b

bsearch226.0ms

Steps

Iters	Range		Point
8	6.573114990353364e+143	1.8305461003977325e+147	1.2504401644554392e+144
7	6.304040304238585e-244	5.231673809435745e-242	6.448648093686567e-244
9	-1.2356307952735333e-300	-3.8488857116735985e-306	-3.533788581774126e-305
6	-1.4396773096708945e+78	-3.2980394925689044e+77	-1.4242621929487041e+78

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	25
1	44	25
2	44	25

end0.0ms

sample672.0ms

Algorithm

intervals

Results

375.0ms

8454×

body

valid