Details

sample73.0ms

Algorithm

intervals

Results

21.0ms	264×	body	80	nan
19.0ms	256×	body	80	valid

simplify40.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	50	17
1	108	17
2	389	17
3	1761	17
4	5002	17

prune5.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* z (sqrt (+ t a)))
0.2b	(/ 2.0 (* t 3.0))
2.3b	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
5.1b	(/ (* z (sqrt (+ t a))) t)

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

75×	`*-un-lft-identity`
63×	`prod-diff`
62×	`associate--r+`
49×	`add-sqr-sqrt`
45×	`add-cube-cbrt`
36×	`times-frac`
31×	`distribute-rgt-in` `distribute-lft-in`
20×	`frac-sub`
16×	`add-exp-log` `add-cbrt-cube`
15×	`distribute-lft-out`
12×	`div-inv`
9×	`flip3--` `flip--`
8×	`frac-times` `associate-*r/`
7×	`fma-neg` `associate-r`
6×	`pow1` `add-log-exp`
5×	`flip3-+` `sqrt-prod` `flip-+`
4×	`cbrt-undiv` `expm1-log1p-u` `sqrt-div` `div-exp` `associate-/r` `log1p-expm1-u` `associate-/l`
3×	`sub-neg` `associate-l` `prod-exp` `cbrt-unprod`
2×	`frac-2neg` `associate-*l/` `associate--l+` `clear-num` `associate-/l/` `unswap-sqr`
1×	`diff-log` `pow-prod-down` `*-commutative`

Counts

4 → 179

Calls

4 calls:

11.0ms	(* z (sqrt (+ t a)))
3.0ms	(/ 2.0 (* t 3.0))
41.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
6.0ms	(/ (* z (sqrt (+ t a))) t)

series356.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* z (sqrt (+ t a)))
16.0ms	(/ 2.0 (* t 3.0))
189.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
85.0ms	(/ (* z (sqrt (+ t a))) t)

simplify55.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1377	2637
1	5001	2324

prune939.0ms

Filtered

191 candidates to 137 candidates (71.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt t)
0.6b	(cbrt t)
0.6b	(cbrt t)
0.9b	(fma (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

0.0ms	(cbrt t)
0.0ms	(cbrt t)
1.0ms	(cbrt t)
0.0ms	(fma (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

series885.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(cbrt t)
180.0ms	(cbrt t)
177.0ms	(cbrt t)
341.0ms	(fma (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

simplify39.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (34.0ms)

Iter	Nodes	Cost
0	144	371
1	345	322
2	1221	312
3	5001	306

prune391.0ms

Filtered

61 candidates to 54 candidates (88.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 2.0 (* t 3.0))
3.3b	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (log (exp (/ 2.0 (* t 3.0)))))))
3.4b	(log (exp (/ 2.0 (* t 3.0))))
5.1b	(/ (* z (sqrt (+ t a))) t)

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

105×	`*-un-lft-identity`
95×	`prod-diff`
94×	`associate--r+`
72×	`log-pow`
63×	`exp-prod`
61×	`add-sqr-sqrt` `add-cube-cbrt`
47×	`distribute-rgt-in` `distribute-lft-in`
39×	`times-frac`
22×	`distribute-lft-out`
14×	`add-exp-log` `add-cbrt-cube`
13×	`pow1` `div-inv`
8×	`frac-sub`
7×	`flip3--` `fma-neg` `flip--`
6×	`add-log-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `frac-times` `associate-r/` `div-exp` `associate-/r` `log1p-expm1-u` `associate-/l*`
3×	`sub-neg` `log-prod`
2×	`frac-2neg` `sqrt-div` `associate-*l/` `prod-exp` `associate--l+` `clear-num` `cbrt-unprod` `associate-/l/`
1×	`flip3-+` `diff-log` `rem-log-exp` `flip-+`

Counts

4 → 199

Calls

4 calls:

3.0ms	(/ 2.0 (* t 3.0))
47.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (log (exp (/ 2.0 (* t 3.0)))))))
4.0ms	(log (exp (/ 2.0 (* t 3.0))))
6.0ms	(/ (* z (sqrt (+ t a))) t)

series296.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ 2.0 (* t 3.0))
183.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (log (exp (/ 2.0 (* t 3.0)))))))
16.0ms	(log (exp (/ 2.0 (* t 3.0))))
81.0ms	(/ (* z (sqrt (+ t a))) t)

simplify62.0ms

Algorithm

egg-herbie

Counts

211 → 211

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1214	3242
1	5001	2728

prune1.0s

Filtered

211 candidates to 140 candidates (66.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(fma (- (/ 5.0 6.0) (/ 2.0 (* t 3.0))) (- (- b c)) (/ (* z (sqrt (+ t a))) t))
0.6b	(* (exp (* a (- c b))) (exp (fma (- (/ 5.0 6.0) (/ 2.0 (* t 3.0))) (- (- b c)) (/ (* z (sqrt (+ t a))) t))))
1.4b	(log (* (exp (* a (- c b))) (exp (fma (- (/ 5.0 6.0) (/ 2.0 (* t 3.0))) (- (- b c)) (/ (* z (sqrt (+ t a))) t)))))
5.1b	(/ (* z (sqrt (+ t a))) t)

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

25×	`associate-l`
23×	`exp-sum`
22×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity`
18×	`prod-diff`
11×	`distribute-rgt-in` `distribute-lft-in` `add-cbrt-cube`
10×	`add-exp-log`
9×	`pow1`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `prod-exp` `associate-/r*`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `associate-*r/` `div-exp` `rem-log-exp` `pow-prod-down` `log-pow` `cbrt-unprod` `fma-udef` `associate-/l/`
1×	`log-prod` `frac-2neg` `flip3-+` `clear-num` `-commutative` `flip-+` `div-inv` `associate-/l` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

0.0ms	(fma (- (/ 5.0 6.0) (/ 2.0 (* t 3.0))) (- (- b c)) (/ (* z (sqrt (+ t a))) t))
27.0ms	(* (exp (* a (- c b))) (exp (fma (- (/ 5.0 6.0) (/ 2.0 (* t 3.0))) (- (- b c)) (/ (* z (sqrt (+ t a))) t))))
9.0ms	(log (* (exp (* a (- c b))) (exp (fma (- (/ 5.0 6.0) (/ 2.0 (* t 3.0))) (- (- b c)) (/ (* z (sqrt (+ t a))) t)))))
6.0ms	(/ (* z (sqrt (+ t a))) t)

series1.2s

Counts

4 → 12

Calls

4 calls:

165.0ms	(fma (- (/ 5.0 6.0) (/ 2.0 (* t 3.0))) (- (- b c)) (/ (* z (sqrt (+ t a))) t))
675.0ms	(* (exp (* a (- c b))) (exp (fma (- (/ 5.0 6.0) (/ 2.0 (* t 3.0))) (- (- b c)) (/ (* z (sqrt (+ t a))) t))))
289.0ms	(log (* (exp (* a (- c b))) (exp (fma (- (/ 5.0 6.0) (/ 2.0 (* t 3.0))) (- (- b c)) (/ (* z (sqrt (+ t a))) t)))))
84.0ms	(/ (* z (sqrt (+ t a))) t)

simplify60.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	584	1558
1	2113	1312
2	5001	1301

prune886.0ms

Filtered

104 candidates to 88 candidates (84.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes249.0ms

Accuracy

0% (0.6b remaining)

Error of 1.6b against oracle of 1.0b and baseline of 1.6b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	22
1	44	22
2	44	22

end0.0ms

sample1.8s

Algorithm

intervals

Results

560.0ms	8000×	body	80	valid
534.0ms	7978×	body	80	nan