Details

sample202.0ms

Algorithm

intervals

Results

87.0ms	1635×	body	80	nan
31.0ms	509×	body	80	valid

simplify52.0ms

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: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- t 1.0) (log a))
0.3b	(* y (log z))
0.7b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.0b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

rewrite122.0ms

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:

12.0ms	(* (- t 1.0) (log a))
4.0ms	(* y (log z))
30.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
74.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

series376.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (- t 1.0) (log a))
36.0ms	(* y (log z))
116.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
165.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

simplify54.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (45.0ms)

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

prune352.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

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

rewrite253.0ms

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:

139.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))
7.0ms	(* y (log (/ 1 z)))
4.0ms	(* (log (/ 1 a)) t)
92.0ms	(/ (* 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)))))
44.0ms	(* y (log (/ 1 z)))
63.0ms	(* (log (/ 1 a)) t)
325.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)

simplify49.0ms

Algorithm

egg-herbie

Counts

211 → 211

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1077	2667
1	5002	2322

prune818.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite316.0ms

Algorithm

rewrite-expression-head

Rules

390×	`add-exp-log`
191×	`div-exp`
153×	`prod-exp`
54×	`pow-exp`
44×	`add-cbrt-cube`
22×	`pow-to-exp`
19×	`cbrt-unprod`
18×	`add-sqr-sqrt` `associate-l`
17×	`cbrt-undiv`
16×	`pow1`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r` `log-pow`
4×	`add-log-exp`
3×	`distribute-lft-neg-out` `pow-flip` `times-frac` `associate-r/` `log-rec` `pow-prod-down` `associate-/r` `*-commutative` `associate-/l/` `inv-pow` `unswap-sqr`
1×	`frac-times` `frac-2neg` `associate-l/` `clear-num` `div-inv` `associate-/l`

Counts

4 → 156

Calls

4 calls:

4.0ms	(* (log (/ 1 a)) t)
4.0ms	(* (log (/ 1 a)) t)
4.0ms	(* (log (/ 1 a)) t)
289.0ms	(/ (* (* x (/ (pow (/ (* (cbrt 1) (cbrt 1)) (sqrt a)) 1.0) (* (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))))) (/ (pow (/ (cbrt 1) (sqrt a)) 1.0) (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))) y)

series755.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (log (/ 1 a)) t)
60.0ms	(* (log (/ 1 a)) t)
66.0ms	(* (log (/ 1 a)) t)
560.0ms	(/ (* (* x (/ (pow (/ (* (cbrt 1) (cbrt 1)) (sqrt a)) 1.0) (* (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))))) (/ (pow (/ (cbrt 1) (sqrt a)) 1.0) (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))) y)

simplify115.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	974	4863
1	3428	4033
2	5002	3858

prune688.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(* y (log (/ 1 z)))
0.3b	(* (log (/ 1 a)) t)
1.0b	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (cbrt (pow (* (log (/ 1 a)) t) 3)) b))))) y)
39.2b	(cbrt (pow (* (log (/ 1 a)) t) 3))

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log`
29×	`add-sqr-sqrt`
26×	`log-prod`
25×	`add-cube-cbrt` `*-un-lft-identity`
21×	`times-frac`
17×	`add-cbrt-cube`
16×	`div-exp`
13×	`distribute-rgt-in` `distribute-lft-in`
12×	`pow1`
9×	`associate-r` `associate-l` `prod-exp`
8×	`cbrt-prod`
6×	`log-pow`
4×	`cbrt-undiv` `pow-exp` `cbrt-unprod` `add-log-exp`
3×	`associate-/r*` `div-inv`
2×	`pow-flip` `log-rec` `pow-prod-down` `*-commutative` `inv-pow` `unswap-sqr`
1×	`distribute-lft-neg-out` `cube-mult` `pow-to-exp` `unpow-prod-down` `rec-exp` `frac-2neg` `pow1/3` `1-exp` `unpow3` `cube-prod` `associate-r/` `clear-num` `distribute-rgt-neg-out` `rem-cbrt-cube` `associate-/l/` `associate-/l` `sqr-pow`

Counts

4 → 116

Calls

4 calls:

7.0ms	(* y (log (/ 1 z)))
5.0ms	(* (log (/ 1 a)) t)
185.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (cbrt (pow (* (log (/ 1 a)) t) 3)) b))))) y)
1.0ms	(cbrt (pow (* (log (/ 1 a)) t) 3))

series606.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* y (log (/ 1 z)))
64.0ms	(* (log (/ 1 a)) t)
425.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (cbrt (pow (* (log (/ 1 a)) t) 3)) b))))) y)
79.0ms	(cbrt (pow (* (log (/ 1 a)) t) 3))

simplify69.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	674	1224
1	2895	1014
2	5003	934

prune632.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes234.0ms

Accuracy

87% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 1.3b

bsearch369.0ms

Steps

Iters	Range		Point
9	1.0845475747405674e+39	1.4468144131924565e+45	8.085756460954374e+39
8	-2.3832728625365243e-91	-1.7151445531670253e-95	-2.3502010261951187e-91

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	60
1	52	60

end0.0ms

sample5.6s

Algorithm

intervals

Results

2.4s	45972×	body	80	nan
967.0ms	15167×	body	80	valid