Details

sample25.0ms

Algorithm

intervals

Results

8.0ms	247×	body	80	valid
1.0ms	8×	body	1280	valid
1.0ms	8×	body	640	valid
1.0ms	7×	body	320	valid
1.0ms	10×	body	160	valid
0.0ms	1×	body	2560	valid

simplify81.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (15.0ms)

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

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 7.8b

Counts

2 → 2

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (- a t))
10.1b	(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))
1.0ms	(fma (/ y (- a t)) (- t z) (+ x y))

series120.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(/ y (- a t))
83.0ms	(fma (/ y (- a t)) (- t z) (+ x y))

simplify52.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 1 (8.0ms)

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

prune193.0ms

Filtered

55 candidates to 43 candidates (78.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	45	10	55
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	46	11	57

Merged error: 4.5b

Counts

57 → 11

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a t))
0.2b	(* y (/ 1 (- a t)))
10.1b	(fma (* y (/ 1 (- a t))) (- t z) (+ x y))

rewrite21.0ms

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))) (- t z) (+ x y))

series154.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(/ 1 (- a t))
29.0ms	(* y (/ 1 (- a t)))
83.0ms	(fma (* y (/ 1 (- a t))) (- t z) (+ x y))

simplify81.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 3 (73.0ms)

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

prune237.0ms

Filtered

108 candidates to 64 candidates (59.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	107	12	119

Merged error: 4.5b

Counts

119 → 12

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ y (- a t))
3.2b	(+ (* (/ y (- a t)) (- t z)) (+ x y))
12.0b	(* (/ y (- a t)) (- t z))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
47×	`add-cube-cbrt`
36×	`prod-diff`
31×	`times-frac`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
21×	`associate-l`
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-*r/` `flip-+`
5×	`pow1` `associate-r` `associate-/r*`
4×	`sub-neg` `associate-/r/`
3×	`expm1-log1p-u` `associate-l/` `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 → 157

Calls

3 calls:

5.0ms	(/ y (- a t))
16.0ms	(+ (* (/ y (- a t)) (- t z)) (+ x y))
18.0ms	(* (/ y (- a t)) (- t z))

series453.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(/ y (- a t))
109.0ms	(+ (* (/ y (- a t)) (- t z)) (+ x y))
314.0ms	(* (/ y (- a t)) (- t z))

simplify119.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	859	1392
1	4016	1146
2	5001	1146

prune444.0ms

Filtered

166 candidates to 119 candidates (71.7%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	164	2	166
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	164	14	178

Merged error: 4.4b

Counts

178 → 14

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (/ 1 (- a t)))
0.6b	(cbrt (/ 1 (- a t)))
0.6b	(cbrt (/ 1 (- a t)))
10.0b	(fma (* (* y (* (cbrt (/ 1 (- a t))) (cbrt (/ 1 (- a t))))) (cbrt (/ 1 (- a t)))) (- t z) (+ x y))

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:

6.0ms	(cbrt (/ 1 (- a t)))
5.0ms	(cbrt (/ 1 (- a t)))
5.0ms	(cbrt (/ 1 (- a t)))
1.0ms	(fma (* (* y (* (cbrt (/ 1 (- a t))) (cbrt (/ 1 (- a t))))) (cbrt (/ 1 (- a t)))) (- t z) (+ x y))

series578.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(cbrt (/ 1 (- a t)))
162.0ms	(cbrt (/ 1 (- a t)))
160.0ms	(cbrt (/ 1 (- a t)))
85.0ms	(fma (* (* y (* (cbrt (/ 1 (- a t))) (cbrt (/ 1 (- a t))))) (cbrt (/ 1 (- a t)))) (- t z) (+ x y))

simplify87.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	253	1030
1	618	971
2	2417	908
3	5001	815

prune313.0ms

Filtered

118 candidates to 71 candidates (60.2%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	116	2	118
Fresh	1	10	11
Picked	0	1	1
Done	0	2	2
Total	117	15	132

Merged error: 4.4b

Counts

132 → 15

regimes437.0ms

Accuracy

-2% (5.8b remaining)

Error of 11.9b against oracle of 6.0b and baseline of 11.7b

bsearch144.0ms

Steps

Iters	Range		Point
10	1.5342650061255457e+193	4.597238696178208e+203	1.379955114303357e+201
6	108.10498260228141	1582.7960665007818	979.4470830857429
8	-2.784670116906131e+24	-1.2582724651754321e+21	-1.9995814290013372e+21

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	27
1	37	27

end0.0ms

sample686.0ms

Algorithm

intervals

Results

259.0ms	7408×	body	80	valid
61.0ms	461×	body	640	valid
43.0ms	253×	body	1280	valid
39.0ms	376×	body	320	valid
17.0ms	255×	body	160	valid
3.0ms	13×	body	2560	valid

Details

sample25.0ms

simplify81.0ms

prune9.0ms

localize14.0ms

rewrite8.0ms

series120.0ms

simplify52.0ms

prune193.0ms

localize11.0ms

rewrite21.0ms

series154.0ms

simplify81.0ms

prune237.0ms

localize10.0ms

rewrite46.0ms

series453.0ms

simplify119.0ms

prune444.0ms

localize15.0ms

rewrite22.0ms

series578.0ms

simplify87.0ms

prune313.0ms

regimes437.0ms

bsearch144.0ms

simplify2.0ms

end0.0ms

sample686.0ms

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