Details

sample251.0ms

Algorithm

intervals

Results

92.0ms	1433×	body	80	nan
37.0ms	500×	body	80	valid

simplify50.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (4.0ms)

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

prune21.0ms

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: 0.2b

Counts

2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- t 1.0) (log a))
0.2b	(* y (log z))
1.0b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.5b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
15×	`add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`add-exp-log` `log-prod`
10×	`pow1` `add-log-exp`
8×	`associate-r` `associate-l`
6×	`distribute-rgt-in` `distribute-lft-in`
5×	`exp-prod`
3×	`times-frac` `exp-sum` `prod-exp` `associate-/r*` `cbrt-unprod` `rem-exp-log`
2×	`cbrt-undiv` `exp-diff` `diff-log` `div-exp` `pow-prod-down` `associate-l/` `log-pow` `-commutative` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`sub-neg` `flip3--` `frac-2neg` `associate-r/` `associate--l+` `clear-num` `sum-log` `flip--` `div-inv` `associate-/l/` `associate-/l`

Counts

4 → 95

Calls

4 calls:

7.0ms	(* (- t 1.0) (log a))
4.0ms	(* y (log z))
6.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
11.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

series131.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (- t 1.0) (log a))
7.0ms	(* y (log z))
44.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
71.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

simplify60.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	569	965
1	2353	793
2	5001	726

prune1.0s

Filtered

107 candidates to 75 candidates (29.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	102	5	107
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	103	6	109

Merged error: 0.0b

Counts

109 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t))))))
0.2b	(* (log (/ 1 z)) y)
0.3b	(* (log (/ 1 a)) t)
1.5b	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t)))))) y)

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
82×	`add-sqr-sqrt` `associate-r`
62×	`*-un-lft-identity`
61×	`add-cube-cbrt`
55×	`unpow-prod-down`
45×	`add-exp-log`
24×	`div-exp`
22×	`add-cbrt-cube`
17×	`exp-sum`
16×	`prod-exp`
15×	`associate-l`
14×	`pow1`
8×	`distribute-lft-neg-out` `log-rec` `pow-exp` `unswap-sqr`
6×	`log-pow` `cbrt-unprod` `div-inv`
5×	`cbrt-undiv` `sqr-pow`
4×	`exp-diff` `associate-/r/` `add-log-exp`
3×	`pow-prod-down` `associate-/r` `-commutative`
2×	`pow-to-exp` `associate-+r-` `rec-exp` `distribute-neg-out` `pow-flip` `1-exp` `associate-*r/` `unsub-neg` `inv-pow`
1×	`frac-2neg` `clear-num` `associate-/l/` `associate-/l*`

Counts

4 → 177

Calls

4 calls:

31.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t))))))
4.0ms	(* (log (/ 1 z)) y)
4.0ms	(* (log (/ 1 a)) t)
19.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t)))))) y)

series285.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t))))))
10.0ms	(* (log (/ 1 z)) y)
11.0ms	(* (log (/ 1 a)) t)
133.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t)))))) y)

simplify114.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1050	2460
1	4978	2167
2	5002	2167

prune2.1s

Filtered

189 candidates to 131 candidates (30.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	185	4	189
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	189	6	195

Merged error: 0.0b

Counts

195 → 6

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

273×	`add-exp-log`
146×	`div-exp`
98×	`prod-exp`
43×	`pow-exp`
39×	`add-cbrt-cube`
18×	`add-sqr-sqrt` `associate-l`
16×	`pow1`
14×	`pow-to-exp`
13×	`cbrt-unprod`
12×	`cbrt-undiv` `add-cube-cbrt` `*-un-lft-identity`
10×	`1-exp`
9×	`associate-r` `log-pow`
4×	`add-log-exp`
3×	`distribute-lft-neg-out` `pow-flip` `times-frac` `associate-r/` `log-rec` `pow-prod-down` `associate-/r` `*-commutative` `associate-/l/` `inv-pow` `unswap-sqr`
1×	`frac-times` `frac-2neg` `associate-l/` `clear-num` `div-inv` `associate-/l`

Counts

4 → 139

Calls

4 calls:

5.0ms	(* (log (/ 1 z)) y)
4.0ms	(* (log (/ 1 a)) t)
4.0ms	(* (log (/ 1 a)) t)
46.0ms	(/ (* (* x (/ (pow (/ (* (cbrt 1) (cbrt 1)) 1) 1.0) (sqrt (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t))))))) (/ (pow (/ (cbrt 1) a) 1.0) (sqrt (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t))))))) y)

series158.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (log (/ 1 z)) y)
10.0ms	(* (log (/ 1 a)) t)
10.0ms	(* (log (/ 1 a)) t)
127.0ms	(/ (* (* x (/ (pow (/ (* (cbrt 1) (cbrt 1)) 1) 1.0) (sqrt (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t))))))) (/ (pow (/ (cbrt 1) a) 1.0) (sqrt (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t))))))) y)

simplify91.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	948	3259
1	3579	2743
2	5001	2743

prune952.0ms

Filtered

151 candidates to 73 candidates (51.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	151	0	151
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	151	6	157

Merged error: 0.0b

Counts

157 → 6

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

180×	`add-exp-log`
81×	`div-exp`
75×	`prod-exp`
44×	`add-cbrt-cube`
19×	`cbrt-unprod`
18×	`add-sqr-sqrt` `associate-l`
17×	`cbrt-undiv`
16×	`pow1` `pow-to-exp` `pow-exp`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r` `log-pow`
4×	`add-log-exp`
3×	`distribute-lft-neg-out` `pow-flip` `times-frac` `associate-r/` `log-rec` `pow-prod-down` `associate-/r` `*-commutative` `associate-/l/` `inv-pow` `unswap-sqr`
1×	`frac-times` `frac-2neg` `associate-l/` `clear-num` `div-inv` `associate-/l`

Counts

4 → 128

Calls

4 calls:

5.0ms	(* (log (/ 1 a)) t)
5.0ms	(* (log (/ 1 a)) t)
4.0ms	(* (log (/ 1 a)) t)
52.0ms	(/ (* (* x (/ (pow (sqrt (/ 1 a)) 1.0) (* (cbrt (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t))))) (cbrt (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t)))))))) (/ (pow (sqrt (/ 1 a)) 1.0) (cbrt (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t))))))) y)

series170.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (log (/ 1 a)) t)
10.0ms	(* (log (/ 1 a)) t)
10.0ms	(* (log (/ 1 a)) t)
140.0ms	(/ (* (* x (/ (pow (sqrt (/ 1 a)) 1.0) (* (cbrt (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t))))) (cbrt (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t)))))))) (/ (pow (sqrt (/ 1 a)) 1.0) (cbrt (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t))))))) y)

simplify102.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	786	3447
1	3465	2709
2	5002	2556

prune868.0ms

Filtered

140 candidates to 74 candidates (47.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	139	7	146

Merged error: 0.0b

Counts

146 → 7

regimes807.0ms

Accuracy

50.9% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 1.1b

bsearch417.0ms

Steps

Iters	Range		Point
8	1.3022887670696334e-138	6.290782744266996e-136	1.2743824429929568e-137
7	-1.969937807864128e-97	-1.9881568618028162e-99	-5.725747184320903e-98

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	54
1	70	54
2	82	54
3	82	54

end0.0ms

sample7.4s

Algorithm

intervals

Results

2.8s	44862×	body	80	nan
1.1s	15060×	body	80	valid

Details

sample251.0ms

simplify50.0ms

prune21.0ms

localize19.0ms

rewrite32.0ms

series131.0ms

simplify60.0ms

prune1.0s

localize20.0ms

rewrite68.0ms

series285.0ms

simplify114.0ms

prune2.1s

localize33.0ms

rewrite71.0ms

series158.0ms

simplify91.0ms

prune952.0ms

localize30.0ms

rewrite72.0ms

series170.0ms

simplify102.0ms

prune868.0ms

regimes807.0ms

bsearch417.0ms

simplify3.0ms

end0.0ms

sample7.4s

Profiling