Details

sample163.0ms

Algorithm

intervals

Results

66.0ms	1178×	body	80	nan
25.0ms	386×	body	80	valid
5.0ms	13×	body	640	valid
1.0ms	2×	body	1280	valid
1.0ms	10×	body	160	valid
1.0ms	4×	body	320	valid

simplify39.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	10
1	58	10
2	129	10
3	318	10
4	1073	10
5	5001	10

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* a (- (log (- 1.0 z)) b))
0.0b	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
0.2b	(* y (- (log z) t))
7.0b	(log (- 1.0 z))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
21×	`log-prod`
16×	`associate--l+`
14×	`add-cube-cbrt`
12×	`distribute-rgt-in` `distribute-lft-in` `associate-r`
11×	`pow1`
9×	`add-exp-log`
8×	`add-cbrt-cube`
7×	`distribute-lft-out--` `add-log-exp`
6×	`associate-l`
5×	`difference-of-squares`
4×	`sub-neg` `associate-*r/`
3×	`exp-prod` `flip3--` `log-pow` `flip--`
2×	`log-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`
1×	`rem-log-exp` `exp-sum` `sum-log`

Counts

4 → 99

Calls

4 calls:

16.0ms	(* a (- (log (- 1.0 z)) b))
21.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
13.0ms	(* y (- (log z) t))
3.0ms	(log (- 1.0 z))

series343.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* a (- (log (- 1.0 z)) b))
146.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
76.0ms	(* y (- (log z) t))
45.0ms	(log (- 1.0 z))

simplify60.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	513	721
1	1897	651
2	5001	633

prune369.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (log z) t)
0.0b	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
0.0b	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
0.2b	(* y (- (log z) t))

rewrite553.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
25×	`associate--l+`
24×	`add-sqr-sqrt`
15×	`log-prod`
14×	`add-cube-cbrt`
13×	`associate-r`
12×	`distribute-rgt-in` `distribute-lft-in`
11×	`pow1`
9×	`distribute-lft-out--`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`sub-neg`
6×	`associate-l`
4×	`associate-*r/`
3×	`exp-prod` `flip3--` `log-pow` `flip--` `difference-of-squares`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`
1×	`diff-log` `exp-sum` `sum-log`

Counts

4 → 102

Calls

4 calls:

4.0ms	(- (log z) t)
421.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
109.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
16.0ms	(* y (- (log z) t))

series414.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- (log z) t)
106.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
171.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
72.0ms	(* y (- (log z) t))

simplify51.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	467	1022
1	1787	915
2	5002	907

prune441.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
0.0b	(* (sqrt (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))) (sqrt (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))))
0.2b	(* y (- (log z) t))
0.2b	(* y (- (log z) t))

rewrite785.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
27×	`add-cube-cbrt`
26×	`sqrt-pow1`
25×	`pow1`
22×	`sqrt-prod`
21×	`exp-prod`
19×	`associate-r`
13×	`associate-l`
12×	`log-prod` `associate--l+`
10×	`add-exp-log` `distribute-rgt-in` `distribute-lft-in` `add-cbrt-cube`
9×	`swap-sqr`
8×	`pow1/2` `pow-prod-down` `pow-prod-up`
7×	`add-log-exp`
6×	`pow-sqr` `unswap-sqr`
5×	`exp-sum`
4×	`sub-neg` `associate-*r/` `distribute-lft-out--`
3×	`prod-exp` `*-commutative` `cbrt-unprod`
2×	`flip3--` `log-pow` `flip--` `rem-exp-log` `difference-of-squares`
1×	`pow2` `pow-plus` `sqrt-unprod` `sum-log` `rem-square-sqrt`

Counts

4 → 140

Calls

4 calls:

106.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
644.0ms	(* (sqrt (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))) (sqrt (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))))
17.0ms	(* y (- (log z) t))
13.0ms	(* y (- (log z) t))

series493.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
178.0ms	(* (sqrt (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))) (sqrt (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))))
73.0ms	(* y (- (log z) t))
72.0ms	(* y (- (log z) t))

simplify65.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	405	2052
1	1669	1790
2	5001	1673

prune709.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
0.0b	(pow (exp 2) (/ (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))) 2))
0.2b	(* y (- (log z) t))
0.2b	(/ (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))) 2)

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

40×	`*-un-lft-identity`
37×	`add-sqr-sqrt`
29×	`add-cube-cbrt`
22×	`associate--l+`
18×	`times-frac`
13×	`pow-unpow` `associate-r`
12×	`distribute-rgt-in` `log-prod` `distribute-lft-in` `associate-*r/`
11×	`pow1`
10×	`add-exp-log` `add-cbrt-cube`
7×	`distribute-lft-out--`
6×	`sub-neg` `flip3--` `associate-l` `flip--` `associate-/l/`
4×	`unpow-prod-down` `pow-pow` `frac-add` `add-log-exp`
3×	`exp-prod` `associate-/r` `associate-/l`
2×	`pow-prod-down` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `div-inv` `difference-of-squares` `unswap-sqr`
1×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `flip3-+` `div-exp` `pow-exp` `clear-num` `flip-+` `exp-lft-sqr` `sqr-pow`

Counts

4 → 135

Calls

4 calls:

419.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
95.0ms	(pow (exp 2) (/ (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))) 2))
13.0ms	(* y (- (log z) t))
541.0ms	(/ (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))) 2)

series753.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
205.0ms	(pow (exp 2) (/ (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))) 2))
91.0ms	(* y (- (log z) t))
352.0ms	(/ (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))) 2)

simplify95.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	759	2215
1	3395	2053
2	5002	2034

prune695.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

regimes425.0ms

Accuracy

0% (0.1b remaining)

Error of 0.5b against oracle of 0.5b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	18
1	40	18
2	40	18

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.3s	40856×	body	80	nan
786.0ms	12476×	body	80	valid
135.0ms	369×	body	640	valid
95.0ms	432×	body	320	valid
47.0ms	66×	body	1280	valid
38.0ms	281×	body	160	valid