Original	0.1
Target	0.1
Herbie	0.1

Details

sample52.0ms

Algorithm

intervals

Results

29.0ms	308×	body	80	valid
4.0ms	12×	body	640	valid
2.0ms	4×	body	1280	valid
1.0ms	5×	body	320	valid
1.0ms	4×	body	160	valid

simplify59.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

59.0ms

(+ (+ (* d1 3) (* d1 d2)) (* d1 d3))

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 1 expressions with local error:

0.0b	(* d1 (+ d2 (+ 3 d3)))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

3×	`associate-r`
2×	`add-cube-cbrt`
2×	`associate-*r/`
2×	`*-un-lft-identity`
2×	`add-sqr-sqrt`
1×	`add-log-exp`
1×	`flip-+`
1×	`*-commutative`
1×	`add-exp-log`
1×	`add-cbrt-cube`
1×	`flip3-+`
1×	`distribute-lft-in`
1×	`pow1`
1×	`distribute-rgt-in`

Counts

1 → 15

Calls

1 calls:

Slowest

2.0ms

(* d1 (+ d2 (+ 3 d3)))

series30.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

30.0ms

(* d1 (+ d2 (+ 3 d3)))

simplify347.0ms

Counts

10 → 18

Calls

10 calls:

Slowest

176.0ms	(+ (* d2 d2) (- (* (+ 3 d3) (+ 3 d3)) (* d2 (+ 3 d3))))
38.0ms	(+ (* d2 d1) (+ (* d3 d1) (* 3 d1)))
28.0ms	(+ (* d2 d1) (+ (* d3 d1) (* 3 d1)))
25.0ms	(+ (* d2 d1) (+ (* d3 d1) (* 3 d1)))
20.0ms	(- d2 (+ 3 d3))

prune152.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize28.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (+ (* d1 3) (* d1 d2)) (* d1 d3))
0.0b	(+ (* d1 3) (* d1 d2))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-log-exp`
4×	`sum-log`
3×	`distribute-lft-out`
2×	`flip-+`
2×	`add-cube-cbrt`
2×	`add-exp-log`
2×	`add-cbrt-cube`
2×	`flip3-+`
2×	`*-un-lft-identity`
2×	`+-commutative`
2×	`pow1`
2×	`add-sqr-sqrt`
1×	`associate-+l+`

Counts

2 → 26

Calls

2 calls:

Slowest

10.0ms	(+ (+ (* d1 3) (* d1 d2)) (* d1 d3))
2.0ms	(+ (* d1 3) (* d1 d2))

series41.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

21.0ms	(+ (+ (* d1 3) (* d1 d2)) (* d1 d3))
20.0ms	(+ (* d1 3) (* d1 d2))

simplify537.0ms

Counts

12 → 32

Calls

12 calls:

Slowest

217.0ms	(* (* (exp (* d1 3)) (exp (* d1 d2))) (exp (* d1 d3)))
158.0ms	(* (exp (+ (* d1 3) (* d1 d2))) (exp (* d1 d3)))
47.0ms	(+ (* d2 d1) (+ (* d3 d1) (* 3 d1)))
33.0ms	(+ (* d2 d1) (+ (* d3 d1) (* 3 d1)))
29.0ms	(* (exp (* d1 3)) (exp (* d1 d2)))

prune264.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* d1 (+ d2 (+ 3 d3)))) (cbrt (* d1 (+ d2 (+ 3 d3)))))
0.5b	(cbrt (* d1 (+ d2 (+ 3 d3))))
0.5b	(cbrt (* d1 (+ d2 (+ 3 d3))))
0.5b	(cbrt (* d1 (+ d2 (+ 3 d3))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

20×	`associate-*r/`
18×	`cbrt-div`
9×	`flip-+`
9×	`flip3-+`
9×	`pow1`
7×	`pow1/3`
6×	`add-cube-cbrt`
6×	`add-exp-log`
6×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`cbrt-prod`
4×	`add-log-exp`
4×	`associate-l`
4×	`associate-r`
4×	`add-cbrt-cube`
4×	`frac-times`
2×	`pow-prod-up`
2×	`associate-*l/`
2×	`pow-prod-down`
1×	`cbrt-unprod`
1×	`*-commutative`
1×	`prod-exp`
1×	`pow-plus`
1×	`pow2`

Counts

4 → 65

Calls

4 calls:

Slowest

12.0ms	(* (cbrt (* d1 (+ d2 (+ 3 d3)))) (cbrt (* d1 (+ d2 (+ 3 d3)))))
2.0ms	(cbrt (* d1 (+ d2 (+ 3 d3))))
2.0ms	(cbrt (* d1 (+ d2 (+ 3 d3))))
2.0ms	(cbrt (* d1 (+ d2 (+ 3 d3))))

series739.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

204.0ms	(* (cbrt (* d1 (+ d2 (+ 3 d3)))) (cbrt (* d1 (+ d2 (+ 3 d3)))))
190.0ms	(cbrt (* d1 (+ d2 (+ 3 d3))))
173.0ms	(cbrt (* d1 (+ d2 (+ 3 d3))))
172.0ms	(cbrt (* d1 (+ d2 (+ 3 d3))))

simplify7.0s

Counts

49 → 77

Calls

49 calls:

Slowest

594.0ms	(+ (* 1/9 (* d2 (exp (* 1/3 (+ (log 3) (log d1)))))) (+ (* 1/9 (* d3 (exp (* 1/3 (+ (log 3) (log d1)))))) (exp (* 1/3 (+ (log 3) (log d1))))))
505.0ms	(* (* d1 (+ d2 (+ 3 d3))) (* d1 (+ d2 (+ 3 d3))))
433.0ms	(* (* d1 (+ d2 (+ 3 d3))) (* d1 (+ d2 (+ 3 d3))))
415.0ms	(* (cbrt (* d1 (- (* d2 d2) (* (+ 3 d3) (+ 3 d3))))) (cbrt (* d1 (+ (pow d2 3) (pow (+ 3 d3) 3)))))
323.0ms	(+ (* 1/9 (* d2 (exp (* 1/3 (+ (log 3) (log d1)))))) (+ (* 1/9 (* d3 (exp (* 1/3 (+ (log 3) (log d1)))))) (exp (* 1/3 (+ (log 3) (log d1))))))

prune757.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

14.8b	(/ (* d1 (- (* d2 d2) (* (+ 3 d3) (+ 3 d3)))) (- d2 (+ 3 d3)))
7.1b	(* d1 (- (* d2 d2) (* (+ 3 d3) (+ 3 d3))))
1.4b	(- (* d2 d2) (* (+ 3 d3) (+ 3 d3)))
0.0b	(* (+ 3 d3) (+ 3 d3))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-cube-cbrt`
9×	`*-un-lft-identity`
9×	`pow1`
9×	`add-sqr-sqrt`
8×	`add-exp-log`
8×	`add-cbrt-cube`
7×	`associate-r`
6×	`add-log-exp`
6×	`flip-+`
6×	`associate-*r/`
6×	`flip3-+`
4×	`flip--`
4×	`flip3--`
4×	`distribute-lft-in`
4×	`frac-times`
4×	`distribute-rgt-in`
3×	`associate-l`
3×	`times-frac`
3×	`sub-neg`
3×	`associate-/r*`
2×	`associate-/l/`
2×	`difference-of-squares`
2×	`associate--r+`
2×	`*-commutative`
2×	`associate-/r/`
2×	`associate-*l/`
1×	`associate-/l*`
1×	`div-inv`
1×	`cbrt-unprod`
1×	`pow-prod-up`
1×	`prod-exp`
1×	`pow-prod-down`
1×	`div-exp`
1×	`diff-log`
1×	`pow-plus`
1×	`frac-2neg`
1×	`clear-num`
1×	`cbrt-undiv`
1×	`pow2`

Counts

4 → 86

Calls

4 calls:

Slowest

12.0ms	(/ (* d1 (- (* d2 d2) (* (+ 3 d3) (+ 3 d3)))) (- d2 (+ 3 d3)))
7.0ms	(* (+ 3 d3) (+ 3 d3))
7.0ms	(* d1 (- (* d2 d2) (* (+ 3 d3) (+ 3 d3))))
4.0ms	(- (* d2 d2) (* (+ 3 d3) (+ 3 d3)))

series200.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

101.0ms	(/ (* d1 (- (* d2 d2) (* (+ 3 d3) (+ 3 d3)))) (- d2 (+ 3 d3)))
70.0ms	(* d1 (- (* d2 d2) (* (+ 3 d3) (+ 3 d3))))
19.0ms	(- (* d2 d2) (* (+ 3 d3) (+ 3 d3)))
9.0ms	(* (+ 3 d3) (+ 3 d3))

simplify7.1s

Counts

67 → 98

Calls

67 calls:

Slowest

457.0ms	(* (- (* 3 3) (* d3 d3)) (+ 3 d3))
383.0ms	(- (* d2 d2) (* (+ 3 d3) (+ 3 d3)))
372.0ms	(* (+ (* 3 3) (- (* d3 d3) (* 3 d3))) (+ (* 3 3) (- (* d3 d3) (* 3 d3))))
330.0ms	(sqrt (- (* d2 d2) (* (+ 3 d3) (+ 3 d3))))
316.0ms	(cbrt (- (* d2 d2) (* (+ 3 d3) (+ 3 d3))))

prune890.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes212.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch2.0ms

end0.0ms

sample1.5s

Algorithm

intervals

Results

987.0ms	9542×	body	80	valid
131.0ms	208×	body	640	valid
50.0ms	114×	body	1280	valid
40.0ms	148×	body	320	valid
17.0ms	93×	body	160	valid

Error

Try it out

Target

Derivation

Reproduce

Details

sample52.0ms

simplify59.0ms

prune18.0ms

localize18.0ms

rewrite3.0ms

series30.0ms

simplify347.0ms

prune152.0ms

localize28.0ms

rewrite12.0ms

series41.0ms

simplify537.0ms

prune264.0ms

localize17.0ms

rewrite19.0ms

series739.0ms

simplify7.0s

prune757.0ms

localize30.0ms

rewrite31.0ms

series200.0ms

simplify7.1s

prune890.0ms

regimes212.0ms

bsearch2.0ms

end0.0ms

sample1.5s

In
Out