Details

sample192.0ms

Algorithm

intervals

Results

82.0ms	1519×	body	80	nan
32.0ms	510×	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

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- t 1.0) (log a))
0.3b	(* y (log z))
0.6b	(/ (* 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))
5.0ms	(* y (log z))
12.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
8.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))

series369.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (- t 1.0) (log a))
39.0ms	(* y (log z))
159.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
114.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))

simplify59.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (49.0ms)

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

prune402.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

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)
0.6b	(/ (* 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)
15.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

series839.0ms

Counts

4 → 12

Calls

4 calls:

341.0ms	(* x (/ (pow (/ 1 a) 1.0) (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)
339.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

simplify90.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (72.0ms)

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

prune786.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

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)
0.6b	(* (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) (/ 1 y))

rewrite59.0ms

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:

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

series819.0ms

Counts

4 → 12

Calls

4 calls:

331.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))
81.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
76.0ms	(fma (log (/ 1 a)) t b)
331.0ms	(* (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) (/ 1 y))

simplify53.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1118	2775
1	5001	2428

prune759.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

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))
0.1b	(fma (log (/ 1 a)) t b)
1.4b	(* x (/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) y))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

541×	`times-frac`
254×	`add-sqr-sqrt`
230×	`*-un-lft-identity`
229×	`add-cube-cbrt`
220×	`associate-r`
159×	`unpow-prod-down`
54×	`fma-udef`
52×	`exp-sum`
27×	`add-exp-log`
16×	`div-inv`
15×	`div-exp`
13×	`add-cbrt-cube` `sqr-pow`
8×	`prod-exp`
7×	`unswap-sqr`
6×	`pow1`
5×	`add-log-exp`
4×	`expm1-log1p-u` `pow-exp` `log1p-expm1-u`
3×	`cbrt-undiv` `exp-prod` `associate-l` `cbrt-unprod`
1×	`pow-to-exp` `rec-exp` `1-exp` `associate-r/` `pow-prod-down` `-commutative` `rem-exp-log`

Counts

4 → 287

Calls

4 calls:

2.0ms	(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)
66.0ms	(* x (/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) y))

series612.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(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))
83.0ms	(fma (log (/ 1 a)) t b)
364.0ms	(* x (/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) y))

simplify78.0ms

Algorithm

egg-herbie

Counts

299 → 299

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1865	4199
1	5002	3972

prune1.5s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes202.0ms

Accuracy

74.3% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 1.3b

bsearch357.0ms

Steps

Iters	Range		Point
8	2.9265299865718764e-158	5.364345010889697e-154	4.936602630976155e-158
10	-6.674424518151835e-33	-2.5869142773886227e-46	-5.277731054367299e-33

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	25
1	35	25

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.5s	46504×	body	80	nan
988.0ms	15230×	body	80	valid