Details

sample202.0ms

Algorithm

intervals

Results

68.0ms	1457×	body	80	nan
31.0ms	499×	body	80	valid

simplify50.0ms

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

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- t 1.0) (log a))
0.2b	(* y (log z))
0.9b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.6b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

rewrite271.0ms

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:

22.0ms	(* (- t 1.0) (log a))
8.0ms	(* y (log z))
70.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
168.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

series413.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (- t 1.0) (log a))
38.0ms	(* y (log z))
126.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
187.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

simplify53.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (44.0ms)

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

prune363.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize21.0ms

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)))))
0.2b	(* y (log (/ 1 z)))
0.3b	(* (log (/ 1 a)) t)
1.6b	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)

rewrite525.0ms

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:

289.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))
15.0ms	(* y (log (/ 1 z)))
10.0ms	(* (log (/ 1 a)) t)
201.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)

series839.0ms

Counts

4 → 12

Calls

4 calls:

372.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))
40.0ms	(* y (log (/ 1 z)))
66.0ms	(* (log (/ 1 a)) t)
361.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)

simplify48.0ms

Algorithm

egg-herbie

Counts

211 → 211

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1077	2667
1	5002	2322

prune805.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (pow (/ 1 a) 1.0) (* (exp (+ (* (log (/ 1 a)) t) b)) (pow (/ 1 z) y))) y)
0.3b	(* (log (/ 1 a)) t)
0.4b	(* (exp (+ (* (log (/ 1 a)) t) b)) (pow (/ 1 z) y))
0.5b	(* x (/ (/ (pow (/ 1 a) 1.0) (* (exp (+ (* (log (/ 1 a)) t) b)) (pow (/ 1 z) y))) y))

rewrite512.0ms

Algorithm

rewrite-expression-head

Rules

320×	`times-frac`
313×	`add-exp-log`
224×	`div-exp`
140×	`add-sqr-sqrt`
124×	`*-un-lft-identity`
123×	`add-cube-cbrt` `prod-exp`
108×	`pow-exp`
107×	`unpow-prod-down`
87×	`associate-r`
31×	`add-cbrt-cube`
27×	`pow-to-exp` `rec-exp` `1-exp`
21×	`associate-/l*`
17×	`div-inv`
13×	`associate-l`
10×	`pow1` `cbrt-undiv`
9×	`sqr-pow`
8×	`cbrt-unprod` `unswap-sqr`
4×	`add-log-exp`
3×	`associate-/r` `log-pow` `-commutative`
2×	`pow-prod-down`
1×	`distribute-lft-neg-out` `pow-flip` `frac-2neg` `associate-*r/` `exp-sum` `log-rec` `clear-num` `associate-/l/` `inv-pow`

Counts

4 → 337

Calls

4 calls:

108.0ms	(/ (/ (pow (/ 1 a) 1.0) (* (exp (+ (* (log (/ 1 a)) t) b)) (pow (/ 1 z) y))) y)
10.0ms	(* (log (/ 1 a)) t)
105.0ms	(* (exp (+ (* (log (/ 1 a)) t) b)) (pow (/ 1 z) y))
266.0ms	(* x (/ (/ (pow (/ 1 a) 1.0) (* (exp (+ (* (log (/ 1 a)) t) b)) (pow (/ 1 z) y))) y))

series963.0ms

Counts

4 → 12

Calls

4 calls:

360.0ms	(/ (/ (pow (/ 1 a) 1.0) (* (exp (+ (* (log (/ 1 a)) t) b)) (pow (/ 1 z) y))) y)
69.0ms	(* (log (/ 1 a)) t)
135.0ms	(* (exp (+ (* (log (/ 1 a)) t) b)) (pow (/ 1 z) y))
399.0ms	(* x (/ (/ (pow (/ 1 a) 1.0) (* (exp (+ (* (log (/ 1 a)) t) b)) (pow (/ 1 z) y))) y))

simplify76.0ms

Algorithm

egg-herbie

Counts

349 → 349

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1581	4899
1	5002	4441

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (exp (+ (* (log (/ 1 a)) t) b)) (pow (/ 1 z) y))
0.4b	(* (exp (+ (* (log (/ 1 a)) t) b)) (pow (/ 1 z) y))
0.4b	(* (exp (+ (* (log (/ 1 a)) t) b)) (pow (/ 1 z) y))
0.5b	(* x (/ (/ (pow (/ 1 a) 1.0) (* (* (cbrt (* (exp (+ (* (log (/ 1 a)) t) b)) (pow (/ 1 z) y))) (cbrt (* (exp (+ (* (log (/ 1 a)) t) b)) (pow (/ 1 z) y)))) (cbrt (* (exp (+ (* (log (/ 1 a)) t) b)) (pow (/ 1 z) y))))) y))

rewrite636.0ms

Algorithm

rewrite-expression-head

Rules

175×	`times-frac`
118×	`associate-r`
117×	`add-exp-log`
116×	`add-sqr-sqrt`
87×	`unpow-prod-down`
84×	`*-un-lft-identity`
81×	`add-cube-cbrt`
56×	`prod-exp`
49×	`div-exp`
26×	`add-cbrt-cube`
24×	`pow-exp`
17×	`unswap-sqr`
15×	`associate-l`
11×	`cbrt-unprod`
10×	`div-inv`
9×	`sqr-pow`
7×	`cbrt-undiv`
6×	`pow1` `pow-to-exp` `rec-exp` `1-exp`
4×	`*-commutative` `add-log-exp`
3×	`exp-sum`
1×	`associate-*r/` `pow-prod-down`

Counts

4 → 230

Calls

4 calls:

103.0ms	(* (exp (+ (* (log (/ 1 a)) t) b)) (pow (/ 1 z) y))
104.0ms	(* (exp (+ (* (log (/ 1 a)) t) b)) (pow (/ 1 z) y))
104.0ms	(* (exp (+ (* (log (/ 1 a)) t) b)) (pow (/ 1 z) y))
312.0ms	(* x (/ (/ (pow (/ 1 a) 1.0) (* (* (cbrt (* (exp (+ (* (log (/ 1 a)) t) b)) (pow (/ 1 z) y))) (cbrt (* (exp (+ (* (log (/ 1 a)) t) b)) (pow (/ 1 z) y)))) (cbrt (* (exp (+ (* (log (/ 1 a)) t) b)) (pow (/ 1 z) y))))) y))

series797.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(* (exp (+ (* (log (/ 1 a)) t) b)) (pow (/ 1 z) y))
137.0ms	(* (exp (+ (* (log (/ 1 a)) t) b)) (pow (/ 1 z) y))
132.0ms	(* (exp (+ (* (log (/ 1 a)) t) b)) (pow (/ 1 z) y))
389.0ms	(* x (/ (/ (pow (/ 1 a) 1.0) (* (* (cbrt (* (exp (+ (* (log (/ 1 a)) t) b)) (pow (/ 1 z) y))) (cbrt (* (exp (+ (* (log (/ 1 a)) t) b)) (pow (/ 1 z) y)))) (cbrt (* (exp (+ (* (log (/ 1 a)) t) b)) (pow (/ 1 z) y))))) y))

simplify62.0ms

Algorithm

egg-herbie

Counts

242 → 242

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1209	5017
1	5001	4329

prune1.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes444.0ms

Accuracy

-14% (1.3b remaining)

Error of 1.4b against oracle of 0.1b and baseline of 1.2b

bsearch292.0ms

Steps

Iters	Range		Point
7	4.538508736621938e-52	1.858673199194124e-50	3.6449231596392034e-51
9	-4.024715380573778e-144	-2.223200618048248e-150	-1.8083024609859046e-147

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	28
1	47	28

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.3s	47292×	body	80	nan
891.0ms	15305×	body	80	valid