Details

sample126.0ms

Algorithm

intervals

Results

48.0ms	256×	body	80	valid
45.0ms	268×	body	80	nan

simplify36.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	50	17
1	106	17
2	374	17
3	1652	17
4	5001	17

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* z (sqrt (+ t a)))
0.5b	(/ 2.0 (* t 3.0))
1.8b	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
5.6b	(/ (* z (sqrt (+ t a))) t)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

20×	`frac-sub`
16×	`add-exp-log` `add-cbrt-cube`
15×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`flip3--` `flip--`
8×	`frac-times` `associate-*r/`
7×	`associate-r`
6×	`pow1` `times-frac` `associate--r+` `add-log-exp`
5×	`flip3-+` `sqrt-prod` `flip-+`
4×	`cbrt-undiv` `sqrt-div` `div-exp` `associate-/r` `associate-/l`
3×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-l` `prod-exp` `cbrt-unprod`
2×	`frac-2neg` `associate-*l/` `associate--l+` `clear-num` `div-inv` `associate-/l/` `unswap-sqr`
1×	`diff-log` `pow-prod-down` `*-commutative` `distribute-lft-out`

Counts

4 → 101

Calls

4 calls:

11.0ms	(* z (sqrt (+ t a)))
3.0ms	(/ 2.0 (* t 3.0))
18.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
6.0ms	(/ (* z (sqrt (+ t a))) t)

series330.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* z (sqrt (+ t a)))
15.0ms	(/ 2.0 (* t 3.0))
174.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
78.0ms	(/ (* z (sqrt (+ t a))) t)

simplify37.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1019	1262
1	5001	1200

prune575.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt t)
0.6b	(cbrt t)
1.8b	(- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
2.7b	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
60×	`frac-sub`
58×	`times-frac`
47×	`*-un-lft-identity`
46×	`associate-r`
39×	`frac-times`
35×	`add-cube-cbrt`
31×	`cbrt-prod`
28×	`sqrt-prod`
27×	`associate-*r/`
25×	`add-exp-log` `flip3--` `flip--`
21×	`associate-*l/`
18×	`add-cbrt-cube`
10×	`unswap-sqr`
9×	`flip3-+` `flip-+`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp` `associate-l`
6×	`pow1` `distribute-lft-out` `associate--r+` `add-log-exp`
3×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
2×	`pow1/3` `associate--l+` `div-inv`
1×	`diff-log` `pow-prod-down` `*-commutative`

Counts

4 → 169

Calls

4 calls:

0.0ms	(cbrt t)
0.0ms	(cbrt t)
30.0ms	(- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
39.0ms	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))

series672.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(cbrt t)
174.0ms	(cbrt t)
219.0ms	(- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
106.0ms	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))

simplify70.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1739	3626
1	5001	3513

prune1.3s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 2.0 (* t 3.0))
1.8b	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (cbrt (pow (/ 2.0 (* t 3.0)) 3)))))
5.6b	(/ (* z (sqrt (+ t a))) t)
43.2b	(cbrt (pow (/ 2.0 (* t 3.0)) 3))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

20×	`cbrt-prod` `frac-sub`
14×	`add-exp-log` `add-cbrt-cube`
13×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
9×	`flip3--` `flip--`
8×	`frac-times`
7×	`cube-div` `unpow-prod-down` `cbrt-div` `cube-prod`
6×	`associate-*r/` `associate--r+` `add-log-exp`
4×	`pow1` `cbrt-undiv` `flip3-+` `div-exp` `associate-/r` `flip-+` `div-inv` `associate-/l`
3×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
2×	`frac-2neg` `sqrt-div` `associate-*l/` `prod-exp` `associate--l+` `clear-num` `cbrt-unprod` `associate-/l/`
1×	`cube-mult` `pow1/3` `diff-log` `unpow3` `rem-cbrt-cube` `sqr-pow`

Counts

4 → 106

Calls

4 calls:

3.0ms	(/ 2.0 (* t 3.0))
21.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (cbrt (pow (/ 2.0 (* t 3.0)) 3)))))
6.0ms	(/ (* z (sqrt (+ t a))) t)
3.0ms	(cbrt (pow (/ 2.0 (* t 3.0)) 3))

series280.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ 2.0 (* t 3.0))
172.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (cbrt (pow (/ 2.0 (* t 3.0)) 3)))))
78.0ms	(/ (* z (sqrt (+ t a))) t)
16.0ms	(cbrt (pow (/ 2.0 (* t 3.0)) 3))

simplify43.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1027	1349
1	5001	1297

prune606.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt t)
0.6b	(cbrt t)
5.2b	(- (* (/ z (* (cbrt t) (log (exp (cbrt t))))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
9.4b	(log (exp (cbrt t)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

60×	`frac-sub`
38×	`frac-times`
26×	`associate-*r/`
25×	`flip3--` `flip--`
20×	`associate-*l/`
9×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `flip3-+` `flip-+`
7×	`log-pow`
6×	`exp-prod` `associate--r+` `add-log-exp`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube`
3×	`distribute-rgt-in` `sub-neg` `log-prod` `distribute-lft-in`
2×	`pow1/3` `associate--l+`
1×	`diff-log` `rem-log-exp`

Counts

4 → 100

Calls

4 calls:

0.0ms	(cbrt t)
0.0ms	(cbrt t)
30.0ms	(- (* (/ z (* (cbrt t) (log (exp (cbrt t))))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
2.0ms	(log (exp (cbrt t)))

series749.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(cbrt t)
180.0ms	(cbrt t)
215.0ms	(- (* (/ z (* (cbrt t) (log (exp (cbrt t))))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
181.0ms	(log (exp (cbrt t)))

simplify51.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1282	2713
1	5002	2628

prune902.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.2b

regimes327.0ms

Accuracy

10% (1.8b remaining)

Error of 2.6b against oracle of 0.7b and baseline of 2.8b

bsearch436.0ms

Steps

Iters	Range		Point
9	1.6122460955319417e-301	2.0209216339307323e-295	3.2534287537046085e-299
8	-1.296868899374355e-231	-3.1024340943049367e-235	-7.929621432689752e-232

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	64
1	79	64

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.5s	8000×	body	80	valid
1.3s	8127×	body	80	nan