Details

sample25.0ms

Algorithm

intervals

Results

7.0ms	232×	body	80	valid
2.0ms	20×	body	640	valid
1.0ms	5×	body	1280	valid
1.0ms	8×	body	320	valid
1.0ms	9×	body	160	valid

simplify88.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (16.0ms)

Iter	Nodes	Cost
0	22	6
1	52	6
2	111	6
3	213	6
4	517	5
5	1051	5
6	2055	5
7	3280	5
8	5002	5

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.1b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (- a t))
12.1b	(fma (/ y (- a t)) (- t z) (+ x y))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/r*`
4×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
3×	`associate-/l*`
2×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `fma-udef` `div-inv`

Counts

2 → 49

Calls

2 calls:

6.0ms	(/ y (- a t))
1.0ms	(fma (/ y (- a t)) (- t z) (+ x y))

series125.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(/ y (- a t))
92.0ms	(fma (/ y (- a t)) (- t z) (+ x y))

simplify52.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	170	278
1	468	257
2	1400	257
3	5002	257

prune209.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.9b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ y (- a t))
2.9b	(+ (* (/ y (- a t)) (- t z)) (+ x y))
11.9b	(* (/ y (- a t)) (- t z))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 157

Calls

3 calls:

6.0ms	(/ y (- a t))
17.0ms	(+ (* (/ y (- a t)) (- t z)) (+ x y))
15.0ms	(* (/ y (- a t)) (- t z))

series331.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(/ y (- a t))
118.0ms	(+ (* (/ y (- a t)) (- t z)) (+ x y))
178.0ms	(* (/ y (- a t)) (- t z))

simplify126.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	859	1392
1	4016	1146
2	5001	1146

prune576.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.9b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t z) (- a t))
1.3b	(* y (/ (- t z) (- a t)))
2.1b	(+ (* y (/ (- t z) (- a t))) (+ x y))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 124

Calls

3 calls:

10.0ms	(/ (- t z) (- a t))
20.0ms	(* y (/ (- t z) (- a t)))
14.0ms	(+ (* y (/ (- t z) (- a t))) (+ x y))

series291.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(/ (- t z) (- a t))
81.0ms	(* y (/ (- t z) (- a t)))
160.0ms	(+ (* y (/ (- t z) (- a t))) (+ x y))

simplify83.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	529	835
1	2239	790
2	5002	788

prune412.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.3b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t z) (- a t))
2.4b	(fma y (/ (- t z) (- a t)) (+ x y))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
14×	`add-cube-cbrt`
12×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

2 → 64

Calls

2 calls:

10.0ms	(/ (- t z) (- a t))
1.0ms	(fma y (/ (- t z) (- a t)) (+ x y))

series205.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(/ (- t z) (- a t))
148.0ms	(fma y (/ (- t z) (- a t)) (+ x y))

simplify71.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	257	444
1	699	419
2	2385	417
3	5003	417

prune187.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.3b

regimes390.0ms

Accuracy

39.3% (5.2b remaining)

Error of 8.5b against oracle of 3.3b and baseline of 11.9b

bsearch53.0ms

Steps

Iters	Range		Point
3	5.062782482725967e+112	6.853081242536654e+112	6.293612880095814e+112
6	-1.2499242660617276e+132	-1.613027370669321e+131	-3.124308255832831e+131

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	14
1	25	14

end0.0ms

sample651.0ms

Algorithm

intervals

Results

243.0ms	7284×	body	80	valid
55.0ms	465×	body	640	valid
42.0ms	264×	body	1280	valid
36.0ms	402×	body	320	valid
16.0ms	260×	body	160	valid
4.0ms	22×	body	2560	valid