Details

sample26.0ms

Algorithm

intervals

Results

8.0ms	239×	body	80	valid
2.0ms	21×	body	320	valid
2.0ms	15×	body	640	valid
1.0ms	4×	body	1280	valid
0.0ms	6×	body	160	valid

simplify88.0ms

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

prune9.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.4b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (- a t))
11.0b	(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))

series115.0ms

Counts

2 → 6

Calls

2 calls:

29.0ms	(/ y (- a t))
85.0ms	(fma (/ y (- a t)) (- t z) (+ x y))

simplify67.0ms

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

prune197.0ms

Filtered

55 candidates to 43 candidates (78.2%)

Pruning

13 alts after pruning (13 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)))
11.0b	(fma (* y (/ 1 (- a t))) (- t z) (+ x y))

rewrite27.0ms

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:

6.0ms	(/ 1 (- a t))
17.0ms	(* y (/ 1 (- a t)))
0.0ms	(fma (* y (/ 1 (- a t))) (- t z) (+ x y))

series156.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(/ 1 (- a t))
30.0ms	(* y (/ 1 (- a t)))
86.0ms	(fma (* y (/ 1 (- a t))) (- t z) (+ x y))

simplify82.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 3 (75.0ms)

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

prune292.0ms

Filtered

108 candidates to 65 candidates (60.2%)

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))
3.1b	(+ (* (/ y (- a t)) (- t z)) (+ x y))
12.2b	(* (/ y (- a t)) (- t z))

rewrite59.0ms

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:

5.0ms	(/ y (- a t))
17.0ms	(+ (* (/ y (- a t)) (- t z)) (+ x y))
26.0ms	(* (/ y (- a t)) (- t z))

series293.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(/ y (- a t))
104.0ms	(+ (* (/ y (- a t)) (- t z)) (+ x y))
156.0ms	(* (/ y (- a t)) (- t z))

simplify115.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 1 (27.0ms)

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

prune545.0ms

Filtered

166 candidates to 119 candidates (71.7%)

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 6.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- t z))
3.5b	(* (* (/ y (- a t)) (* (cbrt (- t z)) (cbrt (- t z)))) (cbrt (- t z)))
8.0b	(+ (* (* (/ y (- a t)) (* (cbrt (- t z)) (cbrt (- t z)))) (cbrt (- t z))) (+ x y))
8.6b	(* (/ y (- a t)) (* (cbrt (- t z)) (cbrt (- t z))))

rewrite300.0ms

Algorithm

rewrite-expression-head

Rules

350×	`cbrt-div`
262×	`frac-times`
176×	`flip3--` `flip--`
126×	`associate-*r/`
106×	`frac-add`
101×	`associate-*l/`
54×	`flip3-+` `flip-+`
34×	`add-exp-log`
29×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
22×	`associate-l`
21×	`add-cbrt-cube`
18×	`pow1`
17×	`prod-exp` `cbrt-unprod`
16×	`add-cube-cbrt` `times-frac`
10×	`cbrt-prod`
9×	`associate-r` `pow-prod-down` `add-log-exp`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`sum-log`
2×	`associate-/r/` `*-commutative` `unswap-sqr`
1×	`+-commutative` `associate-+r+` `fma-def` `pow1/3` `div-inv`

Counts

4 → 285

Calls

4 calls:

2.0ms	(cbrt (- t z))
112.0ms	(* (* (/ y (- a t)) (* (cbrt (- t z)) (cbrt (- t z)))) (cbrt (- t z)))
115.0ms	(+ (* (* (/ y (- a t)) (* (cbrt (- t z)) (cbrt (- t z)))) (cbrt (- t z))) (+ x y))
39.0ms	(* (/ y (- a t)) (* (cbrt (- t z)) (cbrt (- t z))))

series879.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(cbrt (- t z))
406.0ms	(* (* (/ y (- a t)) (* (cbrt (- t z)) (cbrt (- t z)))) (cbrt (- t z)))
107.0ms	(+ (* (* (/ y (- a t)) (* (cbrt (- t z)) (cbrt (- t z)))) (cbrt (- t z))) (+ x y))
200.0ms	(* (/ y (- a t)) (* (cbrt (- t z)) (cbrt (- t z))))

simplify136.0ms

Algorithm

egg-herbie

Counts

297 → 297

Iterations

Useful iterations: 1 (62.0ms)

Iter	Nodes	Cost
0	2722	7534
1	5003	7278

prune1.3s

Filtered

297 candidates to 203 candidates (68.4%)

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 6.5b

regimes587.0ms

Accuracy

35.9% (3.7b remaining)

Error of 10.0b against oracle of 6.2b and baseline of 12.0b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	18
1	30	18

end0.0ms

sample674.0ms

Algorithm

intervals

Results

254.0ms	7354×	body	80	valid
59.0ms	462×	body	640	valid
40.0ms	236×	body	1280	valid
38.0ms	412×	body	320	valid
17.0ms	261×	body	160	valid
3.0ms	18×	body	2560	valid