Details

sample27.0ms

Algorithm

intervals

Results

8.0ms	240×	body	80	valid
2.0ms	16×	body	320	valid
1.0ms	8×	body	1280	valid
1.0ms	10×	body	640	valid
1.0ms	10×	body	160	valid

simplify97.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (19.0ms)

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: 10.4b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (- a t))
12.2b	(fma (/ y (- a t)) (- t z) (+ x y))

rewrite9.0ms

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))

series131.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(/ y (- a t))
97.0ms	(fma (/ y (- a t)) (- t z) (+ x y))

simplify51.0ms

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

prune210.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.6b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) y)
0.7b	(/ 1 (/ (- a t) y))
12.2b	(fma (/ 1 (/ (- a t) y)) (- t z) (+ x y))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
101×	`add-sqr-sqrt` `*-un-lft-identity`
69×	`add-cube-cbrt`
22×	`associate-/r*`
16×	`add-exp-log` `distribute-lft-out--` `difference-of-squares`
10×	`add-cbrt-cube`
8×	`div-exp` `associate-/l*`
6×	`div-inv`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `associate-/l/`
1×	`flip3--` `pow-flip` `div-sub` `associate-/r/` `flip--` `fma-udef` `inv-pow`

Counts

3 → 152

Calls

3 calls:

7.0ms	(/ (- a t) y)
9.0ms	(/ 1 (/ (- a t) y))
1.0ms	(fma (/ 1 (/ (- a t) y)) (- t z) (+ x y))

series214.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(/ (- a t) y)
85.0ms	(/ 1 (/ (- a t) y))
94.0ms	(fma (/ 1 (/ (- a t) y)) (- t z) (+ x y))

simplify67.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	466	1086
1	1950	958
2	5001	852

prune399.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.6b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) y)
4.0b	(+ (/ (- t z) (/ (- a t) y)) (+ x y))
11.8b	(/ (- t z) (/ (- a t) y))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

370×	`times-frac`
309×	`*-un-lft-identity`
304×	`add-sqr-sqrt`
152×	`add-cube-cbrt`
100×	`fma-def`
76×	`distribute-lft-out--` `difference-of-squares`
22×	`associate-/r*`
14×	`div-inv`
10×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
8×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`pow1` `expm1-log1p-u` `div-sub` `sum-log` `log1p-expm1-u` `distribute-lft-out`
2×	`flip3--` `frac-2neg` `flip3-+` `frac-add` `clear-num` `associate-/r/` `flip--` `flip-+`
1×	`+-commutative` `associate-+l-` `associate-+r+`

Counts

3 → 299

Calls

3 calls:

7.0ms	(/ (- a t) y)
51.0ms	(+ (/ (- t z) (/ (- a t) y)) (+ x y))
14.0ms	(/ (- t z) (/ (- a t) y))

series392.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(/ (- a t) y)
242.0ms	(+ (/ (- t z) (/ (- a t) y)) (+ x y))
117.0ms	(/ (- t z) (/ (- a t) y))

simplify108.0ms

Algorithm

egg-herbie

Counts

308 → 308

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	892	1815
1	3565	1754
2	5001	1752

prune871.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt y)
0.5b	(cbrt y)
3.7b	(/ (- t z) (/ (- a t) (cbrt y)))
10.8b	(fma (/ 1 (/ 1 (* (cbrt y) (cbrt y)))) (/ (- t z) (/ (- a t) (cbrt y))) (+ x y))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

350×	`times-frac`
285×	`add-sqr-sqrt` `*-un-lft-identity`
143×	`add-cube-cbrt`
96×	`cbrt-prod`
71×	`distribute-lft-out--` `difference-of-squares`
34×	`associate-/r*`
9×	`add-exp-log`
8×	`add-cbrt-cube`
7×	`div-inv`
5×	`associate-/l*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp`
2×	`pow1/3` `associate-/l/`
1×	`flip3--` `frac-2neg` `div-sub` `clear-num` `associate-/r/` `flip--` `fma-udef`

Counts

4 → 265

Calls

4 calls:

1.0ms	(cbrt y)
1.0ms	(cbrt y)
15.0ms	(/ (- t z) (/ (- a t) (cbrt y)))
1.0ms	(fma (/ 1 (/ 1 (* (cbrt y) (cbrt y)))) (/ (- t z) (/ (- a t) (cbrt y))) (+ x y))

series741.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(cbrt y)
190.0ms	(cbrt y)
170.0ms	(/ (- t z) (/ (- a t) (cbrt y)))
195.0ms	(fma (/ 1 (/ 1 (* (cbrt y) (cbrt y)))) (/ (- t z) (/ (- a t) (cbrt y))) (+ x y))

simplify107.0ms

Algorithm

egg-herbie

Counts

277 → 277

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	982	3142
1	3878	3047
2	5001	2985

prune928.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.2b

regimes328.0ms

Accuracy

36.4% (5.0b remaining)

Error of 8.0b against oracle of 3.0b and baseline of 10.8b

bsearch121.0ms

Steps

Iters	Range		Point
8	7.104008511116258e+116	1.1379081657348373e+120	6.404276833063467e+118
10	-1.756824163423226e+101	-6.317617841719785e+84	-5.017783785458671e+90

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	28
1	36	28

end0.0ms

sample671.0ms

Algorithm

intervals

Results

257.0ms	7376×	body	80	valid
57.0ms	464×	body	640	valid
40.0ms	241×	body	1280	valid
35.0ms	373×	body	320	valid
15.0ms	240×	body	160	valid
4.0ms	19×	body	2560	valid