Details

sample29.0ms

Algorithm

intervals

Results

9.0ms	225×	body	80	valid
2.0ms	19×	body	640	valid
1.0ms	10×	body	1280	valid
1.0ms	12×	body	320	valid
1.0ms	11×	body	160	valid
0.0ms	1×	body	2560	valid

simplify67.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (10.0ms)

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

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.5b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (- a t))
13.9b	(fma (/ y (- a t)) (- t z) (+ x y))

rewrite13.0ms

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))

series95.0ms

Counts

2 → 6

Calls

2 calls:

25.0ms	(/ y (- a t))
70.0ms	(fma (/ y (- a t)) (- t z) (+ x y))

simplify40.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 1 (5.0ms)

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

prune170.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) y)
0.6b	(/ 1 (/ (- a t) y))
13.9b	(fma (/ 1 (/ (- a t) y)) (- t z) (+ x y))

rewrite44.0ms

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:

17.0ms	(/ (- a t) y)
19.0ms	(/ 1 (/ (- a t) y))
0.0ms	(fma (/ 1 (/ (- a t) y)) (- t z) (+ x y))

series167.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(/ (- a t) y)
65.0ms	(/ 1 (/ (- a t) y))
78.0ms	(fma (/ 1 (/ (- a t) y)) (- t z) (+ x y))

simplify50.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (38.0ms)

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

prune331.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.7b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) y)
4.1b	(+ (/ (- t z) (/ (- a t) y)) (+ x y))
8.4b	(/ (- t z) (/ (- a t) y))

rewrite207.0ms

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:

17.0ms	(/ (- a t) y)
136.0ms	(+ (/ (- t z) (/ (- a t) y)) (+ x y))
32.0ms	(/ (- t z) (/ (- a t) y))

series288.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(/ (- a t) y)
177.0ms	(+ (/ (- t z) (/ (- a t) y)) (+ x y))
87.0ms	(/ (- t z) (/ (- a t) y))

simplify81.0ms

Algorithm

egg-herbie

Counts

308 → 308

Iterations

Useful iterations: 2 (62.0ms)

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

prune781.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
0.6b	(/ 1 (/ (* (cbrt (- a t)) (cbrt (- a t))) (* (cbrt y) (cbrt y))))
12.6b	(fma (/ 1 (/ (* (cbrt (- a t)) (cbrt (- a t))) (* (cbrt y) (cbrt y)))) (/ (- t z) (/ (cbrt (- a t)) (cbrt y))) (+ x y))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-exp-log`
22×	`div-exp`
19×	`times-frac`
16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
14×	`add-cbrt-cube`
12×	`prod-exp`
9×	`cbrt-undiv`
6×	`cbrt-prod`
5×	`pow1` `rec-exp` `1-exp` `associate-/r*` `div-inv`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
2×	`pow1/3`
1×	`pow-flip` `frac-2neg` `clear-num` `associate-/r/` `fma-udef` `inv-pow`

Counts

4 → 94

Calls

4 calls:

1.0ms	(cbrt y)
1.0ms	(cbrt y)
38.0ms	(/ 1 (/ (* (cbrt (- a t)) (cbrt (- a t))) (* (cbrt y) (cbrt y))))
0.0ms	(fma (/ 1 (/ (* (cbrt (- a t)) (cbrt (- a t))) (* (cbrt y) (cbrt y)))) (/ (- t z) (/ (cbrt (- a t)) (cbrt y))) (+ x y))

series1.4s

Counts

4 → 12

Calls

4 calls:

172.0ms	(cbrt y)
169.0ms	(cbrt y)
165.0ms	(/ 1 (/ (* (cbrt (- a t)) (cbrt (- a t))) (* (cbrt y) (cbrt y))))
898.0ms	(fma (/ 1 (/ (* (cbrt (- a t)) (cbrt (- a t))) (* (cbrt y) (cbrt y)))) (/ (- t z) (/ (cbrt (- a t)) (cbrt y))) (+ x y))

simplify59.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	532	1229
1	2118	1024
2	5001	944

prune526.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.8b

regimes329.0ms

Accuracy

42.9% (4.8b remaining)

Error of 8.1b against oracle of 3.3b and baseline of 11.6b

bsearch86.0ms

Steps

Iters	Range		Point
9	4.473646891062652e+105	2.9810623560308108e+110	3.5160921484049927e+107
8	-7.045861419912725e+102	-1.6617757044371328e+100	-9.252090162115357e+100

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	26
1	31	26

end0.0ms

sample719.0ms

Algorithm

intervals

Results

218.0ms	7332×	body	80	valid
48.0ms	477×	body	640	valid
37.0ms	405×	body	320	valid
35.0ms	250×	body	1280	valid
14.0ms	262×	body	160	valid
3.0ms	19×	body	2560	valid