Details

sample174.0ms

Algorithm

intervals

Results

74.0ms	1333×	body	80	nan
23.0ms	375×	body	80	valid
5.0ms	25×	body	320	valid
3.0ms	8×	body	640	valid
1.0ms	7×	body	160	valid

simplify38.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
0.1b	(* y (- (log z) t))
0.5b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
4.2b	(log (- 1.0 z))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

27×	`log-prod`
24×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
22×	`associate--l+`
17×	`distribute-rgt-in` `distribute-lft-in`
14×	`add-cube-cbrt` `associate-+r+`
10×	`associate-+l+` `associate-*r/`
9×	`add-log-exp`
8×	`pow1`
7×	`add-exp-log`
6×	`sub-neg` `flip3--` `associate-r` `add-cbrt-cube` `flip--`
5×	`distribute-lft-out--`
4×	`frac-add` `difference-of-squares`
3×	`exp-prod` `associate-l`
2×	`log-div` `sum-log` `log-pow` `rem-exp-log`
1×	`+-commutative` `flip3-+` `rem-log-exp` `exp-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 101

Calls

4 calls:

18.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
13.0ms	(* y (- (log z) t))
16.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
3.0ms	(log (- 1.0 z))

series433.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
67.0ms	(* y (- (log z) t))
185.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
41.0ms	(log (- 1.0 z))

simplify68.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	630	971
1	2443	914
2	5001	902

prune436.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize24.0ms

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	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
0.1b	(* y (- (log z) t))
0.5b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite654.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 123

Calls

4 calls:

108.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
423.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
13.0ms	(* y (- (log z) t))
104.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series582.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
104.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
73.0ms	(* y (- (log z) t))
236.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify84.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	645	1743
1	2810	1639
2	5002	1630

prune589.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))) 3))
0.0b	(pow (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))) 3)
0.1b	(* y (- (log z) t))
0.5b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite328.0ms

Algorithm

rewrite-expression-head

Rules

28×	`associate--l+`
23×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
19×	`add-cube-cbrt`
18×	`log-prod`
17×	`distribute-rgt-in` `distribute-lft-in`
14×	`cbrt-prod` `associate-+r+`
10×	`associate-+l+` `associate-*r/`
8×	`pow1` `sub-neg` `unpow-prod-down` `cube-prod`
7×	`add-cbrt-cube`
6×	`add-exp-log` `associate-r` `add-log-exp`
5×	`flip3--` `flip--`
4×	`pow-pow` `exp-sum` `frac-add`
3×	`pow-unpow` `exp-prod` `associate-l`
2×	`cube-mult` `unpow3` `distribute-lft-out--` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `flip3-+` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `sum-log` `log-pow` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `flip-+` `rem-cube-cbrt` `difference-of-squares` `unswap-sqr`

Counts

4 → 123

Calls

4 calls:

98.0ms	(cbrt (pow (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))) 3))
112.0ms	(pow (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))) 3)
13.0ms	(* y (- (log z) t))
102.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series783.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(cbrt (pow (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))) 3))
309.0ms	(pow (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))) 3)
72.0ms	(* y (- (log z) t))
238.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify89.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	675	2264
1	2911	2128
2	5001	2113

prune614.0ms

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	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
0.0b	(log (exp (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))))
0.1b	(* y (- (log z) t))
0.5b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite559.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 126

Calls

4 calls:

424.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
15.0ms	(log (exp (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))))
13.0ms	(* y (- (log z) t))
103.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series577.0ms

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))
161.0ms	(log (exp (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))))
71.0ms	(* y (- (log z) t))
239.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify81.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	660	1863
1	2814	1732
2	5002	1723

prune649.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

regimes235.0ms

Accuracy

75.8% (3.0b remaining)

Error of 3.1b against oracle of 0.1b and baseline of 12.4b

bsearch657.0ms

Steps

Iters	Range		Point
9	16861747126008094.0	3.5588220617013634e+21	4.688949003054457e+16
11	-2.416358248243101e+20	-1.1909565797971935	-1.2403558215885326
7	-3.137730294173134e+94	-1.9224883127301787e+93	-1.3900972840841056e+94

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	52
1	90	52
2	102	52
3	112	52
4	112	52

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.3s	40675×	body	80	nan
778.0ms	12476×	body	80	valid
125.0ms	362×	body	640	valid
96.0ms	442×	body	320	valid
54.0ms	76×	body	1280	valid
35.0ms	258×	body	160	valid