Details

sample190.0ms

Algorithm

intervals

Results

79.0ms	1468×	body	80	nan
33.0ms	515×	body	80	valid

simplify53.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	32	10
1	65	10
2	181	8
3	522	8
4	2203	8
5	5002	8

prune10.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 0.3b

Counts

2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- t 1.0) (log a))
0.3b	(* y (log z))
0.5b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
0.9b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity`
90×	`add-sqr-sqrt`
84×	`times-frac` `associate-r`
80×	`exp-sum`
74×	`add-cube-cbrt`
72×	`log-prod`
70×	`associate--l+`
36×	`distribute-rgt-in` `distribute-lft-in`
30×	`associate-+l+` `associate-+r+`
28×	`associate-/l*`
27×	`associate-l`
15×	`add-exp-log`
13×	`add-cbrt-cube`
11×	`exp-prod`
10×	`pow1` `distribute-lft-out--` `add-log-exp`
6×	`*-commutative` `distribute-lft-out` `unswap-sqr`
5×	`+-commutative` `sub-neg`
4×	`prod-exp`
3×	`div-exp` `associate-/r*` `cbrt-unprod` `rem-exp-log`
2×	`cbrt-undiv` `exp-diff` `diff-log` `pow-prod-down` `associate-*l/` `log-pow` `difference-of-squares`
1×	`flip3--` `frac-2neg` `associate-*r/` `clear-num` `sum-log` `flip--` `div-inv` `associate-/l/`

Counts

4 → 223

Calls

4 calls:

7.0ms	(* (- t 1.0) (log a))
4.0ms	(* y (log z))
40.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
26.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))

series411.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (- t 1.0) (log a))
40.0ms	(* y (log z))
176.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
129.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))

simplify104.0ms

Algorithm

egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	1036	2693
1	3948	2303
2	5001	2275

prune767.0ms

Filtered

235 candidates to 155 candidates (34.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	227	8	235
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	229	8	237

Merged error: 0.0b

Counts

237 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))
0.3b	(* (log (/ 1 a)) t)
0.3b	(* y (log (/ 1 z)))
0.5b	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)

rewrite843.0ms

Algorithm

rewrite-expression-head

Rules

7657×	`times-frac`
3327×	`add-sqr-sqrt`
3262×	`*-un-lft-identity`
3255×	`add-cube-cbrt`
2610×	`exp-sum`
2288×	`log-prod`
2269×	`associate-r`
2262×	`associate-+l+`
2183×	`unpow-prod-down`
1144×	`distribute-rgt-in` `distribute-lft-in`
616×	`associate-/l*`
349×	`div-inv`
174×	`+-commutative` `associate-+r+`
171×	`sqr-pow`
73×	`add-exp-log`
69×	`associate-/r*`
55×	`associate-/l/`
53×	`associate-*r/`
46×	`div-exp`
26×	`unswap-sqr`
21×	`associate-l`
19×	`add-cbrt-cube`
16×	`pow-exp`
15×	`prod-exp`
12×	`pow1`
6×	`log-rec` `clear-num` `log-pow` `*-commutative`
5×	`cbrt-undiv`
4×	`pow-to-exp` `rec-exp` `1-exp` `cbrt-unprod` `add-log-exp`
3×	`distribute-lft-neg-out` `frac-2neg` `distribute-rgt-neg-out`
2×	`pow-flip` `pow-prod-down` `un-div-inv` `inv-pow`

Counts

4 → 3109

Calls

4 calls:

54.0ms	(/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))
5.0ms	(* (log (/ 1 a)) t)
7.0ms	(* y (log (/ 1 z)))
259.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)

series740.0ms

Counts

4 → 12

Calls

4 calls:

287.0ms	(/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))
64.0ms	(* (log (/ 1 a)) t)
39.0ms	(* y (log (/ 1 z)))
349.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)

simplify732.0ms

Algorithm

egg-herbie

Counts

3121 → 3121

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5046	75644

prune15.4s

Filtered

3121 candidates to 2512 candidates (19.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	3118	3	3121
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	3122	7	3129

Merged error: 0.0b

Counts

3129 → 7

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (* x (exp (- (+ (+ (* y (* 2 (log (cbrt z)))) (* y (log (cbrt z)))) (* (- t 1.0) (log a))) b))) y)
0.6b	(cbrt z)
0.6b	(cbrt z)
0.9b	(exp (- (+ (+ (* y (* 2 (log (cbrt z)))) (* y (log (cbrt z)))) (* (- t 1.0) (log a))) b))

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

310×	`associate-+l+`
240×	`exp-sum`
230×	`associate--l+`
214×	`*-un-lft-identity`
210×	`log-prod`
204×	`associate-r`
180×	`times-frac`
165×	`distribute-rgt-in` `distribute-lft-in`
160×	`add-sqr-sqrt`
150×	`add-cube-cbrt`
96×	`cbrt-prod`
90×	`associate-+r+`
60×	`associate-/l*`
34×	`associate-l`
27×	`distribute-lft-out`
21×	`distribute-lft-out--`
20×	`exp-prod`
14×	`add-log-exp`
11×	`add-exp-log`
10×	`+-commutative`
9×	`add-cbrt-cube`
5×	`sub-neg`
4×	`pow1` `*-commutative` `rem-exp-log` `unswap-sqr`
3×	`diff-log` `div-exp` `associate-/r*` `sum-log`
2×	`cbrt-undiv` `exp-diff` `pow1/3` `prod-exp`
1×	`frac-2neg` `associate-*r/` `clear-num` `cbrt-unprod` `div-inv` `associate-/l/` `difference-of-squares`

Counts

4 → 361

Calls

4 calls:

94.0ms	(/ (* x (exp (- (+ (+ (* y (* 2 (log (cbrt z)))) (* y (log (cbrt z)))) (* (- t 1.0) (log a))) b))) y)
1.0ms	(cbrt z)
1.0ms	(cbrt z)
71.0ms	(exp (- (+ (+ (* y (* 2 (log (cbrt z)))) (* y (log (cbrt z)))) (* (- t 1.0) (log a))) b))

series786.0ms

Counts

4 → 12

Calls

4 calls:

260.0ms	(/ (* x (exp (- (+ (+ (* y (* 2 (log (cbrt z)))) (* y (log (cbrt z)))) (* (- t 1.0) (log a))) b))) y)
178.0ms	(cbrt z)
176.0ms	(cbrt z)
172.0ms	(exp (- (+ (+ (* y (* 2 (log (cbrt z)))) (* y (log (cbrt z)))) (* (- t 1.0) (log a))) b))

simplify90.0ms

Algorithm

egg-herbie

Counts

373 → 373

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1925	7105
1	5001	6244

prune1.1s

Filtered

373 candidates to 227 candidates (39.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	372	1	373
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	373	7	380

Merged error: 0.0b

Counts

380 → 7

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))
0.3b	(* (log (/ 1 a)) t)
0.3b	(* y (log (/ 1 z)))
1.5b	(/ (* x (/ (pow 1 1.0) 1)) (/ y (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))))

rewrite22.7s

Algorithm

rewrite-expression-head

Rules

350996×	`times-frac`
153101×	`add-sqr-sqrt`
132064×	`*-un-lft-identity`
121543×	`add-cube-cbrt`
79563×	`unpow-prod-down`
68130×	`exp-sum`
59072×	`log-prod`
59046×	`associate-+l+`
43834×	`associate-r`
29536×	`distribute-rgt-in` `distribute-lft-in`
15779×	`unswap-sqr`
13133×	`sqr-pow`
10839×	`div-inv`
5268×	`associate-l`
4542×	`+-commutative` `associate-+r+`
3772×	`associate-/r*`
2850×	`associate-/r/`
1755×	`*-commutative`
803×	`associate-/l*`
622×	`add-exp-log`
558×	`div-exp`
144×	`pow-exp`
128×	`prod-exp`
106×	`1-exp`
50×	`pow-to-exp` `clear-num`
47×	`frac-2neg`
46×	`add-cbrt-cube`
22×	`cbrt-undiv` `rec-exp`
15×	`associate-/l/`
13×	`associate-*r/`
12×	`pow1`
8×	`cbrt-unprod`
6×	`log-rec` `log-pow`
4×	`add-log-exp`
3×	`distribute-lft-neg-out` `distribute-rgt-neg-out`
2×	`pow-flip` `pow-prod-down` `un-div-inv` `inv-pow`

Counts

4 → 76831

Calls

4 calls:

48.0ms	(/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))
5.0ms	(* (log (/ 1 a)) t)
7.0ms	(* y (log (/ 1 z)))
1.9s	(/ (* x (/ (pow 1 1.0) 1)) (/ y (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))))

series742.0ms

Counts

4 → 12

Calls

4 calls:

290.0ms	(/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))
63.0ms	(* (log (/ 1 a)) t)
43.0ms	(* y (log (/ 1 z)))
345.0ms	(/ (* x (/ (pow 1 1.0) 1)) (/ y (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))))

simplify32.9s

Algorithm

egg-herbie

Counts

76843 → 76843

Iterations

Useful iterations: 0 (2.4s)

Iter	Nodes	Cost
0	111761	2882293

prune7.9m

Filtered

76843 candidates to 57062 candidates (25.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	76843	0	76843
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	76843	7	76850

Merged error: 0.0b

Counts

76850 → 7

regimes408.0ms

Accuracy

0% (1.1b remaining)

Error of 1.1b against oracle of 0.0b and baseline of 1.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	14
1	28	14

end0.0ms

sample5.9s

Algorithm

intervals

Results

2.9s	46016×	body	80	nan
918.0ms	15367×	body	80	valid

Details

sample190.0ms

simplify53.0ms

prune10.0ms

localize16.0ms

rewrite89.0ms

series411.0ms

simplify104.0ms

prune767.0ms

localize21.0ms

rewrite843.0ms

series740.0ms

simplify732.0ms

prune15.4s

localize23.0ms

rewrite206.0ms

series786.0ms

simplify90.0ms

prune1.1s

localize23.0ms

rewrite22.7s

series742.0ms

simplify32.9s

prune7.9m

regimes408.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.9s

end44.5s