Details

sample27.0ms

Algorithm

intervals

Results

10.0ms	235×	body	80	valid
3.0ms	22×	body	640	valid
1.0ms	12×	body	320	valid
1.0ms	6×	body	1280	valid
1.0ms	10×	body	160	valid
0.0ms	2×	body	2560	valid

simplify73.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (11.0ms)

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

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.3b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (- a t))
14.3b	(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))

series117.0ms

Counts

2 → 6

Calls

2 calls:

29.0ms	(/ y (- a t))
87.0ms	(fma (/ y (- a t)) (- t z) (+ x y))

simplify49.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 1 (7.0ms)

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

prune188.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.5b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a t))
0.2b	(* y (/ 1 (- a t)))
14.2b	(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))

series146.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(/ 1 (- a t))
28.0ms	(* y (/ 1 (- a t)))
80.0ms	(fma (* y (/ 1 (- a t))) (- t z) (+ x y))

simplify81.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 3 (74.0ms)

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

prune288.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.5b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) y)
0.5b	(/ 1 (/ (- a t) y))
14.3b	(fma (/ 1 (/ (- a t) y)) (- t z) (+ x y))

rewrite26.0ms

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:

9.0ms	(/ (- a t) y)
10.0ms	(/ 1 (/ (- a t) y))
0.0ms	(fma (/ 1 (/ (- a t) y)) (- t z) (+ x y))

series205.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(/ (- a t) y)
78.0ms	(/ 1 (/ (- a t) y))
97.0ms	(fma (/ 1 (/ (- a t) y)) (- t z) (+ x y))

simplify57.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (44.0ms)

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

prune373.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 7.5b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ y (- a t))
4.2b	(+ (* (- t z) (/ y (- a t))) (+ x y))
9.4b	(* (- t z) (/ y (- a t)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
31×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
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-*l/` `flip-+`
5×	`pow1` `associate-l` `associate-/r*`
4×	`associate-/r/`
3×	`expm1-log1p-u` `associate-r/` `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 → 113

Calls

3 calls:

6.0ms	(/ y (- a t))
15.0ms	(+ (* (- t z) (/ y (- a t))) (+ x y))
24.0ms	(* (- t z) (/ y (- a t)))

series231.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(/ y (- a t))
134.0ms	(+ (* (- t z) (/ y (- a t))) (+ x y))
69.0ms	(* (- t z) (/ y (- a t)))

simplify93.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	639	842
1	3106	791
2	5001	789

prune359.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 3.6b

regimes458.0ms

Accuracy

40.8% (5.2b remaining)

Error of 8.7b against oracle of 3.5b and baseline of 12.3b

bsearch65.0ms

Steps

Iters	Range		Point
3	5.86891155224441e+121	7.147056432882504e+121	6.1085637173640515e+121
8	-2.3948647331552347e+129	-4.315952245492434e+125	-1.1246798244210936e+126

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	8
1	26	8

end0.0ms

sample655.0ms

Algorithm

intervals

Results

243.0ms	7332×	body	80	valid
63.0ms	473×	body	640	valid
37.0ms	412×	body	320	valid
37.0ms	245×	body	1280	valid
16.0ms	262×	body	160	valid
3.0ms	15×	body	2560	valid