Details

sample27.0ms

Algorithm

intervals

Results

7.0ms	231×	body	80	valid
1.0ms	13×	body	640	valid
1.0ms	13×	body	320	valid
1.0ms	16×	body	160	valid
1.0ms	6×	body	1280	valid
0.0ms	1×	body	2560	valid

simplify96.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (20.0ms)

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

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.8b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (- a t))
11.8b	(fma (/ y (- a t)) (- t z) (+ x y))

rewrite14.0ms

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:

11.0ms	(/ y (- a t))
0.0ms	(fma (/ y (- a t)) (- t z) (+ x y))

series120.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(/ y (- a t))
85.0ms	(fma (/ y (- a t)) (- t z) (+ x y))

simplify57.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 1 (9.0ms)

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

prune196.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.6b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a t))
0.2b	(* y (/ 1 (- a t)))
11.8b	(fma (* y (/ 1 (- a t))) (- t z) (+ x y))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 99

Calls

3 calls:

15.0ms	(/ 1 (- a t))
30.0ms	(* y (/ 1 (- a t)))
0.0ms	(fma (* y (/ 1 (- a t))) (- t z) (+ x y))

series148.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(/ 1 (- a t))
33.0ms	(* y (/ 1 (- a t)))
78.0ms	(fma (* y (/ 1 (- a t))) (- t z) (+ x y))

simplify90.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 3 (82.0ms)

Iter	Nodes	Cost
0	288	510
1	1143	440
2	4305	394
3	5001	391

prune295.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ y (- a t))
4.2b	(+ (* (/ y (- a t)) (- t z)) (+ x y))
9.7b	(* (/ y (- a t)) (- t z))

rewrite105.0ms

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:

11.0ms	(/ y (- a t))
34.0ms	(+ (* (/ y (- a t)) (- t z)) (+ x y))
50.0ms	(* (/ y (- a t)) (- t z))

series299.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(/ y (- a t))
109.0ms	(+ (* (/ y (- a t)) (- t z)) (+ x y))
155.0ms	(* (/ y (- a t)) (- t z))

simplify139.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 1 (28.0ms)

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

prune552.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 6.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt t)
0.6b	(cbrt t)
8.1b	(+ (+ (* (/ y (- a t)) (fma (* (cbrt t) (cbrt t)) (cbrt t) (- (* z 1)))) (* (/ y (- a t)) (fma (- z) 1 z))) (+ x y))
9.7b	(* (/ y (- a t)) (fma (* (cbrt t) (cbrt t)) (cbrt t) (- (* z 1))))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

1.0ms	(cbrt t)
1.0ms	(cbrt t)
96.0ms	(+ (+ (* (/ y (- a t)) (fma (* (cbrt t) (cbrt t)) (cbrt t) (- (* z 1)))) (* (/ y (- a t)) (fma (- z) 1 z))) (+ x y))
30.0ms	(* (/ y (- a t)) (fma (* (cbrt t) (cbrt t)) (cbrt t) (- (* z 1))))

series2.4s

Counts

4 → 12

Calls

4 calls:

199.0ms	(cbrt t)
196.0ms	(cbrt t)
1.7s	(+ (+ (* (/ y (- a t)) (fma (* (cbrt t) (cbrt t)) (cbrt t) (- (* z 1)))) (* (/ y (- a t)) (fma (- z) 1 z))) (+ x y))
326.0ms	(* (/ y (- a t)) (fma (* (cbrt t) (cbrt t)) (cbrt t) (- (* z 1))))

simplify98.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	612	1580
1	2825	1378
2	5001	1270

prune543.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 6.6b

regimes406.0ms

Accuracy

7.1% (5.0b remaining)

Error of 11.3b against oracle of 6.4b and baseline of 11.7b

bsearch43.0ms

Steps

Iters	Range		Point
8	1.7114128752150242e+232	1.6889154279208131e+236	1.1874236633075585e+236

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	6
1	19	6

end0.0ms

sample740.0ms

Algorithm

intervals

Results

241.0ms	7395×	body	80	valid
49.0ms	450×	body	640	valid
38.0ms	401×	body	320	valid
32.0ms	227×	body	1280	valid
19.0ms	278×	body	160	valid
2.0ms	11×	body	2560	valid