Details

sample31.0ms

Algorithm

intervals

Results

12.0ms	246×	body	80	valid
2.0ms	14×	body	640	valid
1.0ms	7×	body	1280	valid
1.0ms	12×	body	160	valid
1.0ms	7×	body	320	valid

simplify89.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (17.0ms)

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

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (- a t))
11.7b	(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))
0.0ms	(fma (/ y (- a t)) (- t z) (+ x y))

series118.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(/ y (- a t))
86.0ms	(fma (/ y (- a t)) (- t z) (+ x y))

simplify50.0ms

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

prune190.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ y (- a t))
3.3b	(+ (* (/ y (- a t)) (- t z)) (+ x y))
11.3b	(* (/ y (- a t)) (- t z))

rewrite61.0ms

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))
19.0ms	(+ (* (/ y (- a t)) (- t z)) (+ x y))
28.0ms	(* (/ y (- a t)) (- t z))

series299.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(/ y (- a t))
104.0ms	(+ (* (/ y (- a t)) (- t z)) (+ x y))
164.0ms	(* (/ y (- a t)) (- t z))

simplify116.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 1 (27.0ms)

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

prune540.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 4.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t z) (- a t))
2.0b	(* y (/ (- t z) (- a t)))
2.6b	(+ (* y (/ (- t z) (- a t))) (+ x y))

rewrite58.0ms

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:

13.0ms	(/ (- t z) (- a t))
26.0ms	(* y (/ (- t z) (- a t)))
14.0ms	(+ (* y (/ (- t z) (- a t))) (+ x y))

series273.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(/ (- t z) (- a t))
75.0ms	(* y (/ (- t z) (- a t)))
153.0ms	(+ (* y (/ (- t z) (- a t))) (+ x y))

simplify74.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (63.0ms)

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

prune374.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt t) (cbrt t))
2.2b	(fma (fma (- z) 1 z) (/ y (- a t)) (+ x y))
7.9b	(+ (* (/ y (- a t)) (fma (* (cbrt t) (cbrt t)) (cbrt t) (- (* z 1)))) (fma (fma (- z) 1 z) (/ y (- a t)) (+ x y)))
11.3b	(* (/ y (- a t)) (fma (* (cbrt t) (cbrt t)) (cbrt t) (- (* z 1))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
27×	`associate-l`
22×	`add-cube-cbrt`
16×	`cbrt-prod` `times-frac`
13×	`pow1`
11×	`add-exp-log`
9×	`associate-r` `add-cbrt-cube`
6×	`pow1/3` `swap-sqr` `fma-udef` `add-log-exp` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
2×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`cbrt-undiv` `+-commutative` `pow2` `associate-+r+` `flip3--` `fma-def` `flip3-+` `pow-plus` `div-exp` `associate-*l/` `sum-log` `flip--` `flip-+` `div-inv`

Counts

4 → 113

Calls

4 calls:

6.0ms	(* (cbrt t) (cbrt t))
0.0ms	(fma (fma (- z) 1 z) (/ y (- a t)) (+ x y))
7.0ms	(+ (* (/ y (- a t)) (fma (* (cbrt t) (cbrt t)) (cbrt t) (- (* z 1)))) (fma (fma (- z) 1 z) (/ y (- a t)) (+ x y)))
18.0ms	(* (/ y (- a t)) (fma (* (cbrt t) (cbrt t)) (cbrt t) (- (* z 1))))

series842.0ms

Counts

4 → 12

Calls

4 calls:

225.0ms	(* (cbrt t) (cbrt t))
76.0ms	(fma (fma (- z) 1 z) (/ y (- a t)) (+ x y))
224.0ms	(+ (* (/ y (- a t)) (fma (* (cbrt t) (cbrt t)) (cbrt t) (- (* z 1)))) (fma (fma (- z) 1 z) (/ y (- a t)) (+ x y)))
315.0ms	(* (/ y (- a t)) (fma (* (cbrt t) (cbrt t)) (cbrt t) (- (* z 1))))

simplify67.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	423	1219
1	1691	1057
2	5002	999

prune557.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 2.1b

regimes321.0ms

Accuracy

33.1% (5.5b remaining)

Error of 8.7b against oracle of 3.2b and baseline of 11.4b

bsearch140.0ms

Steps

Iters	Range		Point
3	4.0910301706116353e+195	5.751632181509589e+195	5.051159983781011e+195
8	6.82792270422599e-132	1.874185897584732e-128	6.953532797602288e-132
8	-3.096534851920775e-204	-3.468909176406779e-207	-4.6048919476334295e-207
4	-6.119555717661402e+211	-3.403986436091667e+211	-4.469700295762919e+211

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	23
1	38	23

end0.0ms

sample691.0ms

Algorithm

intervals

Results

274.0ms	7411×	body	80	valid
58.0ms	454×	body	640	valid
39.0ms	404×	body	320	valid
38.0ms	235×	body	1280	valid
15.0ms	227×	body	160	valid
3.0ms	17×	body	2560	valid