Details

sample129.0ms

Algorithm

intervals

Results

50.0ms	802×	body	80	nan
12.0ms	17×	body	1280	valid
11.0ms	170×	body	80	valid
9.0ms	23×	body	640	valid
6.0ms	27×	body	320	valid
3.0ms	20×	body	160	valid

simplify30.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	22	7
1	38	6
2	53	6
3	61	6
4	78	6
5	110	6
6	175	6
7	284	6
8	363	6
9	392	6
10	476	6
11	476	6

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: 10.1b

Counts

2 → 2

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(* z (log (- 1.0 y)))
0.1b	(fma (log y) x (- (* z (log (- 1.0 y))) t))
6.7b	(log (- 1.0 y))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 59

Calls

3 calls:

7.0ms	(* z (log (- 1.0 y)))
1.0ms	(fma (log y) x (- (* z (log (- 1.0 y))) t))
4.0ms	(log (- 1.0 y))

series234.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(* z (log (- 1.0 y)))
126.0ms	(fma (log y) x (- (* z (log (- 1.0 y))) t))
44.0ms	(log (- 1.0 y))

simplify105.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (99.0ms)

Iter	Nodes	Cost
0	332	427
1	1128	376
2	4553	369
3	5001	366

prune210.0ms

Filtered

68 candidates to 52 candidates (76.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	60	8	68
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	62	8	70

Merged error: 0.1b

Counts

70 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

111×	`add-sqr-sqrt`
80×	`times-frac`
76×	`*-un-lft-identity`
74×	`associate-r`
73×	`add-cube-cbrt`
56×	`unpow-prod-down`
51×	`prod-diff`
46×	`associate--l+`
34×	`distribute-rgt-in` `distribute-lft-in`
29×	`add-exp-log`
24×	`unpow2` `sqr-pow`
21×	`pow1`
18×	`unswap-sqr`
13×	`log-pow`
12×	`log-prod`
11×	`prod-exp` `add-cbrt-cube`
9×	`div-exp`
6×	`pow-to-exp` `associate-l` `pow-exp` `add-log-exp`
5×	`sub-neg`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-*r/` `cbrt-unprod`
2×	`flip3--` `pow-prod-down` `*-commutative` `flip--` `distribute-lft-out--`
1×	`cbrt-undiv` `fma-neg` `diff-log` `fma-udef` `div-inv` `difference-of-squares`

Counts

4 → 233

Calls

4 calls:

21.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
13.0ms	(- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
10.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
1.0ms	(fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

series452.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
121.0ms	(- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
102.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
174.0ms	(fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

simplify119.0ms

Algorithm

egg-herbie

Counts

245 → 245

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	936	3375
1	3893	2186
2	5001	2179

prune722.0ms

Filtered

245 candidates to 148 candidates (60.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	244	1	245
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	244	9	253

Merged error: 0.1b

Counts

253 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (cbrt (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
13.1b	(cbrt (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
13.1b	(cbrt (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
13.1b	(cbrt (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

20×	`associate-*r/`
18×	`cbrt-div`
11×	`pow1`
10×	`add-sqr-sqrt`
9×	`flip3--` `pow1/3` `flip--`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `associate-*l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

7.0ms	(* (cbrt (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (cbrt (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
6.0ms	(cbrt (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
12.0ms	(cbrt (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
7.0ms	(cbrt (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

series1.4s

Counts

4 → 12

Calls

4 calls:

398.0ms	(* (cbrt (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (cbrt (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
354.0ms	(cbrt (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
341.0ms	(cbrt (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
343.0ms	(cbrt (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

simplify69.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	593	2423
1	2300	2263
2	5001	2173

prune515.0ms

Filtered

92 candidates to 75 candidates (81.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	92	9	101

Merged error: 0.1b

Counts

101 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (log y) x (- (+ (* z (log (+ (sqrt 1.0) (sqrt y)))) (* z (log (- (sqrt 1.0) (sqrt y))))) t))
10.7b	(+ (* z (log (+ (sqrt 1.0) (sqrt y)))) (* z (log (- (sqrt 1.0) (sqrt y)))))
14.0b	(log (- (sqrt 1.0) (sqrt y)))
14.2b	(log (+ (sqrt 1.0) (sqrt y)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

42×	`log-prod`
34×	`add-sqr-sqrt` `*-un-lft-identity`
24×	`sqrt-prod`
18×	`associate-+r+`
14×	`distribute-rgt-in` `distribute-lft-in`
12×	`difference-of-squares`
10×	`add-cube-cbrt` `associate-+l+`
7×	`distribute-lft-out`
6×	`pow1` `add-exp-log` `distribute-lft-out--` `add-log-exp`
4×	`expm1-log1p-u` `log-div` `add-cbrt-cube` `log1p-expm1-u`
2×	`flip3-+` `rem-log-exp` `log-pow` `flip-+`
1×	`+-commutative` `flip3--` `fma-def` `sum-log` `flip--` `fma-udef`

Counts

4 → 93

Calls

4 calls:

1.0ms	(fma (log y) x (- (+ (* z (log (+ (sqrt 1.0) (sqrt y)))) (* z (log (- (sqrt 1.0) (sqrt y))))) t))
16.0ms	(+ (* z (log (+ (sqrt 1.0) (sqrt y)))) (* z (log (- (sqrt 1.0) (sqrt y)))))
8.0ms	(log (- (sqrt 1.0) (sqrt y)))
6.0ms	(log (+ (sqrt 1.0) (sqrt y)))

series1.2s

Counts

4 → 12

Calls

4 calls:

501.0ms	(fma (log y) x (- (+ (* z (log (+ (sqrt 1.0) (sqrt y)))) (* z (log (- (sqrt 1.0) (sqrt y))))) t))
409.0ms	(+ (* z (log (+ (sqrt 1.0) (sqrt y)))) (* z (log (- (sqrt 1.0) (sqrt y)))))
155.0ms	(log (- (sqrt 1.0) (sqrt y)))
147.0ms	(log (+ (sqrt 1.0) (sqrt y)))

simplify59.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	542	1280
1	1653	1160
2	5001	1102

prune411.0ms

Filtered

105 candidates to 79 candidates (75.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	105	9	114

Merged error: 0.1b

Counts

114 → 9

regimes188.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	12
1	23	12

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.7s	23982×	body	80	nan
377.0ms	5491×	body	80	valid
339.0ms	904×	body	640	valid
282.0ms	412×	body	1280	valid
178.0ms	781×	body	320	valid
68.0ms	458×	body	160	valid