Details

sample230.0ms

Algorithm

intervals

Results

109.0ms	1638×	body	80	nan
38.0ms	492×	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

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- t 1.0) (log a))
0.3b	(* y (log z))
1.1b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.7b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

rewrite33.0ms

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))
5.0ms	(* y (log z))
7.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
11.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

series363.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (- t 1.0) (log a))
35.0ms	(* y (log z))
109.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
163.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

simplify63.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (51.0ms)

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

prune368.0ms

Filtered

124 candidates to 89 candidates (71.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	119	5	124
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	120	6	126

Merged error: 0.0b

Counts

126 → 6

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 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))
0.1b	(fma (log (/ 1 a)) t b)
1.7b	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

rewrite46.0ms

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:

22.0ms	(* 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)

series817.0ms

Counts

4 → 12

Calls

4 calls:

329.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))
80.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
75.0ms	(fma (log (/ 1 a)) t b)
333.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

simplify98.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (72.0ms)

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

prune603.0ms

Filtered

165 candidates to 124 candidates (75.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	163	2	165
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	165	6	171

Merged error: 0b

Counts

171 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 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))
0.1b	(fma (log (/ 1 a)) t b)
1.7b	(* (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) (/ 1 y))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

120×	`times-frac`
118×	`add-exp-log`
85×	`associate-r`
79×	`add-sqr-sqrt`
67×	`prod-exp`
63×	`*-un-lft-identity`
62×	`add-cube-cbrt`
56×	`div-exp`
55×	`unpow-prod-down`
30×	`add-cbrt-cube`
20×	`pow-exp`
19×	`fma-udef`
17×	`exp-sum`
13×	`rec-exp` `1-exp`
12×	`cbrt-unprod`
11×	`pow1`
6×	`cbrt-undiv` `div-inv` `unswap-sqr`
5×	`pow-to-exp` `sqr-pow`
4×	`expm1-log1p-u` `associate-r/` `associate-l*` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative`
1×	`frac-times` `associate-*l/` `un-div-inv`

Counts

4 → 190

Calls

4 calls:

25.0ms	(* 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)
17.0ms	(* (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) (/ 1 y))

series822.0ms

Counts

4 → 12

Calls

4 calls:

329.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))
80.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
76.0ms	(fma (log (/ 1 a)) t b)
337.0ms	(* (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) (/ 1 y))

simplify51.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1118	2775
1	5001	2428

prune635.0ms

Filtered

202 candidates to 130 candidates (64.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	202	0	202
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	202	6	208

Merged error: 0b

Counts

208 → 6

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
0.1b	(fma (log (/ 1 a)) t b)
0.1b	(fma (log (/ 1 a)) t b)
1.7b	(/ (* (* x (sqrt (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) (sqrt (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) y)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-exp-log` `add-cbrt-cube`
6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `times-frac` `associate-r/` `div-exp` `prod-exp` `associate-/r` `cbrt-unprod` `fma-udef` `associate-/l/`
1×	`frac-times` `frac-2neg` `associate-l/` `clear-num` `div-inv` `associate-/l`

Counts

4 → 58

Calls

4 calls:

1.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
1.0ms	(fma (log (/ 1 a)) t b)
1.0ms	(fma (log (/ 1 a)) t b)
27.0ms	(/ (* (* x (sqrt (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) (sqrt (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) y)

series559.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
72.0ms	(fma (log (/ 1 a)) t b)
78.0ms	(fma (log (/ 1 a)) t b)
325.0ms	(/ (* (* x (sqrt (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) (sqrt (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) y)

simplify47.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	367	1015
1	1433	759
2	5001	754

prune348.0ms

Filtered

70 candidates to 59 candidates (84.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	70	6	76

Merged error: 0b

Counts

76 → 6

regimes323.0ms

Accuracy

79.8% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 1.4b

bsearch327.0ms

Steps

Iters	Range		Point
7	3.1008911368739145e-164	1.5388581765694856e-162	8.754412920530037e-163
8	-320783134448986.44	-178479104048.83572	-906498358069.3627

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	25
1	35	25

end0.0ms

sample6.5s

Algorithm

intervals

Results

3.1s	44664×	body	80	nan
1.2s	15032×	body	80	valid