Details

sample169.0ms

Algorithm

intervals

Results

69.0ms	1343×	body	80	nan
30.0ms	447×	body	80	valid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

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

prune11.0ms

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

localize16.0ms

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)

rewrite35.0ms

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))
5.0ms	(* y (log z))
9.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
11.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

series372.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (- t 1.0) (log a))
36.0ms	(* y (log z))
116.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
163.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

simplify56.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (46.0ms)

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

prune313.0ms

Filtered

107 candidates to 75 candidates (70.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	103	4	107
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	104	5	109

Merged error: 0.0b

Counts

109 → 5

localize20.0ms

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)

rewrite74.0ms

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:

29.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))
7.0ms	(* y (log (/ 1 z)))
7.0ms	(* (log (/ 1 a)) t)
21.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)

series764.0ms

Counts

4 → 12

Calls

4 calls:

333.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))
43.0ms	(* y (log (/ 1 z)))
58.0ms	(* (log (/ 1 a)) t)
330.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)

simplify59.0ms

Algorithm

egg-herbie

Counts

211 → 211

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1077	2667
1	5002	2322

prune709.0ms

Filtered

211 candidates to 145 candidates (68.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	209	2	211
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	211	5	216

Merged error: 0b

Counts

216 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))
0.3b	(* y (log (/ 1 z)))
0.3b	(* (log (/ 1 a)) t)
4.0b	(/ (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) (/ y x))

rewrite193.0ms

Algorithm

rewrite-expression-head

Rules

3067×	`times-frac`
1238×	`add-sqr-sqrt`
1234×	`add-cube-cbrt` `*-un-lft-identity`
728×	`unpow-prod-down`
239×	`exp-sum`
146×	`div-inv`
72×	`associate-/l*`
56×	`sqr-pow`
43×	`add-exp-log`
37×	`div-exp`
26×	`log-prod`
20×	`add-cbrt-cube`
13×	`distribute-rgt-in` `distribute-lft-in` `associate-/r*`
12×	`pow1`
10×	`add-log-exp`
9×	`associate-r` `associate-l`
8×	`cbrt-undiv` `pow-exp`
6×	`log-pow`
3×	`exp-prod` `sum-log` `rem-exp-log`
2×	`pow-to-exp` `rec-exp` `pow-flip` `1-exp` `log-rec` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `inv-pow` `unswap-sqr`
1×	`distribute-lft-neg-out` `frac-2neg` `clear-num` `associate-/r/` `distribute-rgt-neg-out` `associate-/l/`

Counts

4 → 1135

Calls

4 calls:

9.0ms	(exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))
7.0ms	(* y (log (/ 1 z)))
5.0ms	(* (log (/ 1 a)) t)
49.0ms	(/ (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) (/ y x))

series700.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))
44.0ms	(* y (log (/ 1 z)))
64.0ms	(* (log (/ 1 a)) t)
509.0ms	(/ (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) (/ y x))

simplify306.0ms

Algorithm

egg-herbie

Counts

1147 → 1147

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5001	32428

prune4.9s

Filtered

1147 candidates to 878 candidates (76.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	1147	0	1147
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	1147	5	1152

Merged error: 0b

Counts

1152 → 5

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (/ 1 a)) t)
0.8b	(/ (* (sqrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))) (sqrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))))) y)
2.0b	(sqrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))))
2.0b	(sqrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1`
11×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-*r/`
6×	`sqrt-div` `associate-l`
4×	`sqrt-pow1` `add-log-exp`
3×	`times-frac` `associate-r` `pow-prod-down` `associate-/r*` `log-pow` `associate-/l/`
2×	`cbrt-undiv` `pow1/2` `div-exp` `prod-exp` `sqrt-prod` `cbrt-unprod`
1×	`distribute-lft-neg-out` `frac-times` `pow-flip` `frac-2neg` `log-rec` `associate-l/` `clear-num` `-commutative` `div-inv` `associate-/l*` `inv-pow` `unswap-sqr`

Counts

4 → 70

Calls

4 calls:

8.0ms	(* (log (/ 1 a)) t)
42.0ms	(/ (* (sqrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))) (sqrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))))) y)
17.0ms	(sqrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))))
18.0ms	(sqrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))))

series1.5s

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (log (/ 1 a)) t)
522.0ms	(/ (* (sqrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))) (sqrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))))) y)
461.0ms	(sqrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))))
454.0ms	(sqrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))))

simplify64.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	445	1340
1	1730	1084
2	5001	1051

prune387.0ms

Filtered

82 candidates to 68 candidates (82.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	82	5	87

Merged error: 0b

Counts

87 → 5

regimes263.0ms

Accuracy

83.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 1.2b

bsearch425.0ms

Steps

Iters	Range		Point
9	7.348486498325489e-127	2.1932446481510436e-117	4.717642965513083e-120
10	-1.3667098245908305e+37	-1.5465241855074316e+27	-8.226813781604714e+32

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	28
1	39	28

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.4s	45425×	body	80	nan
970.0ms	15222×	body	80	valid