Details

sample29.0ms

Algorithm

intervals

Results

9.0ms	231×	body	80	valid
2.0ms	11×	body	640	valid
1.0ms	8×	body	1280	valid
1.0ms	13×	body	320	valid
1.0ms	13×	body	160	valid
0.0ms	1×	body	2560	valid

simplify73.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (12.0ms)

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: 11.1b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (- a t))
12.0b	(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:

24.0ms	(/ y (- a t))
70.0ms	(fma (/ y (- a t)) (- t z) (+ x y))

simplify45.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 1 (6.0ms)

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

prune265.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.9b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a t))
0.2b	(* y (/ 1 (- a t)))
11.9b	(fma (* y (/ 1 (- a t))) (- t z) (+ x y))

rewrite47.0ms

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:

12.0ms	(/ 1 (- a t))
31.0ms	(* y (/ 1 (- a t)))
0.0ms	(fma (* y (/ 1 (- a t))) (- t z) (+ x y))

series133.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(/ 1 (- a t))
27.0ms	(* y (/ 1 (- a t)))
75.0ms	(fma (* y (/ 1 (- a t))) (- t z) (+ x y))

simplify80.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 3 (70.0ms)

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

prune382.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.9b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ y (- a t))
4.8b	(+ (* (- t z) (/ y (- a t))) (+ x y))
8.5b	(* (- t z) (/ y (- a t)))

rewrite92.0ms

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:

11.0ms	(/ y (- a t))
32.0ms	(+ (* (- t z) (/ y (- a t))) (+ x y))
45.0ms	(* (- t z) (/ y (- a t)))

series201.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(/ y (- a t))
121.0ms	(+ (* (- t z) (/ y (- a t))) (+ x y))
54.0ms	(* (- t z) (/ y (- a t)))

simplify88.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (78.0ms)

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

prune609.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.4b

localize14.0ms

Local error

Found 4 expressions with local error:

11.9b	(fma (* (* (cbrt (/ y (- a t))) (cbrt (/ y (- a t)))) (cbrt (/ y (- a t)))) (- t z) (+ x y))
13.0b	(cbrt (/ y (- a t)))
13.0b	(cbrt (/ y (- a t)))
13.0b	(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:

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

series581.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(fma (* (* (cbrt (/ y (- a t))) (cbrt (/ y (- a t)))) (cbrt (/ y (- a t)))) (- t z) (+ x y))
159.0ms	(cbrt (/ y (- a t)))
159.0ms	(cbrt (/ y (- a t)))
161.0ms	(cbrt (/ y (- a t)))

simplify52.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 3 (40.0ms)

Iter	Nodes	Cost
0	227	1002
1	486	951
2	1449	937
3	5001	915

prune982.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.4b

regimes591.0ms

Accuracy

39.7% (5.4b remaining)

Error of 8.5b against oracle of 3.1b and baseline of 12.1b

bsearch143.0ms

Steps

Iters	Range		Point
9	9.431360896625045e+142	3.4238022363760936e+152	3.3448761331383943e+149
10	-1.6665039713361392e+171	-7.543125008895663e+160	-2.179298102265825e+167

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	8
1	27	8

end0.0ms

sample800.0ms

Algorithm

intervals

Results

308.0ms	7355×	body	80	valid
69.0ms	455×	body	640	valid
49.0ms	270×	body	1280	valid
45.0ms	388×	body	320	valid
20.0ms	272×	body	160	valid
5.0ms	23×	body	2560	valid