Details

sample173.0ms

Algorithm

intervals

Results

72.0ms	1303×	body	80	nan
32.0ms	459×	body	80	valid

simplify68.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

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

prune12.0ms

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: 0.2b

Counts

2 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- t 1.0) (log a))
0.3b	(* y (log z))
1.0b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.1b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

rewrite37.0ms

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:

8.0ms	(* (- t 1.0) (log a))
5.0ms	(* y (log z))
8.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
13.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

series438.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (- t 1.0) (log a))
45.0ms	(* y (log z))
129.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
198.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

simplify67.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	493	869
1	2033	715
2	5001	683

prune346.0ms

Filtered

107 candidates to 75 candidates (70.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	104	3	107
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	104	5	109

Merged error: 0.0b

Counts

109 → 5

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))
0.3b	(* y (log (/ 1 z)))
0.3b	(* (log (/ 1 a)) t)
1.1b	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
96×	`add-sqr-sqrt`
81×	`associate-r`
76×	`*-un-lft-identity`
75×	`add-cube-cbrt`
55×	`unpow-prod-down`
45×	`add-exp-log`
26×	`log-prod`
24×	`div-exp`
22×	`add-cbrt-cube`
17×	`exp-sum`
16×	`prod-exp`
14×	`pow1`
13×	`distribute-rgt-in` `distribute-lft-in`
12×	`associate-l`
8×	`pow-exp` `div-inv` `unswap-sqr`
6×	`log-pow` `cbrt-unprod`
5×	`cbrt-undiv` `sqr-pow`
4×	`add-log-exp`
3×	`pow-prod-down` `associate-/r` `-commutative`
2×	`pow-to-exp` `rec-exp` `pow-flip` `1-exp` `associate-*r/` `log-rec` `inv-pow`
1×	`distribute-lft-neg-out` `frac-2neg` `clear-num` `distribute-rgt-neg-out` `associate-/l/` `associate-/l*`

Counts

4 → 199

Calls

4 calls:

36.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))
7.0ms	(* y (log (/ 1 z)))
5.0ms	(* (log (/ 1 a)) t)
21.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)

series905.0ms

Counts

4 → 12

Calls

4 calls:

383.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))
53.0ms	(* y (log (/ 1 z)))
75.0ms	(* (log (/ 1 a)) t)
394.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)

simplify63.0ms

Algorithm

egg-herbie

Counts

211 → 211

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1077	2667
1	5002	2322

prune754.0ms

Filtered

211 candidates to 145 candidates (68.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	209	2	211
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	211	5	216

Merged error: 0b

Counts

216 → 5

localize29.0ms

Local error

Found 4 expressions with local error:

1.1b	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)
1.6b	(cbrt (/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y))
1.6b	(cbrt (/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y))
1.6b	(cbrt (/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-exp-log`
21×	`cbrt-prod`
16×	`div-exp`
13×	`add-cbrt-cube`
12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
7×	`prod-exp`
4×	`pow1` `cbrt-undiv` `pow-exp` `div-inv` `add-log-exp`
3×	`cbrt-div` `pow1/3` `associate-/r*`
2×	`cbrt-unprod`
1×	`pow-to-exp` `rec-exp` `frac-2neg` `1-exp` `associate-r/` `clear-num` `associate-/l/` `associate-/l`

Counts

4 → 77

Calls

4 calls:

22.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)
21.0ms	(cbrt (/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y))
18.0ms	(cbrt (/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y))
18.0ms	(cbrt (/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y))

series2.1s

Counts

4 → 12

Calls

4 calls:

426.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)
545.0ms	(cbrt (/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y))
556.0ms	(cbrt (/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y))
550.0ms	(cbrt (/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y))

simplify76.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	516	1900
1	1947	1663
2	5001	1628

prune554.0ms

Filtered

89 candidates to 78 candidates (87.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	89	5	94

Merged error: 0b

Counts

94 → 5

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (exp b) (pow (/ 1 a) t))
0.5b	(* (/ y (pow (/ 1 a) 1.0)) (pow (/ 1 z) y))
0.6b	(/ x (* (* (/ y (pow (/ 1 a) 1.0)) (pow (/ 1 z) y)) (* (exp b) (pow (/ 1 a) t))))
2.5b	(* (* (/ y (pow (/ 1 a) 1.0)) (pow (/ 1 z) y)) (* (exp b) (pow (/ 1 a) t)))

rewrite233.0ms

Algorithm

rewrite-expression-head

Rules

2729×	`add-exp-log`
1754×	`prod-exp`
1406×	`div-exp`
1128×	`pow-exp`
282×	`pow-to-exp` `rec-exp` `1-exp`
160×	`add-sqr-sqrt`
148×	`times-frac`
101×	`unpow-prod-down`
77×	`*-un-lft-identity`
65×	`add-cube-cbrt`
61×	`add-cbrt-cube`
59×	`associate-l`
35×	`associate-r` `unswap-sqr`
29×	`cbrt-unprod`
17×	`sqr-pow`
12×	`cbrt-undiv`
7×	`div-inv`
6×	`pow1`
5×	`associate-*l/`
4×	`add-log-exp`
3×	`-commutative` `associate-/l`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `associate-/r/`

Counts

4 → 841

Calls

4 calls:

12.0ms	(* (exp b) (pow (/ 1 a) t))
36.0ms	(* (/ y (pow (/ 1 a) 1.0)) (pow (/ 1 z) y))
40.0ms	(/ x (* (* (/ y (pow (/ 1 a) 1.0)) (pow (/ 1 z) y)) (* (exp b) (pow (/ 1 a) t))))
30.0ms	(* (* (/ y (pow (/ 1 a) 1.0)) (pow (/ 1 z) y)) (* (exp b) (pow (/ 1 a) t)))

series1.2s

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (exp b) (pow (/ 1 a) t))
224.0ms	(* (/ y (pow (/ 1 a) 1.0)) (pow (/ 1 z) y))
482.0ms	(/ x (* (* (/ y (pow (/ 1 a) 1.0)) (pow (/ 1 z) y)) (* (exp b) (pow (/ 1 a) t))))
392.0ms	(* (* (/ y (pow (/ 1 a) 1.0)) (pow (/ 1 z) y)) (* (exp b) (pow (/ 1 a) t)))

simplify162.0ms

Algorithm

egg-herbie

Counts

853 → 853

Iterations

Useful iterations: 1 (39.0ms)

Iter	Nodes	Cost
0	2763	10510
1	5001	9936

prune886.0ms

Filtered

853 candidates to 170 candidates (19.9%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	853	0	853
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	853	5	858

Merged error: 0b

Counts

858 → 5

regimes448.0ms

Accuracy

0% (1.2b remaining)

Error of 1.3b against oracle of 0.0b and baseline of 1.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	14
1	28	14

end0.0ms

sample5.6s

Algorithm

intervals

Results

2.4s	45429×	body	80	nan
1.0s	15235×	body	80	valid