Details

sample123.0ms

Algorithm

intervals

Results

53.0ms	805×	body	80	nan
14.0ms	198×	body	80	valid
8.0ms	20×	body	640	valid
6.0ms	8×	body	1280	valid
5.0ms	20×	body	320	valid
2.0ms	12×	body	160	valid

simplify74.0ms

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

prune8.0ms

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: 6.7b

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))
7.1b	(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))

series306.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(* (- z 1.0) (log (- 1.0 y)))
218.0ms	(fma (log y) (- x 1.0) (- (* (- z 1.0) (log (- 1.0 y))) t))
45.0ms	(log (- 1.0 y))

simplify37.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	364	521
1	1204	461
2	5001	449

prune214.0ms

Filtered

72 candidates to 55 candidates (76.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	3	73

Merged error: 0.1b

Counts

73 → 3

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b

(- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)

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))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

51×	`prod-diff`
46×	`associate--l+`
44×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
38×	`add-cube-cbrt`
34×	`distribute-rgt-in` `distribute-lft-in`
18×	`pow1`
13×	`log-pow`
12×	`log-prod`
7×	`flip3--` `flip--`
6×	`associate-r`
5×	`add-exp-log` `sub-neg` `associate-l` `add-cbrt-cube` `add-log-exp`
4×	`frac-times`
3×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--`
2×	`associate-r/` `associate-l/` `difference-of-squares`
1×	`fma-neg` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

3 → 129

Calls

3 calls:

16.0ms

(- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)

14.0ms

(* (- 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))

series451.0ms

Counts

3 → 9

Calls

3 calls:

152.0ms

(- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)

68.0ms

(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))

231.0ms

(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))

simplify85.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	547	3086
1	2354	1998
2	5002	1990

prune467.0ms

Filtered

138 candidates to 87 candidates (63.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	135	3	138
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	135	6	141

Merged error: 0.1b

Counts

141 → 6

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (* (- 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)
0.1b	(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))
0.1b	(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.4b	(* (* (- 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)))))))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

192×	`sqrt-prod`
171×	`prod-diff`
124×	`add-sqr-sqrt` `*-un-lft-identity`
112×	`add-cube-cbrt`
89×	`distribute-rgt-in` `distribute-lft-in`
88×	`associate--l+`
37×	`pow1`
32×	`frac-times`
26×	`log-pow`
22×	`flip3--` `flip--`
16×	`associate-r` `associate-*l/`
12×	`flip3-+` `flip-+`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-*r/`
6×	`associate-l` `add-log-exp`
5×	`sub-neg` `difference-of-squares`
4×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--`
3×	`distribute-lft-out`
2×	`*-commutative`
1×	`fma-neg` `diff-log` `fma-udef` `unswap-sqr`

Counts

4 → 292

Calls

4 calls:

34.0ms	(- (* (* (- 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))))))) t)
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))
14.0ms	(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
26.0ms	(* (* (- 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)))))))

series1.7s

Counts

4 → 12

Calls

4 calls:

487.0ms	(- (* (* (- 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))))))) t)
740.0ms	(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))
161.0ms	(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
276.0ms	(* (* (- 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)))))))

simplify143.0ms

Algorithm

egg-herbie

Counts

304 → 304

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1175	13860
1	5001	10397

prune1.1s

Filtered

304 candidates to 166 candidates (54.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	303	1	304
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	304	6	310

Merged error: 0.1b

Counts

310 → 6

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (log y) (- x 1.0) (- (/ (* (- (- (log 1.0) (* 1.0 y)) (* 1/2 (/ (pow y 2) (pow 1.0 2)))) (* (- 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))
0.1b	(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.2b	(* (- (- (log 1.0) (* 1.0 y)) (* 1/2 (/ (pow y 2) (pow 1.0 2)))) (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
11.0b	(/ (* (- (- (log 1.0) (* 1.0 y)) (* 1/2 (/ (pow y 2) (pow 1.0 2)))) (* (- 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)))))))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

108×	`frac-times`
74×	`associate-*r/`
69×	`flip3--` `flip--`
44×	`associate-/l/`
36×	`frac-sub`
34×	`flip3-+` `flip-+`
30×	`associate-*l/`
26×	`*-un-lft-identity`
20×	`add-exp-log` `add-cbrt-cube`
14×	`pow1`
13×	`add-sqr-sqrt`
12×	`sqrt-prod`
9×	`add-cube-cbrt` `distribute-lft-out`
8×	`associate-l`
7×	`associate-r` `prod-exp` `cbrt-unprod`
6×	`times-frac` `associate-/r*`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `log-pow`
2×	`associate-/r/` `*-commutative`
1×	`frac-2neg` `clear-num` `fma-udef` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 190

Calls

4 calls:

1.0ms	(fma (log y) (- x 1.0) (- (/ (* (- (- (log 1.0) (* 1.0 y)) (* 1/2 (/ (pow y 2) (pow 1.0 2)))) (* (- 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))
14.0ms	(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
23.0ms	(* (- (- (log 1.0) (* 1.0 y)) (* 1/2 (/ (pow y 2) (pow 1.0 2)))) (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
31.0ms	(/ (* (- (- (log 1.0) (* 1.0 y)) (* 1/2 (/ (pow y 2) (pow 1.0 2)))) (* (- 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)))))))

series726.0ms

Counts

4 → 12

Calls

4 calls:

231.0ms	(fma (log y) (- x 1.0) (- (/ (* (- (- (log 1.0) (* 1.0 y)) (* 1/2 (/ (pow y 2) (pow 1.0 2)))) (* (- 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))
157.0ms	(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
271.0ms	(* (- (- (log 1.0) (* 1.0 y)) (* 1/2 (/ (pow y 2) (pow 1.0 2)))) (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
66.0ms	(/ (* (- (- (log 1.0) (* 1.0 y)) (* 1/2 (/ (pow y 2) (pow 1.0 2)))) (* (- 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)))))))

simplify91.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1298	6786
1	5003	6436

prune1.3s

Filtered

202 candidates to 178 candidates (88.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	202	0	202
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	202	6	208

Merged error: 0.1b

Counts

208 → 6

regimes227.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b 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

sample3.5s

Algorithm

intervals

Results

1.5s	24046×	body	80	nan
410.0ms	5885×	body	80	valid
275.0ms	757×	body	640	valid
168.0ms	244×	body	1280	valid
153.0ms	685×	body	320	valid
64.0ms	453×	body	160	valid

Details

sample123.0ms

simplify74.0ms

prune8.0ms

localize16.0ms

rewrite16.0ms

series306.0ms

simplify37.0ms

prune214.0ms

localize22.0ms

rewrite37.0ms

series451.0ms

simplify85.0ms

prune467.0ms

localize23.0ms

rewrite95.0ms

series1.7s

simplify143.0ms

prune1.1s

localize25.0ms

rewrite80.0ms

series726.0ms

simplify91.0ms

prune1.3s

regimes227.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.5s

Profiling