Details

sample22.0ms

Algorithm

intervals

Results

9.0ms

283×

body

valid

simplify68.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	17	5
1	32	5
2	60	4
3	112	4
4	172	4
5	231	4
6	279	4
7	352	4
8	485	4
9	648	4
10	1074	4
11	1358	4
12	1399	4
13	1399	4

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (- a t))
2.2b	(fma (/ y (- a t)) (- z t) x)

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)) (- z t) x)

series225.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(/ y (- a t))
194.0ms	(fma (/ y (- a t)) (- z t) x)

simplify112.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 3 (40.0ms)

Iter	Nodes	Cost
0	166	265
1	444	246
2	1278	244
3	4359	243
4	5001	243

prune169.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a t))
0.3b	(* y (/ 1 (- a t)))
2.2b	(fma (* y (/ 1 (- a t))) (- z t) x)

rewrite22.0ms

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))
11.0ms	(* y (/ 1 (- a t)))
1.0ms	(fma (* y (/ 1 (- a t))) (- z t) x)

series266.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(/ 1 (- a t))
37.0ms	(* y (/ 1 (- a t)))
191.0ms	(fma (* y (/ 1 (- a t))) (- z t) x)

simplify79.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	284	497
1	1119	429
2	4119	381
3	5001	381

prune255.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

2.2b	(fma (* (* (cbrt (/ y (- a t))) (cbrt (/ y (- a t)))) (cbrt (/ y (- a t)))) (- z t) x)
13.3b	(cbrt (/ y (- a t)))
13.3b	(cbrt (/ y (- a t)))
13.3b	(cbrt (/ y (- a t)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

63×	`cbrt-prod`
49×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
31×	`add-cube-cbrt`
9×	`distribute-lft-out--` `difference-of-squares`
6×	`associate-/r/`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `flip3--` `pow1/3` `flip--` `div-inv`
1×	`fma-udef`

Counts

4 → 106

Calls

4 calls:

1.0ms	(fma (* (* (cbrt (/ y (- a t))) (cbrt (/ y (- a t)))) (cbrt (/ y (- a t)))) (- z t) x)
5.0ms	(cbrt (/ y (- a t)))
5.0ms	(cbrt (/ y (- a t)))
6.0ms	(cbrt (/ y (- a t)))

series799.0ms

Counts

4 → 12

Calls

4 calls:

239.0ms	(fma (* (* (cbrt (/ y (- a t))) (cbrt (/ y (- a t)))) (cbrt (/ y (- a t)))) (- z t) x)
187.0ms	(cbrt (/ y (- a t)))
183.0ms	(cbrt (/ y (- a t)))
190.0ms	(cbrt (/ y (- a t)))

simplify128.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 3 (41.0ms)

Iter	Nodes	Cost
0	223	989
1	467	940
2	1319	925
3	4542	901
4	5001	901

prune476.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (fma (* y (/ 1 (- a t))) (- z t) x))
2.2b	(fma (* y (/ 1 (- a t))) (- z t) x)
2.2b	(fma (* y (/ 1 (- a t))) (- z t) x)
2.2b	(fma (* y (/ 1 (- a t))) (- z t) x)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `fma-udef`
1×	`pow1/3`

Counts

4 → 43

Calls

4 calls:

1.0ms	(cbrt (fma (* y (/ 1 (- a t))) (- z t) x))
1.0ms	(fma (* y (/ 1 (- a t))) (- z t) x)
5.0ms	(fma (* y (/ 1 (- a t))) (- z t) x)
1.0ms	(fma (* y (/ 1 (- a t))) (- z t) x)

series1.3s

Counts

4 → 12

Calls

4 calls:

680.0ms	(cbrt (fma (* y (/ 1 (- a t))) (- z t) x))
190.0ms	(fma (* y (/ 1 (- a t))) (- z t) x)
190.0ms	(fma (* y (/ 1 (- a t))) (- z t) x)
195.0ms	(fma (* y (/ 1 (- a t))) (- z t) x)

simplify71.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 3 (65.0ms)

Iter	Nodes	Cost
0	160	414
1	445	365
2	2178	354
3	5001	347

prune230.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes176.0ms

Accuracy

42.4% (1.8b remaining)

Error of 1.8b against oracle of 0.0b and baseline of 3.1b

bsearch91.0ms

Steps

Iters	Range		Point
7	1.1995418658416891e-150	4.775338770032058e-149	3.820792784014782e-149
9	-4.292405555715696e-14	-2.6084029452864883e-23	-2.7620314914513706e-14

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	9
1	23	9

end0.0ms

sample763.0ms

Algorithm

intervals

Results

486.0ms	8721×	body	80	valid
0.0ms	1×	body	640	valid
0.0ms	1×	body	160	valid