Details

sample229.0ms

Algorithm

intervals

Results

106.0ms	1538×	body	80	nan
40.0ms	467×	body	80	valid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	33	10
1	73	10
2	197	8
3	558	8
4	2287	8
5	5001	8

prune10.0ms

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: 0.3b

Counts

2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- 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))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`add-exp-log` `log-prod` `exp-sum`
10×	`pow1` `add-log-exp`
9×	`prod-diff`
8×	`associate-r` `associate-l`
6×	`distribute-rgt-in` `distribute-lft-in`
5×	`exp-prod`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`times-frac` `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 → 112

Calls

4 calls:

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

series371.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (- t 1.0) (log a))
37.0ms	(* y (log z))
164.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
113.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))

simplify61.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	580	1143
1	2309	897
2	5002	860

prune357.0ms

Filtered

124 candidates to 89 candidates (71.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	119	5	124
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	121	5	126

Merged error: 0.0b

Counts

126 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))
0.1b	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
0.2b	(fma (log (/ 1 a)) t b)
0.5b	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
74×	`add-sqr-sqrt`
72×	`associate-r`
58×	`*-un-lft-identity`
57×	`add-cube-cbrt`
55×	`unpow-prod-down`
41×	`add-exp-log`
24×	`div-exp`
19×	`fma-udef`
18×	`add-cbrt-cube`
17×	`exp-sum`
14×	`prod-exp`
8×	`pow-exp`
6×	`pow1` `div-inv` `unswap-sqr`
5×	`cbrt-undiv` `sqr-pow`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `associate-/r*`
2×	`pow-to-exp` `rec-exp` `1-exp` `associate-*r/`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `associate-/l/` `associate-/l`

Counts

4 → 153

Calls

4 calls:

24.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))
1.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
1.0ms	(fma (log (/ 1 a)) t b)
14.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

series830.0ms

Counts

4 → 12

Calls

4 calls:

338.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))
83.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
80.0ms	(fma (log (/ 1 a)) t b)
329.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

simplify92.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	904	2177
1	4141	1915
2	5001	1905

prune615.0ms

Filtered

165 candidates to 124 candidates (75.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	164	1	165
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	165	5	170

Merged error: 0b

Counts

170 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))
0.1b	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
0.2b	(fma (log (/ 1 a)) t b)
5.6b	(/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (/ y x))

rewrite202.0ms

Algorithm

rewrite-expression-head

Rules

3049×	`times-frac`
1216×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
728×	`unpow-prod-down`
241×	`fma-udef`
239×	`exp-sum`
144×	`div-inv`
72×	`associate-/l*`
56×	`sqr-pow`
39×	`add-exp-log`
37×	`div-exp`
16×	`add-cbrt-cube`
13×	`associate-/r*`
8×	`cbrt-undiv` `pow-exp`
5×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`exp-prod`
2×	`pow-to-exp` `rec-exp` `1-exp`
1×	`frac-2neg` `clear-num` `associate-/r/` `rem-exp-log` `associate-/l/`

Counts

4 → 1087

Calls

4 calls:

3.0ms	(exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))
1.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
1.0ms	(fma (log (/ 1 a)) t b)
49.0ms	(/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (/ y x))

series791.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))
82.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
77.0ms	(fma (log (/ 1 a)) t b)
538.0ms	(/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (/ y x))

simplify286.0ms

Algorithm

egg-herbie

Counts

1099 → 1099

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5001	28990

prune5.0s

Filtered

1099 candidates to 847 candidates (77.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	1099	0	1099
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	1099	5	1104

Merged error: 0b

Counts

1104 → 5

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
0.2b	(fma (log (/ 1 a)) t b)
0.2b	(* x (pow (/ 1 a) 1.0))
5.9b	(/ (* x (pow (/ 1 a) 1.0)) (* y (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-exp-log`
25×	`prod-exp`
23×	`add-sqr-sqrt`
20×	`div-exp`
18×	`add-cbrt-cube`
17×	`associate-r`
16×	`unpow-prod-down`
14×	`*-un-lft-identity`
13×	`add-cube-cbrt`
12×	`times-frac` `pow-exp`
5×	`cbrt-unprod` `unswap-sqr`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `rec-exp` `1-exp` `associate-l`
2×	`fma-udef` `div-inv` `sqr-pow`
1×	`frac-2neg` `clear-num` `associate-/r` `-commutative` `associate-/l*`

Counts

4 → 95

Calls

4 calls:

1.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
1.0ms	(fma (log (/ 1 a)) t b)
9.0ms	(* x (pow (/ 1 a) 1.0))
10.0ms	(/ (* x (pow (/ 1 a) 1.0)) (* y (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))

series669.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
81.0ms	(fma (log (/ 1 a)) t b)
150.0ms	(* x (pow (/ 1 a) 1.0))
351.0ms	(/ (* x (pow (/ 1 a) 1.0)) (* y (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))

simplify68.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	559	1001
1	2471	833
2	5002	818

prune360.0ms

Filtered

107 candidates to 72 candidates (67.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	107	5	112

Merged error: 0b

Counts

112 → 5

regimes317.0ms

Accuracy

46.2% (3.3b remaining)

Error of 3.6b against oracle of 0.4b and baseline of 6.4b

bsearch136.0ms

Steps

Iters	Range		Point
9	4.246232520144737e-105	4.332396423131368e-100	1.14244769217726e-102

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	24
1	29	24

end0.0ms

sample6.6s

Algorithm

intervals

Results

3.1s	45631×	body	80	nan
1.2s	15205×	body	80	valid

Details

sample229.0ms

simplify51.0ms

prune10.0ms

localize16.0ms

rewrite35.0ms

series371.0ms

simplify61.0ms

prune357.0ms

localize20.0ms

rewrite48.0ms

series830.0ms

simplify92.0ms

prune615.0ms

localize19.0ms

rewrite202.0ms

series791.0ms

simplify286.0ms

prune5.0s

localize25.0ms

rewrite24.0ms

series669.0ms

simplify68.0ms

prune360.0ms

regimes317.0ms

bsearch136.0ms

simplify1.0ms

end0.0ms

sample6.6s

Profiling