Details

sample94.0ms

Algorithm

intervals

Results

37.0ms	753×	body	80	nan
11.0ms	203×	body	80	valid
7.0ms	21×	body	640	valid
3.0ms	5×	body	1280	valid
3.0ms	13×	body	320	valid
2.0ms	14×	body	160	valid

simplify68.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	27	9
1	57	8
2	136	8
3	312	8
4	709	8
5	1629	8
6	3564	8
7	5001	8

prune7.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 5.3b

Counts

2 → 1

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z 1.0) (log (- 1.0 y)))
0.1b	(fma (log y) (- x 1.0) (- (* (- z 1.0) (log (- 1.0 y))) t))
7.4b	(log (- 1.0 y))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
15×	`log-prod`
8×	`add-cube-cbrt`
7×	`pow1`
6×	`add-exp-log`
5×	`distribute-rgt-in` `distribute-lft-in` `associate-l` `add-cbrt-cube`
4×	`associate-r` `distribute-lft-out--` `difference-of-squares`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`log-div` `flip3--` `associate-*l/` `log-pow` `flip--`
1×	`rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

3 → 63

Calls

3 calls:

9.0ms	(* (- z 1.0) (log (- 1.0 y)))
1.0ms	(fma (log y) (- x 1.0) (- (* (- z 1.0) (log (- 1.0 y))) t))
4.0ms	(log (- 1.0 y))

series305.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(* (- z 1.0) (log (- 1.0 y)))
214.0ms	(fma (log y) (- x 1.0) (- (* (- z 1.0) (log (- 1.0 y))) t))
44.0ms	(log (- 1.0 y))

simplify37.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	361	521
1	1194	461
2	5002	449

prune179.0ms

Filtered

72 candidates to 55 candidates (76.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	68	4	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	4	73

Merged error: 0.1b

Counts

73 → 4

localize20.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.1b	(fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

117×	`*-un-lft-identity`
56×	`prod-diff`
45×	`associate-l`
40×	`distribute-lft-out`
34×	`add-sqr-sqrt`
33×	`distribute-rgt-in` `distribute-lft-in`
28×	`add-cube-cbrt`
23×	`pow1`
19×	`log-pow`
14×	`associate-r`
11×	`distribute-lft-out--`
6×	`log-prod` `flip3--` `associate--l+` `flip--`
4×	`add-exp-log` `frac-times` `add-cbrt-cube`
2×	`expm1-log1p-u` `sub-neg` `associate-r/` `associate-l/` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

2 → 117

Calls

2 calls:

80.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
1.0ms	(fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

series295.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
228.0ms	(fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

simplify77.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	423	3002
1	1933	2019
2	5003	2012

prune222.0ms

Filtered

123 candidates to 45 candidates (36.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	118	5	123
Fresh	3	0	3
Picked	0	1	1
Done	0	0	0
Total	121	6	127

Merged error: 0.1b

Counts

127 → 6

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
0.1b	(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.1b	(fma (log y) (- x 1.0) (- (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t))
0.5b	(* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

rewrite346.0ms

Algorithm

rewrite-expression-head

Rules

278×	`*-un-lft-identity`
249×	`sqrt-prod`
225×	`add-sqr-sqrt`
140×	`prod-diff`
119×	`associate-l`
106×	`distribute-lft-out`
79×	`add-cube-cbrt`
74×	`distribute-rgt-in` `distribute-lft-in`
57×	`unswap-sqr`
47×	`pow1`
46×	`associate-r`
36×	`hypot-def`
35×	`log-pow`
32×	`frac-times` `times-frac`
21×	`flip3--` `flip--`
16×	`unpow-prod-down` `associate-*l/` `unpow2` `sqr-pow`
13×	`flip3-+` `flip-+` `distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-*r/`
6×	`difference-of-squares`
4×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`+-commutative` `sub-neg` `sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 343

Calls

4 calls:

67.0ms	(sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
76.0ms	(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
1.0ms	(fma (log y) (- x 1.0) (- (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t))
171.0ms	(* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

68.0ms	(sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
158.0ms	(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
722.0ms	(fma (log y) (- x 1.0) (- (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t))
287.0ms	(* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

simplify137.0ms

Algorithm

egg-herbie

Counts

355 → 355

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1193	14018
1	5001	10830

prune1.0s

Filtered

355 candidates to 171 candidates (48.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	353	2	355
Fresh	3	1	4
Picked	1	0	1
Done	0	1	1
Total	357	4	361

Merged error: 0.1b

Counts

361 → 4

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (fma (log y) (- x 1.0) (- (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)))
0.5b	(cbrt (fma (log y) (- x 1.0) (- (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)))
0.5b	(cbrt (fma (log y) (- x 1.0) (- (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)))
0.6b	(* (cbrt (fma (log y) (- x 1.0) (- (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t))) (cbrt (fma (log y) (- x 1.0) (- (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
8×	`add-cbrt-cube`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative`

Counts

4 → 84

Calls

4 calls:

1.0ms	(cbrt (fma (log y) (- x 1.0) (- (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)))
1.0ms	(cbrt (fma (log y) (- x 1.0) (- (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)))
1.0ms	(cbrt (fma (log y) (- x 1.0) (- (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)))
6.0ms	(* (cbrt (fma (log y) (- x 1.0) (- (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t))) (cbrt (fma (log y) (- x 1.0) (- (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t))))

series4.4s

Counts

4 → 12

Calls

4 calls:

933.0ms	(cbrt (fma (log y) (- x 1.0) (- (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)))
890.0ms	(cbrt (fma (log y) (- x 1.0) (- (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)))
879.0ms	(cbrt (fma (log y) (- x 1.0) (- (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)))
1.7s	(* (cbrt (fma (log y) (- x 1.0) (- (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t))) (cbrt (fma (log y) (- x 1.0) (- (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t))))

simplify84.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	482	5048
1	1695	4453
2	5001	3961

prune466.0ms

Filtered

96 candidates to 72 candidates (75.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	91	5	96
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	91	9	100

Merged error: 0.0b

Counts

100 → 9

regimes423.0ms

Accuracy

0% (0.1b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	14
1	25	14

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.2s	24607×	body	80	nan
321.0ms	5840×	body	80	valid
252.0ms	810×	body	640	valid
170.0ms	268×	body	1280	valid
121.0ms	651×	body	320	valid
53.0ms	462×	body	160	valid